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In this study, we seek to characterise the behaviour of Spatial modulation (SM) in the multiple access scenario. By only activating a single transmit antenna for any transmission, SM entirely avoids inter-channel interference, requires no synchronisation between the transmit antennas and a single radio frequency chain at the transmitter. Most contributions thus far have only addressed aspects of SM for a point-to-point communication system. We propose a maximum-likelihood (ML) detector which can successfully decode incoming data from multiple simultaneous transmissions and does not suffer from the near-far problem. We analyse the performance of the interference-unaware and interference-aware detectors. We look at the behaviour of SM as the signal-to-interference-plus-noise ratio goes to infinity and compare it to the complexity and cost equivalent single-input-multiple-output (SIMO) system. Two systems are considered to be equivalent in terms of complexity if their respective detection algorithms are of the same order in notation. Simulation results show that the interference-aware SM detector performs better than the complexity equivalent multi-user ML-SIMO detector by at least 3 dB at an average bit-error-ratio of 10−3.
Multiple-antenna systems are fast becoming a key technology for modern wireless systems. They offer improved error performance and higher data rates, at the expense of increased complexity and power consumption [1]. Spatial modulation (SM) is a recently proposed approach to multiple-input-multiple-output (MIMO) systems which entirely avoids inter-channel interference, requires no synchronisation between the transmit antennas and achieves a spatial multiplexing gain [2]. This is performed by mapping a block of information bits into a constellation point in the signal and spatial domains [3]. In SM, the number of information bits, ℓ, that are encoded in the spatial domain can be related to the number of transmit antennas Nt as Nt = 2ℓ. This means that the number of transmit antennas must be a power of two unless fractional bit encoding [4] or generalised SM [5] are used. SM offers an intrinsic flexibility to trade off the number of transmit antennas with the modulation order in the signal domain to meet the desired data rate. It should be noted that SM is shown to outperform other point-to-point MIMO schemes in terms of average bit-error-ratio (ABER) [3].
In the single user scenario, only a single transmit antenna is active at any instance, this avoids the need for complicated interference cancellation algorithms at the SM receiver. In addition, unlike other MIMO schemes, the number of receive antennas is independent of the number of transmit antennas. Several articles are available in literature which are aimed at understanding and improving the performance of SM in various scenarios, e.g., [6-8]. The study in [6] seeks to improve the ABER performance of SM by introducing trellis coding on the transmitting antennas. The study in [9] shows that the detector complexity of SM is independent of the number of transmit antennas. The optimal detector is known with and without channel state information at the receiver in [10-12]. The optimal power allocation problem for a two-transmit with one receive antenna system is solved in closed form in [13] and the performance of SM in correlated fading channels is considered in [14,15]. Recent work has also shown that SM can be combined with space–time block codes to attain spectral efficiency gains [16] by exploiting transmit-side diversity. At this point, it is worth noting that if we choose to use only the spatial constellation of SM to transmit information, then SM is reduced to space-shift-keying (SSK) as proposed in [17]. To this extent, we note that all presented work can be extended to SSK without loss of generality.
MIMO techniques can also be used in relaying networks to improve the diversity, provide multiplexing gains and aid in interference cancellation. To this extent, the orthogonal decode and forward (DF) algorithm decodes the received signal at the relay, then re-encodes and retransmits this information, establishing a regenerative system. Outage probabilities, mutual information calculations and transmit diversity bounds for orthogonal amplify and forward (AF) and DF relaying are derived in [18] with the end-to-end performance being considered in [19] where DF is shown to perform better in terms of the ABER when compared to AF. However, the ABER of regenerative systems depends on the ABER on the individual links. In particular, since SM is shown to outperform other spatial multiplexing techniques on a single link, the application of SM to relaying systems is also shown to provide significant signal-to-noise ratio (SNR) gains when compared to orthogonal DF [20]. Nonetheless, these results are only applicable in a noise-limited relaying system. The deployment of relaying systems around the cell edges, however, may result in interference-limited systems. Therefore, to enable the deployment of SM in a relaying scenario, the ABER performance of SM on a single link must also be assessed in the interference-limited environment.
Most contributions thus far, however, have only addressed SM aspects for point-to-point communication systems, i.e. the single user scenario. Notable exceptions are given in [21,22], where the authors focus their analysis on scenarios employing SSK. The aim of this study is to characterise the behaviour of SM in the multi-user, interference-limited scenario and compare it to the complexity and cost equivalent multi-user MIMO system. We emphasise that SM requires only a single radio frequency (RF) chain at the transmit side since only one is active at any particular instance. Requiring only a single RF chain at the transmitter means that multi-user SM is not comparable in terms of cost to the more complicated spatial-multiplexing multi-user systems analysed in [23-26].
Furthermore, the study in [27] shows that the most energy consuming part of a wireless base station is the power amplifiers and consequently RF chains associated with each transmitter. The study in [28] demonstrates that the power requirements of a base station increase linearly with the number of RF chains added. In addition to higher power consumption, multiple RF chains imply higher manufacturing costs and inter-antenna synchronisation problems. To this extent, SM is an optimal system for utilising the advantages of multiple transmit antennas while still maintaining a single RF chain for Green communications. The aggregate power usage in a system employing SM is significantly lower than a system employing classical MIMO techniques. Furthermore, the lower detection complexity for SM reduces mobile station power usage, enabling a longer battery life for the mobile terminal [9]. Understanding the performance of SM in a multi-user system is necessary to assess its suitability for practical deployment scenarios. In this context, it is of interest if the particular structure of the SM encoding scheme can be exploited to devise novel multi-user detection techniques.
In this study, we first characterise the performance of a single user detector as applied in an interference-limited scenario, i.e. we analyse a ML interference-unaware optimal receiver. We then propose an ML detector which can successfully decode incoming data in the multi-user scenario and is not interference limited, i.e. an interference-aware detector which can successfully decode data from several nodes. For each detector, we develop an analytical framework to support simulation results and closed form solutions are provided to compute the ABER over identical and independently distributed (i.i.d.) Rayleigh fading channels.
The remainder of this article is organised as follows. In the "System model" section, the system and channel models are introduced. In the "Analytical modelling and receiver design" section, the performance of SM in the multiple access scenario is characterised and the analytical modelling for the multi-user detector is proposed. The "Simulation results and discussion" section provides simulation results to substantiate the accuracy of the developed analytical framework. In the "Summary and conclusions" section, we summarise and conclude this study.
System model
The basic idea of SM is to map blocks of information bits onto two information carrying units [3]: (i) a symbol, chosen from a complex signal-constellation diagram, and (ii) a unique transmit-antenna, chosen from the set of transmit-antennas in an antenna-array, i.e. the spatial-constellation. Jointly, the spatial and signal constellation symbols form a single SM constellation symbol. If, for example, we wish to transmit a total of 4 bits/s/Hz using SM with four available transmit antennas; then the first 2 bits would define the spatial-constellation point identifying the active antenna, while the remaining 2 bits would determine the signal-constellation point that will be transmitted.
In the following work, we assume multiple nodes/users, as shown in Figure 1. A total of Nu transmit nodes, denoted as {1,…,ξ,…Nu}, broadcast simultaneously on the same time-frequency slot to a single receiver. Each node broadcasts a signal constellation symbol, x(u), from one of its available antennas.
Figure 1. Multi-user SM system setup. Nodes 1,…,ξ,…Nu broadcast simultaneously to the receiver on the same time-frequency resource block. Each solid line represents the active transmit antenna on each node to every receiving antenna. Each dashed line represents the inactive channel from every transmit antenna at a particular node to every receiving antenna.
The received signal at antenna r is given by
where Em is the average transmit energy per symbol, is the index of the active transmit antenna from a total of available on node u, r is the index of the receive antenna from a total of Nr available on the receiving node, is the power of the channel attenuation coefficients between all receive antennas and all transmit antennas on the link between node u and the receiver, is the fast fading channel coefficient between the active transmit antenna nt on node u and the receiving antenna r, x(u) is the signal constellation symbol transmitted from the set of all possible signal constellation points, , for node u and ηr, is additive white Gaussian noise (AWGN), defined as a complex normally random variable with zero mean and variance No, .
Throughout the study EX[|x|2] = 1, meaning the average power in the signal constellation is normalised to one for all u. To avoid repetitive definitions of symbols, we note that symbols denoted with are simply an element of the same set as the symbol without , i.e. comes from the same set as x. Furthermore, all bold letters are vectors. If we set the signal constellation to be only a single constellation point, where Nt is chosen such that log2(Nt) equals the spectral efficiency, then all presented work can directly be applied to any system employing SSK by simply replacing x(u) = 1.
Analytical modelling and receiver design
We analyse the ML detector for use in the multiple access scenario. The detector computes the Euclidean distance between the received vector signal, y, and the set of all possible received signals, selecting the closest one.
Interference-unaware detection
Starting from the system model presented in the "System model" section, the decoded pair , formed from the estimated symbol xest emitted from antenna Nt on node ξ is given by
where is the number of available transmit antennas on node ξ, ||·||F is the Frobenius norm and has a total of M(ξ) constellation points. We note that u represents the index of a general node in the system, and ξ is the index of the desired node whose data stream is being decoded.
We can use union bound techniques to describe the behaviour of the interference-unaware SM detector in the high SNR regions. From here, we proceed to characterise the behaviour of the interference-unaware detector by defining
such that
define the symbols at the receive antenna r. With this, we can pose y = A + B + η.
The pairwise error probability (PEP) can now be derived as
where (·)∗ represents the complex conjugate, is the distribution of the PEP defined by which represents the normal distribution with mean μ and variance σ2. Knowing that is the only remaining random variable with a known distribution, enables us to define the PEP in (4) using the Q-function. Considering and (4), we can see that the PEP can be defined as
where defines the Q-function. It should be noted that this PEP is valid for all channel fading statistics. We can further simplify it if we assume that the fast fading channel statistics of each element of B are Rayleigh distributed, i.e. and has Nr number of elements. To this end, we define
where we can see that
such that and define . We can remove the channel effects of B from the expression by taking the expectation of (5) across the fading channel hB, such that
where and Eh [·] represents the expectation of the system with respect to the fast fading channel h. From here, we can apply ( [29], eq. 3.66) which results in
After some analytical manipulations we obtain (10)
represents half of the signal-to-interference-plus-noise ratio (SINR) between node ξ and the receiver. Throughout the study, we average only across the fast fading channel statistics. As (11) shows, γI is still dependent on the magnitude of the modulated signal symbols of the interfering nodes, |x(u)|. This means that all expressions using γI maintain their conditioning on the modulated signal symbols of the interfering nodes.
