Total System Energy Minimization for Wireless Image Transmission.
In this paper, we focus on the total-system-energy minimization of a wireless image transmission system including both digital and analog components. Traditionally, digital power consumption has been ignored in system design, since transmit power has been the most significant component. However, as we move to an era of pico-cell environments and as more complex signal processing algorithms are being used at higher data rates, the digital power consumption of these systems becomes an issue. We present an energy-optimized image transmission system for indoor wireless applications which exploits the variabilities in the image data and the wireless multipath channel by employing dynamic algorithm transformations and joint source-channel coding. The variability in the image data is characterized by the rate-distortion curve, and the variability in the channel characteristics is characterized by the path-loss and impulse response of the channel. The system hardware configuration space is characterized by the error-correction capability of the channel encoder/decoder, number of powered-up fingers in the RAKE receiver, and transmit power of the power amplifier. An optimization algorithm is utilized to obtain energy-optimal configurations subject to end-to-end performance constraints. The proposed design is tested over QCIF images, IMT-2000 channels and 0.18m, 2.5 V CMOS technology parameters. Simulation results over various images, various distances, two different channels, and two different rates show that the average energy savings in utilizing a total-system-energy minimization over a fixed system (designed for the worst image, the worst channel and the maximum distance) are 53.6% and 67.3%, respectively, for short-range (under 20 m) and long-range (over 20 m) systems.
Introduction
There is widespread use of portable wireless technology in the form of cellular phones, wireless
networks, wireless surveillance systems and other wireless devices. In order to avoid frequent
recharging and possible down-time, the power consumption of these systems must be minimized.
Currently, most low-power wireless systems are designed by minimizing the transmit power, since
it is usually the most significant component of the total system power consumption. In addition
to hardware design techniques, powerful channel-coding algorithms provide coding gain and significantly
reduce transmit power. Complex source coding algorithms provide the reduction in data
rates necessary for e#cient use of bandwidth. Traditionally, the power consumption due to these
complex signal processing algorithms has been considered negligible. However, as we move towards
an era of micro-cells and pico-cells, the power consumption of the baseband processing unit becomes
comparable to that of the power amplifier. E#orts such as Bluetooth [1] for short-range radio links
in portable devices such as mobile PCs and mobile phones, as well as the HomeRF [2] open industry
specification for RF digital communications in the home, are some examples of steps toward
pico-cell communications. Therefore, techniques which jointly minimize the power consumption in
the power amplifier and the baseband processing unit are desirable.
Increasing the complexity of the channel coding algorithm to increase coding gain and lower
power increases the baseband processing power. Similarly, at short distances, using a less
complex source coder which keeps some redundancy in the encoded stream may allow us to use
a less complex channel coder, thereby providing more energy for the power amplifier. In [3], Lan
and Tewfik found that, for low transmission power, a less e#cient source coder, which consumes
less power and achieves less compression, combined with a channel coder that adds very little
redundancy, is energy-optimal. Therefore, the task of minimizing the baseband processing power
and minimizing the power amplifier power are inseparable.
The joint minimization of the total system power is subject to the system resource constraint
of bandwidth and the performance constraint of end-to-end image quality. For source image data
requiring a high rate to achieve a desired image quality, the channel coder can only introduce a
small amount of redundancy due to the bandwidth constraint, and more power may be drawn by
the power amplifier. There are operating conditions for which coding gain is more important than
transmit power, and other operating conditions for which leaving the redundancy in the source
consumes less power than adding redundancy in the channel coder. An adaptive technique which
chooses the optimal system configuration based on the input and channel condition is necessary to
achieve maximum performance in all regimes.
In this work, we focus on the design of a reconfigurable wireless image transmission system that
achieves low power by exploiting both the variabilities in the image data and the multipath wireless
channel. Reconfigurable digital signal processing (RDSP) [4] has been proposed as a low-power
technique that exploits variabilities in the environment. Energy savings are achieved by tailoring
the architecture to the environment. In [5]- [6], dynamic algorithm transforms (DAT) were proposed
as a systematic framework for designing low-power reconfigurable signal processing systems. DAT
requires the definition of: (1) input state-space, (2) configuration-space, (3) energy models and (4)
DSP algorithm performance models. The input state-space models the input variabilities, and the
configuration-space is the set of possible hardware configurations. Energy models and performance
models are employed to obtain estimates of the energy consumption and a performance metric
(such as distortion or bit-error rate).
In order to exploit the relationship between the configuration space, the input space and the
DSP algorithm performance metric, we employ recent advances in joint source-channel coding
past work on joint source-channel coding has shown that the
tradeo# between data and redundancy can be exploited to design optimal realizable systems [8],
[9], [10]. The application of joint source-channel coding in heterogeneous, multi-media environments
leads to general matching techniques, which have been the focus of some current research [7], [11],
[12]. In [7], we developed a general matching technique which can be applied to a wide variety of
source coders and channel coders. These methods maximize the end-to-end quality of a transmitted
image subject to constraints on the transmit power and bandwidth. In this work, we combine these
methods with techniques for RDSP to jointly optimize the baseband processing power and the
transmit power of a reconfigurable system.
The proposed system can be motivated as follows. In Figure 1(a), we have plotted the rate-distortion
curves for di#erent images encoded via a set partitioning in hierarchical trees (SPIHT) [13]
encoder, which is a state-of-the-art compression scheme. It can be seen that the encoder needs to
operate at di#erent rates to obtain a specified distortion (in terms of peak signal-to-noise-ratio
PSNR) of 35dB. Similarly, channel variabilities are characterized by di#erent values of E b /N 0
(where E b is the energy per bit and N 0 is the noise power spectral density) in Figure 1(b). Each
curve in Figure 1(b) corresponds to a di#erent number of correctable errors, t, for a Reed-Solomon
code. It can be seen that the channel encoder needs to operate at a di#erent t (for di#erent
to meet a specified bit-error rate (BER) constraint of 10 -3 . Thus, if the image changes from
"coastguard" to "carphone" and the channel E b /N 0 changes from 5dB to 7dB, then to keep the
PSNR the same, one must adjust the source rate, the number of correctable errors, the transmit
power, and the number of RAKE fingers (in case of multipath channels). There are numerous
choices for these parameters that can meet the end-to-end distortion constraint. The optimal
parameters which minimize the total power consumption are obtained via joint source-channel
coding techniques and dynamic algorithm transforms developed in this paper.
In this paper, we develop a technique for optimizing power consumption in flexible systems with
performance constraints and time-varying inputs. We apply our energy minimization technique to
image transmission over an indoor wireless link to demonstrate the power