Given this formulation, we can now define the ABER of the single-user detector using the union bounding techniques in the presence of interference as
where the uth summation from the (Nu−1) summations above is defined for all and u ≠ ξ with M(ξ) being the cardinality of . The symbol is defined as a fourfold summation, two for all and two for the indices . In addition, , where denotes the Hamming distance between the binary representations any two symbols coming from the same set for node ξ.
As with the interfering nodes, we assume that the desired node's fast fading follows a Rayleigh distribution. To obtain the average PEP, we define , with a variance of
where is the variance of SM using a variable amplitude modulation scheme. In particular, it is the variance per receive antenna of the argument inside the Q-function in (10). We define the random variable
which has a central Chi-squared distribution with 2Nr degrees of freedom given as
where (·)! represents the factorial function. We can now pose
By direct inspection, we can now apply the solution to ( [30], eq. 62) and obtain
We note that (12) presents an analytical bound for a system employing quadrature-amplitude-modulation (QAM). If we choose to use constant-amplitude modulation such as phase-shift-keying (PSK), then for a fixed channel realisation, we define , and pose
where arg (·) represents the phase of a complex symbol. We realise that the amplitude of all constellation points is unity and thus
From the definition of , it is clear that its variance is defined as
In this case, (12) reduces to
such that
The average power carried by any signal-symbol constellation in (12) is 1. Nonetheless, a variable amplitude modulation scheme means that the instantaneous SINR changes. The instantaneous SINR must strictly be defined to study the asymptotic behaviour of the system. This is necessary because the instantaneous SINR is an argument of the PEP which is defined using the Q-function. To obtain the ABER, the PEP must be averaged across all channel realisations and all signal-symbol constellations. A closed-form expression for the asymptotic behaviour of (12) and (13) is therefore difficult to obtain. However, we note that (22) and (23) are special cases of (12) and (13) which enable a simpler theoretical analysis of the asymptotic behaviour of the system as the SINR grows to infinity. Simulation results in the "Simulation results and discussion" section show that the asymptotic bounds derived for SM using a constant amplitude modulation scheme are also valid for SM using 4-QAM. In addition, it is shown that for the point-to-point single user scenario, SM using PSK may have a better ABER performance than SM using QAM depending on the number of available transmit antennas [31]. We now proceed with the asymptotic analysis of this system.
Asymptotic analysis of an interference-unaware detector
In this section, we investigate some asymptotic cases to highlight trends in SM at high SNR. Simulations in the "Simulation results and discussion" section show that the presented results are asymptotically tight in the high SNR region. We first define and . With these definitions, we look at three systems, the asymptotic performance of SM and SIMO in the noise-limited scenario and the asymptotic performance of SM in the interference-limited scenario.
SNRξ ≫1 and SINR≈SNR (noise-limited scenario)
This is the classic single user scenario where multiple access interference can be neglected, and high-SNR analysis for the probe link can be considered. We look at (12), where in the limit . Since interference can be neglected,
To simplify (26), the limit in (17) and (24) can be tackled by considering a Taylor expansion with two terms of (18) and obtain
We realise that the average symbol-error-ratio (ASER) for SM is defined similar to the ABER and can be posed as
From here, we know that . In particular, this is a close approximation for ABER of SM, since the fast fading channel coefficients effectively make the SM constellation completely random at the receiver. This negates any benefits from advanced bit-to-symbol mappings such as Gray coding. In effect, the detector will create a long binary sequence which has at most 50% bit-errors within the erroneous symbol sequence, i.e. the ABER is bounded to be at most 1/2 of the ASER. The tightness of this bound can be seen in the "Simulation results and discussion" section. This step eliminates the dependence on the Hamming distance between the various SM symbols, which permits us to pose
is the expectation of across the various possibilities of for and . We are not aware of a closed form solution to the more generic expression for (30) given a variable-amplitude modulation. However, we can upper bound (30) by setting . In particular, the general form of is defined by the underlying SM signal-symbol constellation size, M(ξ). To this extent, expressions for are defined using the upper bound for square QAM constellation sizes. A summary of the derivation of (32) is provided in Appendix.
When M(ξ) = 4, then
When M(ξ) = 16, then
With this in mind, the closed form of the limit is defined as
At this point, the work can be simplified by considering a constant-amplitude modulation scheme such as PSK where is either 2 or 0 as shown in (22), then the expression in (30) is unity which simplifies further analysis. In such a scenario, however, the study in [31] shows that SM using PSK cannot always guarantee a better performance than SM using QAM. In particular, the authors of [31] demonstrate that there is a crossing point where the ABER of SM using PSK improves over SM using QAM. Nonetheless, there are two conclusions that we can drawn from this limit: (i) the system error increases with the product of the spatial constellation size, , and symbol constellation size, M(ξ), (ii) the system error decreases exponentially with the addition of each received antenna, i.e. the diversity order is equal to Nr. In addition, we quantify the coding gains with respect to the number of receive antennas as . This is apparent considering
In general, it can be shown that as Nr →∞, the inverse of (35) tends to zero and is always less than 1. Since the inverse of (35) is always less than 1, the addition of an extra receive antenna implies a smaller ratio, which means a lower ABER and hence coding gains for the system.
SIMO system utilising QAM (noise-limited scenario)
To quantify the SNR difference between SM and SIMO using QAM, we need to look at the ABER performance of a SIMO system using QAM in the asymptote. We use ( [32], eq. 9.23) which provides a closed form solution for the ASER of a SIMO system using QAM with i.i.d. inputs, i.e. no correlation between the receive antennas. To begin the asymptotic analysis, ( [32], eq. 9.23) is tightly upper bounded by
where . The interested reader is invited to look at the work in [32] for more details in obtaining (36). We can now pose provided Gray mapping is used ( [32], eq. 8.7), where .
Using (27) and evaluating (36) in the limit as γ tends to infinity, it reduces to
If we look at the ratio of (34) with (31) to (37) then, after some analytical manipulations shown in the "Reaching (38) from (34) with (31) and (37)" section in the Appendix, we can pose
for M(ξ) = 4. If we equate the right-hand side of (38) to 1, then the expression cannot be solved in closed form. However, since Nr and are natural numbers we can readily evaluate (38). When evaluating (38), if the result is greater than 1, then SIMO transmission using only QAM is better than using SM. If the result is less than 1, then transmission using SM performs better than transmission using only QAM. The results for where q ∈ {1,…,6} and Nr ∈ {1,2,3} are presented in Table 1, which shows that SM is always better if Nr ≥ 2. In addition, the ratio of the two, as given in Table 1, exactly quantifies the minimum coding gain of SM relative to QAM for the same spectral efficiency of in a noise-limited scenario, given M(ξ) = 4.
Table 1. Relative coding gains of SM using 4-QAM compared to SIMO using-QAM
Proceeding in a similar manner as for (38), we pose the general ratio of the relative coding gains achieved by SM, using a variable-amplitude modulation, over a SIMO system using QAM as
where Ψ must be defined for the desired SM signal constellation size, M(ξ). The exact ratios as given in Table 1 will vary depending on M(ξ), but the trend (SM outperforming SIMO) will remain, as can be seen in Table 2 for M(ξ) = 16, i.e. the values in the last two rows of the tables are smaller than one.
Table 2. Relative coding gains of SM using 16-QAM compared to SIMO using -QAM
Similarly, using a constant-amplitude modulation scheme such as PSK, we realise that the only difference is that Ψ will be unity in (39). Implementing this change means removing the dependence on the signal constellation size for SM and resulting in a single table of values for (39), as given in Table 3.
Table 3. Relative coding gains of SM using PSK compared to SIMO using -QAM
From Tables 1, 2, and 3, we can conclude that a single-input-single-output system using QAM performs better than SM using QAM or PSK, i.e. the values in the first row of each table are greater than 1. These results are applicable only to SM which means that at least 1 bit must be sent via the signal-symbol.
SIRξ ≫ 1 and SINR ≈ SIRξ (interference-limited scenario)
In this case, we neglect the AWGN in the channel and realise that the SIRξ is the dominant term dictating the ABER performance of the system. Looking at the expression for the SIR, we realise that γI is a function of the signal-symbol amplitude for all users and their respective channel attenuations. Thus, we cannot simply extract γI from (34). In particular, in the expression for γI in (11), |x(u)| may be greater than 1, which would increase the interference from the remaining users. Due to the complexity of the expressions, further asymptotic study of the interference-limited scenario for SM will be constrained to using a constant-amplitude modulation scheme such as PSK. SM using PSK is shown to perform better than SM using QAM in certain cases [31]. For SM using PSK,
in the interference-limited scenario. We see that the limit of the ABER tends to (34) with a slight, but very important distinction: the system reaches an error floor. This is to be expected when the receiver is interference-unaware. If γI or are not large enough, i.e. the channel attenuations of the various nodes are similar, then this study presents an upper bound for the ABER of the system since (34) still defines the behaviour of the system in the limit. There are three consequences that should be considered similar to the noise-limited scenario analysed above: (i) the system error performance improves when more receive antennas are added at the receiver, (ii) the system error performance worsens as more SM constellation points are added, as either or M(ξ) is increased and (iii) the detector will fail to decode any data emitted from a node whose desired signal is weaker than the interfering signal. Although analytical work for SM using QAM becomes intractable, numerical results demonstrate that SM using a variable-amplitude modulation performs in a similar fashion to SM using PSK and leads to the same conclusions. In the remainder of this study, we show that the near–far problem is completely mitigated by applying a jointly optimal ML detector for SM in an interference-limited scenario. In other words, all incoming streams will be decoded and, in particular, the error performance of the system will tend to zero as AWGN approaches zero, despite any interference.
Interference-aware detection
Starting from the system model presented in the "System model" section, the decoded pair , formed from the estimated symbol xest emitted from antenna Nt on node ξis given by
Similar to the work in the "Interference-unaware detection" section, the union bound technique is used to describe the behaviour of the interference-aware SM detector in the high SNR regions. The main difference between the two detectors comes from the computation of the PEP between the possible received symbols. The union bound for the interference-aware SM detector, which estimates the ABER for node ξ, can be expressed as
The pairs, and , come from the set of all possible symbol-antenna pairings for all nodes, i.e. they independently take values from the set of all possible spatial and signal constellation points, Ω. We define to be the PEP between the symbol x(Ω) emitted from antenna being detected as symbol emitted by antenna .
Similar to the analytical derivation of (4) in the "Interference-unaware detection" section, the ABER for node ξ is shown in (42), where the PEP is given as
A more detailed derivation of (43) is given in the "Derivation of (43)" section in the Appendix. We note that thus far no assumptions have been made as to the channel distribution. Considering Rayleigh fading channels for all links in the system, we can derive the closed form solution for EH[PEP(·)] in (42) in the same manner as shown in the "Interference-unaware detection" section with (16) and (17) such that
Note that (42) presents an analytical treatment of the most general case of SM using variable amplitude modulation for the signal symbol. Given this, the system using the interference-aware detector behaves in a similar fashion to the noise-limited system, in that for an arbitrarily high SNR, each user can achieve an arbitrarily low ABER. It should be pointed out that due to the simultaneous detection process, the users with the best SNR will not be able to achieve their single-user-lower-bound (SULB). The exact effect of the additional nodes/users is further discussed in the "Simulation results and discussion" section.
Simulation results and discussion
In this section, we aim to show the performance of the interference-unaware and interference-aware detectors proposed in (2) and (41). In particular, we aim to show that (41) can successfully decode the incoming streams for all nodes. Numerical results demonstrate that (12) and (42) provide tight upper bounds for the ABER of the detectors at high SNR in the interference-limited scenario. Furthermore, we demonstrate that the interference-aware detector for SM performs better than the ML detector for a multi-user SIMO system using QAM.
The proposed interference-aware detector is jointly optimal for all nodes and does not suffer from the near–far problem, but it needs full channel state information (CSI) from all possible transmitting antennas to each receiving antenna. In addition, finding the optimal solution is an exponentially complex problem. Assuming each node has the same number of transmit antennas, Nt, and uses the same signal constellation with M points, then the interference-aware ML detector proposed has computational complexity which is proven to be NP-complete [33].
To justify our complexity, we point to the key difference between SM and other multi-user MIMO schemes, the signal and spatial domains combine to form a single SM symbol. The constellation size, i.e. the spectral efficiency of any SM system, depends on the multiplication of the number of available transmit antennas and the signal-symbol constellation used, MNt. This is in stark contrast to other MIMO systems where each spatial branch is used to increase the diversity or multiplexing gains. In such a system, if each transmit antenna is used for multiplexing gains, the system has a maximum spectral efficiency of MNt. From here, the detection complexity of a single user SM system is given by , while the detection complexity of a single user MIMO system used for multiplexing gains is given by . In this case, the two systems have different spectral efficiencies. Alternatively, if the two systems operate at the same spectral efficiency, then their complexities will be of the same order, but the cost, in terms of RF chains and power consumption would not be. The aim of this study is to characterise the behaviour of SM in the multi-user, interference-limited scenario and compare it to the complexity and cost equivalent multi-user MIMO system. As discussed in the "Introduction" section and given the complexity expressions for the single user MIMO system and the single user SM system, it is apparent that the only valid complexity and cost equivalent comparison is to compare multi-user SM with multi-user SIMO. The optimal ML detector for the interference-aware SIMO system has computational complexity, where from the "SIMO system utilising QAM (noise-limited scenario)" section, making it comparable to the interference-aware SM detector. Recent work on sphere detection algorithms may be used to alleviate this computational cost [9]. Despite the generality of our results, we restrict our simulation results to two and three node scenarios for the sake of conciseness.
Simulation setup
A frequency-flat Rayleigh fading channel with no correlation between the transmitting antennas and AWGN is assumed. Perfect CSI is assumed at the receiving node, with no CSI at the transmitter. Only one of the available transmit antennas for each node is active at any transmitting instance. In theory, each node independently decides the number of transmit antennas, and, by extension, the signal-symbol modulation it uses. In the simulation each node has the same number of transmit antennas as well as the same spectral efficiency target. In each of the figures, there are three sets of results presented: (i) the simulation results for the multi-user detector for each node, denoted by Sim (N(ξ)), (ii) the theoretical results from (12) or (42) for the node of interest and (iii) the SULB, denoted by SULB (N(ξ)). We define the asymptotically tight SULB as the system performance in a noise-limited scenario given in (26) which is governed purely by its SNR, defined as Em/No. It should be noted that in Figures 2, 3 and 4 in addition to (26), ASER/2, i.e. (28) divided by 2, is presented and overlaps (26); both are denoted as SULB (N(ξ)) in Figures 2, 3 and 4. This serves to justify the use of (28) in our asymptotic analysis in the "Asymptotic analysis of an interference-unaware detector" section. In addition, (26) is based on the union bound technique and, in some results, SULB(N(ξ)) is above 1, which is impossible for a real system. In this regard, the SULB is a lower bound on the analytical performance of each system only at low ABER. To help illustrate the difference in the behaviour of the two detectors, the channel attenuations, , are set in 10-dB intervals. In general, may be any real number. Throughout the results, QAM modulation is used for the signal-symbol modulation in SM with the notable exception of Figure 2, where PSK modulation is used to illustrate the accuracy of work done in the "Asymptotic analysis of an interference-unaware detector" section.
Figure 2. and a spectral efficiency of 4 bits/s/Hz. ABER for node 1 using the interference-unaware detector with and node 2 with a varying . Dashed lines denote simulation results for node 1 while solid lines denote the analytical upper bound. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap. Each constant value dashed-dot line with '+' markers corresponds to the asymptote derived in (34) using (40) for the different values of .
Figure 3. and a spectral efficiency of 4 bits/s/Hz. ABER for node 1 using the interference-unaware detector with and node 2 with a varying . Dashed lines denote simulation results for node 1 while solid lines denote the analytical upper bound. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap.
Figure 4. and a spectral efficiency of 4 bits/s/Hz. ABER for node 1 using the interference-unaware detector with and node 2 with a varying . Dashed lines denote simulation results for node 1 while solid lines denote the analytical upper bound. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap.
Results for interference-unaware detection
Asymptotic results in the "Asymptotic analysis of an interference-unaware detector" section, in particular (34) using QPSK for the signal-symbol modulation are verified in Figure 2. In this case, Ψis strictly defined by (22). The horizontal lines in Figure 2 represent (34) for varying values of using QPSK modulation. From Figures 3, 4 and 5, where QAM is used for the signal-symbol modulation, the developed analytical framework is accurate in all the presented instances. By moving from Figure 3 to Figure 3, where an additional receive antenna is added, the analytical model presented in (12) is a tight upper bound on the system in the high SINR region. As the channel attenuations for the interfering nodes increase, the detector approaches SULB. Similar to the effects observed in Figures 2 and 3, Figure 4 shows how the tightness of the bound improves as the number of receive antennas increases. In all instances where the interference-unaware detector is used, the node with the strongest SNR dominates the detection. The bit streams of all other nodes are not decoded. Since the SINR does not change, all other nodes remain below the effective noise floor at the receiver. This is apparent by looking at the simulation results for N(2) and N(3) in Figures 2, 3 and 4. By looking at the presented results, we conclude that (34) tightens as the system approaches its ideal transmission and the mass of the complex Gaussian distributions around each SM constellation point concentrates around the mean. This is achieved by decreasing the interference in the system or by increasing the number of receive antennas.
Figure 5. , a varying Nrand a spectral efficiency of 4 bits/s/Hz. ABER for node 1 using the interference-unaware detector with , node 2 with and node 3 with . All presented curves are for node 1 unless otherwise stated in the legend. Dashed lines denote simulation results for node 1 while solid lines denote the analytical upper bound. We note that the addition of more receive antennas reduces the ABER and hence closes the gap between the analytical and simulation results.
Figure 4 shows that the increase in diversity resulting from the addition of only a single receive antenna significantly influences the system performance. The addition of the receive antenna increases the Euclidean distance between the received and hypothesis vectors, which results in a lower ABER. Comparing Figure 2 with Figure 3 and similarly Figure 3 with Figure 4 where the number of receive antennas is increased in each figure, showing how the addition of a single receive antenna is equivalent to lowering the interference by more than 10 dB. In fact, the effect of each receive antenna is more pronounced as the imbalance between the desired and interfering links increases. By looking at the results for in Figure 2, the results for in Figure 3, and the results for in Figure 4 at an SNR of 40 dB, we see the error rate of the simulation and analytical prediction moving from 2 × 10−1 in Figure 2, to 4 × 10−3 in Figure 3, to 9 × 10−5in Figure 4. This ABER decrease shows how the number of receive antennas dominates the performance of SM in general, and particularly in an interference limited scenario. Figure 5demonstrates that the findings can be extended even in the presence of two interfering nodes.
From the presented results it is clear that when the interference-unaware detector is used, the system ABER plateaus at the derived limits, irrespective of the transmit power being used. As discussed in the "Interference-unaware detection" section, and as work in [20] has shown, the ABER improves when the number of transmit or receive antennas is increased, i.e. the system achieves coding gains.
Results for interference-aware detection
In Figure 6 we see the performance of the jointly optimal interference-aware ML detector for a two user scenario. Figure 6 clearly demonstrates that the analytical model presented in (42) represents an asymptotically tight upper bound for the system in the high SNR region. The node with the worse channel attenuation performs close to its SULB. This is not the case for the node with the better channel.
Figure 6. and a spectral efficiency of 4 bits/s/Hz. ABER using the interference-aware detector for node 1 with and node 2 with .Ana (N(u)) denotes the analytical upper bound for node u. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap.
To understand this, we can think of the multi-user ML detector as employing interference cancellation for the node with the worse channel attenuation. If the interfering user is sufficiently powerful, then the primary source of errors for the weakest node is the background AWGN rather than the randomness caused by the interfering signal [29]. All users that have good channel conditions can be considered as strong interferers, so when they are removed, the weakest nodes obtain performance closer to their SULB, i.e. the interference-aware detector is akin to strong interference cancellation for the weakest node. On the contrary, for the nodes with better channel conditions, the primary source of errors is the randomness caused by the interfering signal rather than the background AWGN, which is why the nodes with better channel conditions never perform near their SULB.
The addition of more transmit antennas at each of the nodes results in coding gains for each node as can be seen when Figures 6 and 7 are compared. The reduction in ABER as the number of transmit antennas increases is explained by realising that as the number of transmit antennas increases, the average variance increases. As increases, it leads to a larger Euclidean distance in (10) and (43). The Euclidean distance is increased because there are more cases where the variance is the summation of the individual symbol constellation points, rather than the difference, i.e. occurs less frequently. Effectively, more transmit antennas mean that the transmit vectors are spread in a larger Euclidean space. This effect can only be observed when the same spectral efficiency is maintained. In particular, a 2-dB coding gain is apparent when comparing Figures 6and 7 at an ABER of 10−4. However, increasing the number of transmit antennas does not change the relative behaviour of the system, i.e. the SNR difference between the ABER curves of the two nodes remains constant. This behaviour is expected when we consider that (17) is independent of Nt and influenced only by Nr.
Figure 7. and a spectral efficiency of 4 bits/s/Hz. ABER using the interference-aware detector for node 1 with and node 2 with .Ana (N(u)) denotes the analytical upper bound for node u. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap.
Figure 8 shows the performance of the system when the number of receive antennas is increased. On the one hand, moving from Figures 7 to 8, for a fixed spectral efficiency and a fixed number of transmit antennas, the addition of more receive antennas results in an increasing gap between the analytical ABER curves of the two nodes. In particular, a gap of 4 dB between the performance of nodes 1 and 2 with Nr = 2 is increased to around 7 dB when Nr = 4 and further increased to 9 dB for Nr = 8. On the other hand, given that the two nodes experience a channel gain difference of 10 dB, we know that the interference-aware detector cannot reach the performance of independent detection and the SULB for the node with the better channel attenuation. Nonetheless, the gap between their respective ABER curves tends toward the difference between their respective channel attenuation as Nr grows.
Figure 8. , a varying Nr and a spectral efficiency of 4 bits/s/Hz. ABER using the interference-aware detector for node 1 with and node 2 with . Dashed lines denote the performance of node 1 with a varying number of receive antennas while solid lines denote the performance of node 2 with a varying number of receive antennas.
These trends can also be observed if we look at the progression of the ABER curves in Figures 9 and 10. Figures 9 and 10 show the system performance of three users and varying Nr. Similar to the two user scenario, as Nr increases, for the three user case, each user performs better and slowly closes the gap to its SULB. As expected, the addition of more nodes increases the interference and pushes the performance of each node further from its SULB, noticeable when comparing Figures 7 and 10 for node 2.
Figure 9. and a spectral efficiency of 4 bits/s/Hz. ABER for node 1 with , node 2 with and node 3 with .Ana(N(u)) denotes the analytical upper bound for node u. Since the analytical bound is asymptotically tight, at low ABER the dashed and solid lines overlap.
Figure 10. and a spectral efficiency of 4 bits/s/Hz. ABER for node 1 with , node 2 with and node 3 with .Ana (N(u)) denotes the analytical upper bound for node u. The analytical bound is again shown to be asymptotically tight at low ABER.
Lastly, Figure 11 demonstrates that in the multiple access interference-limited scenario, by using the interference-aware detector, SM performs better than the complexity and cost equivalent ML detector for the multi-user SIMO system. Specifically, SM exhibits an approximately 3 dB better performance in terms of SNR at an ABER of 10−4 for each user. The relatively constant coding gain is the result of the similar detection used for both systems. While multi-user SM and multi-user SIMO may be comparable in terms of detector complexity and the number of transmit and receive RF chains required, each SM node requires multiple transmit antenna elements. The multiple transmit antennas mean that the SM constellation points are spread in a larger Euclidean space and thus have lower error probability.
Figure 11. and a spectral efficiency of 4 bits/s/Hz. ABER of multi-user SM and multi-user SIMO using interference-aware detectors with node 1 experiencing channel attenuation of , node 2 with and node 3 with .
Summary and conclusions
In this study, the performance of SM in the multiple access, interference-limited scenario was investigated. Two ML detectors for use with SM were discussed.
The interference-unaware detector was defined and studied in the limit as the SNR approached infinity. Its performance over uncorrelated Rayleigh fading channels was studied and a closed form solution for the upper bound of the system was provided. It was shown that this detector inevitably reaches an error floor which is dependent on the system SINR. The exact level was defined as a function and concrete examples were provided. It was shown that the increase in the number of receive antennas has a greater impact on the asymptotic performance of the system compared to reducing the interference in the system. The addition of a single receive antenna resulted in greater SNR gains than reducing the interference, , by more than 10 dB at high SNR. This implies that the number of receive antennas dominates the performance of SM in general, and particularly in an interference-limited scenario.
The interference-aware ML detector for SM was proposed. As with the interference-unaware detector, its performance over uncorrelated Rayleigh fading channels was studied and a closed form solution for the upper bound of the system was provided. In addition to avoiding the error floor present in the interference-unaware detector, the jointly optimal detector results in a noise-limited scenario for the detection of all transmitted streams, i.e. an arbitrarily small ABER can be obtained by any user for a sufficiently high SNR. On the one hand, for the same spectral efficiency, increasing the number of transmit antennas at each of the nodes from 2 to 4 resulted in SNR gains of around 2 dB. This measure did not, however, have any effect on the coding gain difference between the ABER curves. On the other hand, increasing the number of receive antennas increased the diversity of the system. This, increased the coding gain difference between the ABER curves of the nodes because the receiver could distinguish the channels more easily and better mitigate interference. The impact on the diversity and coding gains further shows the importance of the number of receive antennas in any SM system. A limiting factor, as with all ML detectors, is the complexity. In addition, the receiver must have channel knowledge from all transmitting nodes. These two limitations constrain the application of this detector to the uplink scenario. The interference-aware detector enabled SM to perform better in terms of ABER than the complexity and cost equivalent multi-user SIMO system in an interference-limited environment.
This study demonstrated that in order to effectively apply SM in an interference-limited scenario, the number of receive antennas should be maximised. Although more computationally complex than the interference-unaware detector, the interference-aware detector can guarantee that the system does not reach an error floor.
Derivation of (32)
We begin by considering which corresponds to . For this event, we seek to bound to two which implies that we should consider
where ε ∈ {(1,1),(2,1),(3,1)} and dε are the distances defined in Figure 12 and . We introduce the normalising factor gQAM, given in [32], to maintain unity power in our constellation. We see that there are only four possible combinations that satisfy (46). In particular
• , occurs (M(ξ))2/8 = 32 times,
Figure 12. The red squares denote 16-QAM constellation points. In this image, the constellation is not normalised. The figure shows possible distance combinations between each of the constellation points and their distances to the origin.
• , occurs (M(ξ))2/4 = 64 times,
• , occurs (Mξ))2/8 = 32 times and
• , occurs (M(ξ))2/2 = 128 times.
We know that these combinations occur for every instance when . For a system with transmit antennas, we have unique pairings. This leads to
Having established the derivation of , we turn our attention to which corresponds to . If we look at Figure 12, we see there are additional combinations aside from the ones denoted. To this extent, our bound, , serves to simplify the counting and set many of them to 2. In particular, we see that when , then . In this case, we bound to 2 and realise that d(4,2) is the largest distance that we must account for in our expectation analysis. We note that our approach is applicable to larger constellation sizes and, after some careful counting, we see that in general for a given constellation size of M(ξ) we have that
• d(1,2) occurs a total of times,
• d(2,2) occurs a total of times,
• d(3,2) occurs a total of times and,
• d(4,2) occurs a total of times.
By looking at Figure 12, we can easily see that for M(ξ) = 16:
• , occurs exactly 36 times and
We realise that the combinations counted above are applicable for every transmit antenna. This implies that we must multiply each count by which leads to
To arrive at a final solution, we set all other combination values to gQAM as we enforce our bound on giving
which is the number of elements for which was set to 2, i.e. . We now average and arrive at Ψ. To achieve this, we merely normalise our sum by to account for the number of possible events, resulting in
which when simplified becomes (32).
In Figure 13 we compare the asymptote of SM, given by (34), in the noise-limited scenario for M(ξ) = 16 with and without using (32). Figure 13 exemplifies the accuracy and tightness of our approach.
Figure 13. The dashed lines with circle markers denote the asymptote for the system if the expectation for is obtained via simulations. The solid lines with square markers denote the asymptote when (32) is used. Moving from the rightmost to the leftmost pairs of curves, each pair corresponds to an incremental increase in Nr from 2 to 6. The system is using two transmit antennas and has an overall spectral efficiency of 5 bits/s/Hz.
Reaching (38) from (34) with (31) and (37)
Combining (34) with (31) results in
Restating (37) for convenience, we have
Taking the ratio of (49) over (37) gives (38) as
Derivation of (43)
where and . If we consider a Rayleigh fading channel, then we can derive the closed form solution for EH [PEP(·)] in (42) by using ( [30], eq. 62). We note that by assuming a Rayleigh fading channel, the argument within (43) can be represented as the summation of 2Nr squared Gaussian random variables, with zero mean and variance equal to 1, which means that they can be described by a central Chi-squared distribution with 2Nr degrees of freedom and a probability density function of
The result for EH [PEP(·)] is given as
Competing interests
The authors declare that they have no competing interests.
We gratefully acknowledge the support from the Engineering and Physical Sciences Research Council (EP/G011788/1) in the United Kingdom for this study.
J Mietzner, R Schober, L Lampe, WH Gerstacker, PA Hoeher, Multiple-antenna techniques for wireless communications—a comprehensive literature survey. IEEE Commun. Surv. Tutor 11(2), 87–105 (2009)
R Mesleh, H Haas, Y Lee, S Yun, Interchannel interference avoidance in MIMO transmission by exploiting spatial information. in Proc, ed. by . of the 16th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), vol. 1 ((Berlin Germany, 11–14 September 2005), pp. 141–145)
R Mesleh, H Haas, S Sinanović, CW Ahn, S Yun, Spatial modulation. IEEE Trans. Veh. Technol 57(4), 2228–2241 (2008)
N Serafimovski, S Sinanović, RY Mesleh, H Haas, M Di Renzo, Fractional bit encoded spatial modulation (FBE–SM). IEEE Commun. Lett 14(5), 429–431 (2010)
A Younis, N Serafimovski, R Mesleh, H Haas, Generalized spatial modulation. Asilomar Conference on Signals, Systems, and Computers ((Pacific Grove, CA, USA, November 2010))
R Mesleh, M Di Renzo, H Haas, PM Grant, Trellis coded spatial modulation. IEEE Trans. Wirel. Commun 9(7), 2349–2361 (2010)
A Younis, R Mesleh, H Haas, PM Grant, Reduced complexity sphere decoder for spatial modulation detection receivers. 2010 IEEE Global Telecommunications Conference (GLOBECOM 2010) ((Miami, Florida, USA, December 2010), pp. 1–5)
MD Renzo, H Haas, Performance analysis of spatial modulation. International ICST Conference on Communications and Networking in China (CHINACOM) ((Beijing, China, August 2010, pp. 1–7))
A Younis, R Mesleh, H Haas, M Renzo, Sphere decoding for spatial modulation. in Proc, ed. by . of IEEE International Conference on Communications (IEEE ICC 2011) ((Kyoto, Japan, 5–9 June 2011), pp. 1–6)
J Jeganathan, A Ghrayeb, L Szczecinski, Spatial modulation: optimal detection and performance analysis. IEEE Commun. Lett 12(8), 545–547 (2008)
SU Hwang, S Jeon, S Lee, J Seo, Soft-output ML detector for spatial modulation OFDM systems. IEICE Electron Exp 6(19), 1426–1431 (2009). Publisher Full Text
M Di Renzo, H Haas, Spatial modulation with partial-CSI at the receiver: optimal detector and performance evaluation. Proceedings of the 33rd IEEE conference on Sarnoff ((IEEE Press, Piscataway, NJ, USA, 2010), pp. 58–63) (http://portal), . acm.org/citation.cfm?id=1843486.1843498 webcite
M Di Renzo, H Haas, Improving the performance of Ssace shift keying (SSK) modulation via opportunistic power allocation. IEEE Commun. Lett 14(6), 500–502 (2010)
T Handte, A Muller, J Speidel, BER analysis and optimization of generalized spatial modulation in correlated fading channels. Vehicular Technology Conference Fall (VTC Fall-2009) (Anchorage Alaska, USA, IEEE, (September 2009), pp. 1–5)
MD Renzo, H Haas, Bit error probability of SM-MIMO over generalized fading channels. IEEE Trans. Veh. Technol 61(3), 1124–1144 (2012)
E Basar, U Aygolu, E Panayirci, VH Poor, Space-time block coded spatial modulation. IEEE Trans. Commun 59(3), 823–832 (2011)
J Jeganathan, A Ghrayeb, L Szczecinski, A Ceron, Space shift keying modulation for MIMO channels. IEEE Trans. Wirel. Commun 8(7), 3692–3703 (2009)
JN Laneman, DNC Tse, GW Wornell, Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans. Inf. Theory 50(12), 3062–3080 (2004). Publisher Full Text
MO Hasna, M-S Alouini, End-to-end performance of transmission systems with relays over Rayleigh-fading channels. IEEE Trans. Wirel. Commun 2(6), 1126–1131 (2003). Publisher Full Text
N Serafimovski, S Sinanovic, M Di Renzo, H Haas, Dual-hop spatial modulation (Dh-SM). in Proc, ed. by . of the Vehicular Technology Conference (VTC Spring) (Budapest, Hungary, IEEE, 15–18, May 2011), pp. 1–5)
M Di Renzo, H Haas, On the performance of SSK modulation over multiple-access Rayleigh fading channels. IEEE Global Telecommunications Conference (GLOBECOM) ((Miami, Florida, USA, December 2010), pp. 1–6)
M Di Renzo, H Haas, Bit error probability of space-shift keying MIMO over multiple-access independent fading channels. IEEE Trans. Veh. Technol 60(8), 3694–3711 (2011)
J Duplicy, B Badic, R Balraj, R Ghaffar, P Horvth, FKR Knopp, IZ Kovacs, HT Nguyen, D Tandur, G Vivier, MU-MIMO in LTE systems. EURASIP J. Wirel. Commun. Netw 2011, 13 (2011). BioMed Central Full Text
JG Andrews, W Choi, RW Heath Jr, Overcoming interference in spatial multiplexing MIMO cellular networks. IEEE Wirel. Commun. Mag 14(6), 95–104 (2007)
D Gesbert, M Kountouris, RW Heath, C byoung Chae, T Salzer, From single user to multiuser communications: shifting the MIMO paradigm. IEEE Signal Process. Mag 24, 36–46 (2007)
CW Tan, AR Calderbank, Multiuser detection of alamouti signals. IEEE Trans. Commun 57, 2080–2089 (2009) (http://dl, 2009), . acm.org/citation.cfm?id=1651065.1651094
G Auer, V Gianni, I Godor, P Skillermark, M Olsson, M Imran, M Gonzalez, C Desset, O Blume, A Fehske, How much energy is needed to run a wireless network? IEEE Wirel. Commun 11, 40–49 (2011)
C Desset, B Debaillie, V Giannini, A Fehske, G Auer, H Holtkamp, W Wajda, D Sabella, F Richter, MJ Gonzalez, H Klessig, I Godor, M Olsson, MA Imran, A Ambrosy, O Blume, Flexible power modeling of LTE base stations. IEEE Wireless Communications and Networking Conference (WCNC) ((Paris, France, April 2012), pp.2858–2862)
S Verdu, Multiuser Detection (Cambridge University Press, Cambridge,MA, 1998)
M-S Alouini, A Goldsmith, A unified approach for calculating error rates of linearly modulated signals over generalized fading channels. IEEE Trans. Commun 47(9), 1324–1334 (1999). Publisher Full Text
M Di Renzo, H Haas, Bit error probability of spatial modulation (SM) MIMO over generalized fading channels. IEEE Trans Veh. Technol 61, 1124–1144 (2012)
MK Simon, M Alouini, Digital Communication over Fading Channels (John Wiley & Sons, Inc, NEw York, 2005) ISBN: 978-0-471-64953-3
S Verdu, Computational complexity of optimum multiuser detection. Algorithmica 4, 303–312 (http://dx, 1989), . doi.org/10.1007/BF01553893 Publisher Full Text


text:
Gretna F.C. 2008
|Full name
|Gretna Football Club 2008
|Raydale Park, Gretna
|Stuart Rome
|Lowland Football League
|Lowland Football League, 3rd
Gretna F.C. 2008 (commonly referred to as Gretna 2008 and colloquially as Gretna) is a football club from the town of Gretna. It was founded in 2008 after the bankruptcy and demise of Gretna F.C., which had existed since 1946. Gretna 2008 is not a direct continuation of the old club, being under a completely different management and set-up;[1] the club trades under the name Gretna FC 2008 Ltd to avoid confusion with the old Gretna.
In 2013, the club became founder members of the Lowland League, having previously played in the East of Scotland Football League Premier Division. The team played for most of the 2008–09 season at the Everholm Stadium in Annan. Late in the season, however, the new owners of Raydale Park allowed Gretna 2008 to move to the ground in their home town.[2] In May 2011, the Raydale Community Partnership, of which Gretna FC 2008 is a member, negotiated the purchase of the site.
The original Gretna F.C. were founded in 1946, and joined the Scottish Football League in 2002. After being taken over by the late millionaire Brooks Mileson, the club had a meteoric rise, gaining promotion three years in a row to make the Scottish Premier League in 2007. However, the club could not financially support itself and following Mileson's illness and withdrawal of financial support, the club slipped into administration and then bankruptcy in the summer of 2008. The club were relegated from the SPL and then forced to resign their place in the Scottish Football League.[3]
With Gretna heading out of business, on 2 July 2008, the Gretna Supporters' Society, a supporters' trust, founded "a new Gretna Football Club", and appointed Anton Hodge as chairman. In August 2009, the trust amended its articles of governance and Gretna FC 2008 is now managed directly by the members of the trust board, whose chairman is Craig Williamson. The new club is wholly owned by the society and its board elected by the society's members. The club appointed the University of Cumbria's football officer Stuart Rome as team manager and recruited much of the playing squad from Workington's reserve team.[4] Technically, Gretna 2008 coexisted briefly with the old Gretna, which was not formally liquidated until 8 August 2008.[5]
Unable to play at the old Gretna's home ground of Raydale Park, they instead moved into the Everholm Stadium in Annan.[6] Gretna 2008 played their first match against Workington on 12 July 2008.[7] Four days later, they were successfully accepted into the East of Scotland Football League First Division,[8] and on 9 August 2008, won their first competitive match as a new club, beating Kelso United 3–0 away in their first match of the league season.[9] The new owners of Raydale Park allowed Gretna 2008 to move to the ground in their home town in May 2009, and the Raydale Community Partnership, of which Gretna FC 2008 is a member, negotiated the purchase of the site in May 2011. They finished their first season as a new club in fourth place in the league. They narrowly missed promotion again in their second season, but finished their third, in 2010–11 being promoted as First Division champions.
In 2013 Gretna FC 2008 were elected founder members of the new Lowland League.
Colours and badge[edit]
Gretna 2008's colours are black and white hoops.[10] Gretna F.C. had used white shirts after Brooks Mileson took control of the club, but black and white hoops were the club's traditional colours.
The badge of the club is largely similar to that of Gretna, except that 2008 has been added to reflect the change of status in that year. The anvil represents the famous Blacksmith's Shop wedding site at Gretna Green, and the thistles represent the club's Scottish location.
- Alex Jack Cup: 1
- 2008–09
- Image Printers Cup: 2
- 2009–10, 2012–13
- East of Scotland Cup (aka City Cup): 1
- 2012–13
- East of Scotland League Division One: 1
- 2010–11
Current Squad[edit]
Note: Flags indicate national team as defined under FIFA eligibility rules. Players may hold more than one non-FIFA nationality.
- ^ Anderson, Keith (11 July 2008). "Gretna given place in the East of Scotland League". Edinburgh News. The Scotsman. Retrieved 2009-08-11.
- ^ "Gretna enjoys football homecoming". BBC News. 2009-05-02. Retrieved 2009-08-11.
- ^ Rinaldi, Giancarlo (2008-06-04). "How Gretna paid the ultimate price". BBC News. Retrieved 2009-08-11.
- ^ "Gretna 'hope to do the East League proud'". Peeblesshire News. Retrieved 2009-08-11.
- ^ "Liquidation signals the final nail in Gretna coffin". Cumberland News. 2008-08-08. Retrieved 2009-08-11.
- ^ "Gretna are saved – but they will be playing in Annan". Cumberland News. 2008-07-12. Retrieved 2009-08-11.
- ^ "Stuart Rome leads Gretna FC 2008 into battle for first time". The Daily Record. Retrieved 2009-08-11.
- ^ "New Gretna club joins East league". Dumfries and Galloway Standard. 2008-07-16. Retrieved 2009-08-11.
- ^ "Perfect start for Gretna". Dumfries and Galloway Standard. 2008-08-15. Retrieved 2009-08-11.
- ^ "Gretna are on the long road back". Scotsman.com Sport. Retrieved 2009-08-11.
External links[edit]

subset: commoncrawl


text:
An Oak Harbor woman was taken by Life Flight medical helicopter to St. Vincent Mercy Medical Center in Toledo following a single-car crash Sunday on Ohio 19 in Carroll Township.
- Filed Under
An Oak Harbor Iraq war veteran said he used some of his military training when he responded to a wreck Sunday afternoon in Carroll Township.
Michael Lattea, who served in the U.S. Army infantry, and his friend Michael Greider were traveling a few cars behind the scene of the one-vehicle wreck on Ohio 19.
The Sandusky post of the Ohio Highway Patrol reported Julie Walls, 59, of Oak Harbor, was northbound on Ohio 19 between Bier and Genzman roads at 4:30 p.m. Sunday, when she drove off the right side of the road, back on the road, across the center line and back off the right side of the road. ...


text:
Everywhere in interdenominational settings, people are talking about the Kingdom and how the church needs to develop and move in a "Kingdom Mindset." This lesson will explore what that means.
First of all, we need to determine what the Kingdom of God is. The denomination I grew up in defined the Kingdom as the church. They taught that the Kingdom – a.k.a the church – was birthed on the day of Pentecost. Therefore the Kingdom of God has already come and we cannot, should not pray the section of the Lord's prayer that says, "Thy Kingdom come." (Matthew 6:10, Luke 17:20-21) But is this accurate? What is the Kingdom of God?
The Kingdom of God is a foundational concept of Christianity because it is the central theme of Jesus' message in the synoptic Gospels. That's because, in the Lord's Prayer, He said that the Kingdom belongs to God. (Matthew 6:13) The phrase occurs almost 150 times in the New Testament. A large part of it is defined by parable – some of which are controversial in interpretation. Even after His resurrection, He continued speaking to the disciples about "the things pertaining to the Kingdom of God. (Acts 1:3)
Mark and Luke use a Greek term that is usually translated as "Kingdom of God," while Matthew used the Greek term that is translated "Kingdom of Heaven." Scholars speculate that Matthew did this because he was writing to Jews and the custom of Jews even today is to avoid using God's name. We get letters from our Jewish friends and they spell God, G-D.
The word "kingdom" is a translation of a Greek word (basileia) which is a translation of the Hebrew and Aramaic words, "malkuth and malkutha. These Hebrew and Aramaic words do not define kingdom by territory but by dominion. And, in fact, Jesus did say that we could not say, "Look here it is!" or "There it is!" because the Kingdom of God is within us. (Luke 17:20-21) But others believe that the Kingdom of God has yet to come and that it refers to the millennial reign of Christ here on earth with Jerusalem as its headquarters.
So what is the Kingdom of God? From a purely etymological viewpoint, the word "basileia" is believed to have derived from the Greek word for base or foundation. Can we then, substitute either one of these words and say, the Foundation of God or the Foundation of Heaven? Well, that would preach but would it be the full truth?
No matter what your belief is concerning modern-day Israel and Jews in general, everyone has to admit that Christianity has its roots in the Hebrew people and the Hebrew Scriptures. Since Jesus came to the Jews and was Himself a Jew, we need to acknowledge that He assumed that his audience understood the Kingdom as defined in the Hebrew Scriptures, the Old Testament. When He spoke of the Kingdom of God (Kingdom of Heaven) He spoke of the time of the fulfillment of the Abrahamic and Davidic covenants. This will be a time of a restored earth where the faithful will worship and serve God under the ruler- ship of a righteous leader of the Davidic line. After all, Kingdom implies that there is
This was the Messianic hope of the Old Testament prophets and it was echoed by John the Baptist, Jesus, Peter, Paul and the other disciples. It's why the disciples asked Him questions like, "Is it now that you're going to restore the Kingdom to Israel?" (Acts 1:6)
At the same time, Romans 14:17 tells us that, "the Kingdom of God is not eating and drinking, but righteousness and peace and joy in the Holy Spirit." In fact, the scepter of God's Kingdom is the scepter of righteousness. (Hebrews 1:9 quoting Psalm 45:6)
1 Corinthians 4:20 says, "For the Kingdom of God is not in word but in power."
So what is the Kingdom of God? Whatever it is, we're told that it can't be shaken. (Hebrews 12:28) But is it simply an attitude or a belief system held by people? Or is it more than that? And if it's more than that, where is it?
Old Testament Jews were very literal in their interpretation of Scripture. As the New Testament Church has evolved, we tend to spiritualize much or everything, especially those parts of the Bible that we either don't like or don't understand.
I believe that it is not an either/or concept but a both/and entity. The more I study Scripture, the more literal, and therefore applicable, it is to my daily life. At the same time, I have a tremendous appreciation for the ethereal, philosophical aspect of scripture. I find it very interesting that when the disciples asked Him when He was going to restore the Kingdom, He didn't deny that their belief in a literal Israeli kingdom would be formed at His bidding. Instead, He said, "It's not your business to know when." (Acts 1:7)
Nevertheless, I believe firmly that when it comes to any point of doctrine, if it isn't true in every time and in every place and culture on the earth, then it's cultural and not the solid Truth. So, let's look at specific scriptures of what Jesus said the Kingdom of God is and what it entails.
Let me warn you that as we look at these passages, you may end up with more questions than answers. I encourage you to write them down and study them out for yourself. And if you're wise, you will be willing to look at all sides rather than just accept whatever you've been taught by the denomination you grew up in or have become a part of.
Both John the Baptist and Jesus preached that since the Kingdom of God was at hand, people needed to repent. (Matthew 3:2, Matthew 4:17, Mark 1:14-15)
When the Pharisees accused Jesus of casting out demons by Beelzebub, He started talking to them about the Kingdom, that if it were divided it would not stand ((Matthew 12:25, Mark 3:22-29, Luke 11:17-19) and that if He "cast out demons by the Spirit of God" (which of course, He did), then "the Kingdom of God has come upon you." (Matthew 12:28, Luke 11:20) That's past tense.
He told the Old Testament Scholar who asked about the first commandment and answered Jesus wisely that he was not far from the Kingdom. (Mark 12:34)
When He sent the 70 out to preach He told them to say, "The Kingdom of God has come near to you. (Luke 10:9-12)
He told some of His followers that they would literally see Him coming in His Kingdom (Matthew 16:28) – which seems to imply that it came before the day of Pentecost, and that some would see the Kingdom of God (Luke 9:27) and that some would see the Kingdom of God come (or present) with power. (Mark 9:1), which gives the impression that the Kingdom is something physical.
He also said that He'd not celebrate the Passover or drink the "fruit of the vine" until the Kingdom of God comes. (Matthew 26:29, Mark 14:25, Luke 22:16-18) That's something He hasn't done yet.
When the thief on the cross asked Jesus to remember him when He came into His Kingdom, Jesus promised him that he'd be with Him in Paradise that day. (Luke 23:42-43) Is Paradise the same thing as the Kingdom of God?
It was because Joseph of Arimathea was waiting for the Kingdom of God that he was able to take courage and ask Pilate for the body of Jesus. (Mark 15:43, Luke 23:51)
Paul told the Colossians that Jesus has – past tense – "delivered us from the power of darkness and conveyed us into the Kingdom of the Son of His love." (Colossians 1:13)
Yet, in John's revelation of heaven, he heard a loud voice saying that when the accuser of our brethren who accused us before God day and night, has been cast down, then salvation, strength and the Kingdom of God and the power of His Christ will have come. (Revelation 12:10) Some would argue that this already happened when Jesus rose from the dead. But are we not still being accused by Satan? Someone else would say that the operative words here are "who accused them before our God day and night." That until the resurrection, Satan was able to enter the courtroom of heaven at will and bring accusation against us as we see he did in the book of Job. But when Jesus descended into hell and ascended into heaven, He threw Satan out of the courtroom and he no longer has free access there.
Gabriel told Mary that God would give her baby the throne of His father David and that He would reign over the house of Jacob forever. (Luke 1:32-33) That was a literal throne over a specific people and territory.
Yet Jesus said, "My Kingdom is not of this world. . . (John 18:36)
Jesus said that the poor, the poor in spirit and those who are persecuted for righteousness' sake would receive the Kingdom of Heaven. (Matthew 5:3, 10, Luke 6:20; James 2:5)
He also said that you had to be born again of water and the Spirit to enter the Kingdom of God. (John 3:3-5) Since this is so, what does it mean? Denominations differ on the interpretation of this passage. Some teach that being born of water and Spirit refers to physical birth (water) and spiritual birth (Spirit). Others teach that it refers to water baptism and the baptism of the Holy Spirit. Which is correct?
Jesus told Peter he would give him the keys of the Kingdom of Heaven. With these keys he could bind and loose according to what is bound and loosed in heaven. (Matthew 16:19)
He said that children made up the Kingdom of Heaven (Matthew 19:14) and that whoever does receive the Kingdom of God must be like a little child. (Mark 10:13-16, Luke 18:15-17)
The only way rich people are able to enter the Kingdom of God is because with God all things are possible. (Matthew 19:23-26)
He said that some would make themselves eunuchs for the Kingdom of Heaven's sake. (Matthew 19:12)
The Kingdom of God will be given to the nation that bears the fruits of it. (Matthew 21:43, 44) Notice here that He's talking about nations, not individuals. In fact, a little later on when He talked about coming in His glory with all the holy angels with Him and sitting on the throne of His glory, there would be whole nations that would inherit the Kingdom prepared for them from the foundation of the world because of how they as a nation, had dealt with the hungry, thirsty, naked, sick, the stranger and the prisoner. (Matthew 25:31-46)
In his vision of heaven, the apostle John saw angels and heard loud voices saying, "The kingdoms of this world have become the Kingdoms of our Lord and of His Christ" (Revelation 11:15) This seems to indicate that the Lord's Kingdom is tangible in such a way that earthly kingdoms can join His.
In Mark 9:47 Jesus indicated that only those who deal with sin that comes in through their eye-gate will enter the Kingdom of God.
He warned us that we must "strive to enter through the narrow gate, for many. . . will seek to enter and will not be able." In fact, people will say, "Wait a minute, You were in our midst and we were with You." But God will answer, "I don't know you, or don't know where you are from for you are workers of iniquity. (Luke 13:24-30)
Peter encouraged us to be very diligent to make our call and election sure so that we would
Paul wrote that the unrighteous will not inherit the Kingdom of God. Then in 1 Corinthians 6:9-10 he gave a long list of who he considered to be unrighteous; They are. .
Paul added to this a list of sins that would keep a person out of the Kingdom in Galatians 5:19-21, calling them "the works of the flesh."
Notice the word "inherit" in both these passages. He used it again in Ephesians 5:5 in a short list of those who have no inheritance in the Kingdom of God. After he wrote what he did to the Corinthians, he went on to say that flesh and blood cannot inherit the Kingdom of God, then went on to talk about how we'll all be changed in a moment , in the twinkling of an eye, at the last trumpet. (1 Corinthians 15:50) If there is a significance to the use of the word "inherit" in these two passages, is he saying that people who practice the 10 things he listed cannot possibly be a child of God, one who has been adopted into God's family, thereby becoming a heir of eternal salvation?
When Philip preached the things concerning the Kingdom of God and the Name of Jesus Christ, both men and women were baptized in Samaria. (Acts 8:12) Notice that it doesn't say that Philip preached a message of salvation. What's the difference? Salvation is simply the entrance into the Kingdom. But as we shall see, the Gospel of the Kingdom is much more than salvation for eternity.
When Matthew talked about Jesus preaching the Gospel of the Kingdom, he would add, AND healing sickness and disease. (Matthew4:23, Matthew 9:35) When He sent the disciples out to preach the Kingdom message, they were also to heal the sick, cleanse the lepers, raise the dead and cast out demons. (Matthew 10:7, 8, Luke 9:2) When the disciples returned, He spoke to them more about the Kingdom of God AND healed the sick as He did so. (Luke 9:11) This gives the indication that where the Gospel is preached, healings will occur also, but since the Gospel of the Kingdom and healing are listed separately, there seems to be a difference. Could this be because the Kingdom of God will continue beyond this age? And that healing, deliverance, etc. are only needed now?
All my life, I've heard about the Gospel of Salvation. Yet in doing a word study on that phrase, I find that in only one place is a similar term used. In Ephesians 1:13 Paul used the phrase "the gospel of your salvation." Everywhere else the term is the. . .
I believe we miss the point when we talk about the gospel of salvation because salvation is only the first step, the entry point into the full gospel that Jesus preached. When we center our attention only on salvation, we get a lot of babies birthed – which is excellent – but then we leave them that way. We don't grow them up. I believe that centering on salvation so that people don't go to hell is why the American church has fallen down when it comes to making disciples and we have trouble finding qualified people to lead small groups or any other type of ministry.
Some are gifted with the ability to introduce people to the Lord. Others are great at taking new babies and growing them up. What we have lacked have been individuals and churches that will take the adult believers, those who have a foundation in the Word of God, and equip them to be sent out into their ministries. I see that happening more and more but it's primarily only in the interdenominational and non-denominational circles. Here in America, if you take a look at denominational church growth, the majority of the growth doesn't come from new believers but from believers moving around and changing churches. The apostle Paul taught "the things of the Kingdom of God and look at the results. (Acts 19:8 Acts 20:25; Acts 28:23, 30-31)
We've already covered the scripture about Jesus telling Nicodemus that he must be born again, by water and the Spirit to enter the Kingdom. Is there anything else we must do to enter in?
In Luke 12:32, Jesus said, "Do not fear, little flock, for it is your Father's good pleasure to give you the Kingdom." And He even tells us that if we seek the Kingdom of God as well as God's righteousness first before we seek other things, we'll be assured food, clothing and shelter. (Matthew 6:33, Luke 12:31)
But He added that we must do the will of His Father to enter. In fact, there would be those who call Him Lord who won't enter. (Matthew 7:21, Matthew 8:11, 12)
He further said that not only does the Kingdom of Heaven suffer violence but that the violent take it by force. (Matthew 11:11-12) What does that mean? Well, we know that we're not to take up the sword and force people to convert as Islam teaches. In the past, teachers have, for the most part, ignored this passage. I have always interpreted this to mean that we must do violence to all the negative INSIDE OURSELVES. There is a growing consensus in the Body of Christ that this also means we're to praise and worship violently. In other words, when we're in some spiritual warfare, we're to praise following one of the Hebrew words for praise which is Hallel, meaning exuberant praise. Getting your body involved.
Paul and Barnabas exhorted the disciples in Lystra, Iconium and Antioch saying, "We must through many tribulations enter the Kingdom of God." (Acts 14:21-22)
When John was on the island of Patmos, he identified himself as a brother and companion in the tribulation, Kingdom and patience of Jesus Christ. (Revelation 1:9)
Many Christians hold the belief that at the Cross; the Law of Moses was done away with. But that's not what Scripture says. Jesus said He came to fulfill it, not wipe it out. The Law of Moses is full of principles that God wants us to live by. No, we no longer need to offer blood sacrifices; Jesus took care of that. But He said Himself that whoever breaks even the least of the Mosaic commandments and teaches others to do so also would be called least in the Kingdom of Heaven but that whoever obeys the commands and teaches others to do so also would be called great. He further said that to teach obedience to the law but to not follow it is the type of righteousness that was practiced by the scribes and Pharisees and you would NOT enter the Kingdom of Heaven at all!!! (Matthew 5:19-29)
In fact, the principles laid down in the Law of Moses are so permanent – as well as beneficial – that Jesus said it would be easier for heaven and earth to pass away than for one tittle of the law to fail. (Luke 16:16-17) He further said that scholars of the Old Testament (the scribes) who taught concerning the Kingdom would be able to bring out new and old "treasures" of understanding. (Matthew 13:51-52)
Apparently, there are levels within the Kingdom. The Matthew 5 scripture I just referred to tells us that some would be "least" and others "great." In another place, Jesus said the least in the Kingdom would be greater than John the Baptist. (Matthew 11:11, Luke 7:28) When the disciples asked Him who was the greatest in the Kingdom, He told them essentially not to worry about the hierarchy because if they weren't converted they wouldn't even enter! But if they truly wanted to be great, they'd have to humble themselves as a little child to be the greatest. (Matthew 18:1-4, Mark 10:13-16, Luke 18:15-17)
Referring to the Kingdom of God, Jesus said that there would be those who are "last who will be first and there are first who will be last." (Luke 13:30)
Both the living and the dead will be judged at the appearing of Jesus and His Kingdom. (2 Timothy 4:1
The Lord will deliver us from every evil work and will present us for His heavenly Kingdom. (2 Timothy 4:18)
Those who leave all for the sake of the Kingdom of God will "receive many times more in this present time, and in the age to come, eternal life." (Luke 18:28-30)
He told the 12 that each of them would receive a kingdom and sit on thrones judging the 12 tribes of Israel and would eat and drink at His table in His Kingdom. (Luke 22:29-30) This sounds like physical kingdoms.
At the end, Jesus will deliver the Kingdom to God and put an end to all rule and all authority and power. (1 Corinthians 15:24) This statement lets us know that the Kingdom is an entity, something tangible that can be handed over. Is it a world with nations under His dominion or simply a collection of individuals? Surely it's not an organization!!!
When we suffer with patience and faith in the midst of persecutions and tribulations we are counted worthy of the Kingdom of God. (2 Thessalonians 1:5)
Jesus told parables so that only His disciples would understand the MYSTERIES of the Kingdom of Heaven. (Matthew 13:11, Mark 4:11, Luke 8:10) Much of what He had to say about the Kingdom of God was with parables and some of them are still mysteries in that people are divided as to what they mean. Nevertheless, I'll briefly tackle them now, giving the primary characteristics of the Kingdom of God.
After praying a lot about this, God gave me a vision of the globe of the world. Surrounding it and over it in the heavenly-realm was the spiritual Kingdom of God. Coming down from this heavenly city/realm were shafts of light that pierced the earth-realm and I came to realize that the heavenly Kingdom literally invades the earth in reality wherever a believer or group of believers take dominion, thus bringing the Kingdom of God into physical reality. God's desire is for the Kingdom of God to be in operation here on earth in dominion, in physical reality as much as in the spirit-realm.
OK, so now, with this understanding that the Kingdom of God is both earthly/physical and spiritual/heavenly and that it is also both now and in the future, what do we need to understand, change or alter to have a Kingdom Mindset?
The first thing we need to deal with is Matthew 6:33 – Seek first the Kingdom of God and His righteousness, and all these things shall be added to you. With that always in mind, we need to recognize our particular place in history and where we've been. There's been a shifting and a shaking going on in the Body of Christ for some time now and there have been various moves of God.
Since the Dark Ages we've been in restoration and revelation. Each new season of the church, God has highlighted a truth of Scripture that we've overlooked in the past. The first thing He did was to use Martin Luther to give attention to salvation by faith alone 490 years ago. This was not a new doctrine but it was new to the church at that time and it started the Protestant Reformation. There was the Presbyterian Movement that changed the structure of the church. In the early 1900s there was the Holiness Movement that gave birth to the Pentecostal Movement. In the late '40s and early '50s was the Healing Movement. Then we had the Charismatic Movement in the '60s and '70s. At the end of that the Prayer Movement began, followed by the Prophetic, then the Apostolic Movement that we've been in for the past 10 years.
Each of these movements "introduced" to modern-day believers an emphasis on what appeared to be a "new" doctrine. They were not new to God or to the Bible, just new to each generation. In time, each of the doctrines "introduced" at those particular times in history are still valid but we could also call them "old wineskins." Haven't you noticed that many of the churches and denominations that were so on fire and used by God in the various movements that took place in the 20th century have lost their fire? That can happen. We can loose our fire if we simply camp on truths that still apply but without moving on to the hidden treasures in Scripture that God is bringing to our attention now.
That's why it's important to get informed and find out what God is doing in the world today within the larger body of Christ, not just our favorite denomination or tradition. We need to find out what God is doing NOW so we can join Him. When we find out what He's doing, what truths He's showing us that have been in the Word all long, we'll find ourselves meeting that "new" truth every time we turn around because God, as a good parent, repeats Himself. We'll also find ourselves talking about it over and over and over until those we're responsible for "get it." And when we and they finally get it, we can move on to the next truth. We can camp anywhere along the way but if we do, we'll become an old wineskin. With or without us, the fire and cloud of God's covering protection and guidance moves on.
Oh Lord, may I never be an old wineskin!!!! Keep me teachable. Not vulnerable to deceit, but teachable and receptive as a new wineskin for the new wine You are even now pouring out!!!
Dr. Chuck Pierce wrote in a newsletter on August 28, 2007, "The Kingdom cannot be controlled by civil government. Through the ages, civil government has made the attempt to govern and rule God's government in the earth. However, the Kingdom is not based on worldly patterns. Another important fact that we must all recognize is that we cannot comprehend the Kingdom by our natural mind. The mind is at enmity with God and longs to be conformed to the world around it. However, as we renew our minds, we break out of worldly conformity and move into seeing Kingdom life in the midst of the societal structures that are molding us."
So where are we? The last three Movements I mentioned were the apostolic, prophetic and prayer movements. Actually, they are three parts of a whole. The Prayer Movement expanded so explosively that back in the '90s Dr. C. Peter Wagner announced that it was totally out of control. As the Prayer Movement grew and people moved from prayer into intercession, they quickly became prophetic intercessors and we had to study the gift and office of prophet. Thus the Prophetic Movement came into being as the church across the nation and around the world was able to recognize those whom God had placed in the Body as Prophets. Out of that came the understanding and recognition of Apostles and the apostolic. Now, in 2008, we're ready to meld these three Movements into one and move ahead. . As Chuck also wrote, "The exciting thing about the Kingdom is that it cannot be POSTPONED! The Kingdom is filled with power. Over these last two decades, we have seen Kingdom government for the next season of God in the earth realm. God has appointed Kingdom administrators for every age. We find those gifts listed in Ephesians 4:11-14." They are apostles, prophets, evangelists, pastors and teachers, for. . .
As this is happening we're hearing more and more about The Kingdom and "having a Kingdom Mentality. We're realizing that when Jesus announced the church in Matthew 16:17 when He talked to Peter about the Keys of the Kingdom, He did it in the context of the Kingdom. Jesus told Peter that he received the revelation of who He was from the Father. In the same way, the Father has to reveal the Kingdom to us – by revelation. As Chuck Pierce wrote in August 28, 2007, "He is bringing us into a place of dominion, occupation and ruling with Him in the spheres and places He has assigned us. . . The Kingdom is NOT based on needs, since "the poor will always be with us." Jesus gave us a responsibility to work with the poor, orphans, and widows, but on the other hand, He also showed us the necessity to lavishly worship Him as Mary did in John 10."
We're going to have to shift from our current church and local church mentality to a Kingdom mentality that includes the church but is not just the church. Remember, a kingdom is a domain – the domain, the rule and the sphere of a king. Our King rules over all. This includes the church but also business, education, government, family, the arts.
As the church is waking up and realizing this, acquiring a Kingdom Mentality, we're seeing dramatic shifts in how "church" is done. Prayer has been moving out of the church, into the streets and through the halls – literally of business, government and educational facilities. We've coined new terms to accommodate this move. Terms like prayerwalking and prayer journeys.
People in business are realizing that it was God Who called them into business and that they are doing more than working to earn money for the church; they are the church and they're to fulfill their call to minister as priests on the job. Consequently, business people have begun to "do the work of the ministry" instead of seeing a need, then calling the Pastor to come talk to so and so. In the process, they're learning how to minister to people just like them. As you know, the Full Gospel Businessmen's Fellowship was/is a tremendous vehicle for bringing businessmen to the Lord. However, a friend recently told me that in the city where he was living at the time, the church didn't know what to do with all those Type A personalities so it made it very hard for many of the newly-converted business people to fit into the typical church setting. Now, in the last 10 years, people are having "church" on the job, in the office chapel. A good friend of mine started having "church" on her lunch hour with other women outside the office building. Eventually, they were given a room inside. The Holy Spirit began to invade the operation of the business and the attitude of the people. As time went on, she was asked to help start the same type of church (nicely called a Bible Study) for another business in her city. Businesses are also, literally, hiring people to intercede for their companies and minister to their employees. One of the pastors who used to be an accountability partner with Vawtermark Ministries is now working for a corporation in this kind of a job. I have another friend who has been hired to literally go to work and pray for the company, its business deals and all the employees. Is this scriptural? Of course! That's what Anna did in the Temple and how she was supported. (Luke 2:36-38) That tradition is what Paul was referring to when he told Timothy to not put a woman on the payroll unless she was over 60 years old and met other conditions. (1 Timothy 5:9-16)
This is what a Kingdom mentality is all about – the dominion of God – everywhere! A local church mentality is all about us because we're the church. If we focus first on the church we have to focus on ourselves because we're the church! The church is dear to the Lord so it's OK to teach, preach and instruct in and through the church, but if you focus on the church, you'll focus on self. You can't focus on kingdom and focus on self because the Kingdom is bigger than the church and it's about the King.
We're going to have to preach the Gospel of the Kingdom not just salvation. We're not told to preach the gospel of the cross. We're told to preach the Gospel (good news) of the Kingdom of God. The Gospel of the cross is salvation, the entry into the Kingdom. The Good News goes beyond the cross. When we preach and teach the Kingdom, we get into the restoration of the dominion that we lost in Genesis. You see how much bigger Kingdom is? It's God's Kingdom functioning now on earth in a people – you and me!
When we think Kingdom rather than church, we go to another level of authority. As Dutch Sheets emphasized in a talk he gave in Denton January 2008, a local church-first emphasis can be selfish. It can be mine. I can build walls. I can emphasize what is best and what will benefit me at the expense of others. But we can't build walls around the Kingdom; it's too big. And we can't obtain the kingdom by ambition.
The cross is the entrance. The Kingdom is the realm.
The cross gives us life. The Kingdom gives us something to live for.
The cross is about redemption. The Kingdom is about restoration.
We move from saving souls and growing churches to producing disciples of the Kingdom.
January 3, 2008
Kingdom disciples have eternity in their hearts and weapons in their hands.
They are kingdom thinkers, difference makers and culture shapers.
Things that describe Kingdom people.
I would add one more mark of Kingdom people and that would be that Kingdom people work on reconciliation of the races and between genders. There are many divisions and ugly, separatist, prejudicial attitudes between people: There's prejudice between
I don't believe that all these divisions will be reconciled before the return of Jesus, but in the house of the Lord, they will be. After all, Revelation 7:9 says that the "Great Multitude" in heaven will be made up of ALL nations, tribes, peoples and tongues. People with a Kingdom mentality will work with all and be open to all kinds of people. The Kingdom is not segregated with rampant racism. When we become Kingdom minded and Kingdom centered, we will be that "one new man of Ephesians 2:15. We'll be one people, one body; one flock with one Shepherd Who unites us all in one flow of His forgiving, overcoming love. The local Kingdom-minded church will become a colony of heaven and a picture of God's eternal life on earth. "A Kingdom people understand Kingdom grace. The Kingdom is ruled by grace and love – not by rules, regulations and laws." (Chuck Pierce, August 28, 1007)
When we expand our thinking to a Kingdom world view, a Kingdom mentality, everything changes because we realize that we're here to extend the dominion of God in this place. It's a new twist to the 1970 expression, "Bloom where you're planted."
It's as Apostle Jim Hodges taught in Denton at the first of 2008, "A kingdomized church will open gates." He went on to explain that Joseph's pillow became a pillar when he had his dream about his future. And it changed his identity. That's because the gate of heaven is not in heaven. The access to the gate of heaven is on the earth. So God's called us to re-harmonize heaven and earth and in a very real sense, to cooperate with God so that His Kingdom in heaven will come on earth and we live, move and breathe the Lord's prayer: Thy Kingdom come on earth as it is in heaven.
With a Kingdom mindset, we move into an understanding of the realm of the Spirit in a completely higher realm than we did before. After all, we're part of a Kingdom that is not earth-bound so we've got to stop thinking that way. Kingdom disciples have eternity in their hearts so we've got to move into a realm of revelation that moves us far above anything we've known before. Kingdom people are supposed to be dangerous everywhere we go – so dangerous that we exemplify the enigma of the Kingdom of God being inside us, coming, having come, yet to come, and near to anyone around us. We become a participator in the shaking that God is doing on the earth. And from deep within we find ourselves crying Maranatha! Come Lord Jesus!
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To that unnatural brightness, add a live studio audience. The vast majority of workaday people have never addressed a large room full of strangers. Nothing can prepare most patients/guests of Dr. Phil's for walking onto that soundstage, where their intimate problems will be the subject of "entertainment" and "information," to crib from DrPhil.com's disclaimer.
On that stage, the patients/guests interact with a consummate performer, who's also what we call "a star." They've already invested him with tremendous authority or they wouldn't be there. They've relinquished their privacy in return for his help. Now, under the bright lights, in front of rows of peering strangers and with Dr. Phil himself, they must make their stand. By definition, they're troubled. Now they're also surrounded and outnumbered. Can healing possibly take place in such an arena? What could be further from the environment and process of therapy? Yet these people think they're going to a doctor.
Any TV program, by virtue of its repetition, partakes of ritual. Quiz show and sitcom, newscast and episodic drama, talk show and sports show, each establishes a format and rhythm, enhanced by repetitive theme music, which creates a particular signature. A prime pleasure of television viewing is to sync in with the ritualistic repetitions of each favored program, surrendering to the (usually narrow) spectrum of responses that the program dependably, predictably elicits. A successful program achieves its own defined space, which it repeats and repeats and repeats. Each program is, in an archetypal sense, a kind of Mass, with its own particular and peculiar Communion. You know what's going to happen before you get there, though you don't exactly know--and this knowing-but-not-quite-knowing sustains both the comfort level and the interest.
Dr. Phil's TV show works this form masterfully.
To appear on the show, you send Dr. Phil a home video in which you reveal your troubles. If he and/or his staff chooses your video, they interview you on film, and sometimes place cameras in your home to watch your troubles firsthand and collect clips to be aired on the program. If they decide you're telegenic enough, you're invited on the show, where your average screen time with Dr. Phil is eight minutes (though subjects that are especially telegenic get more).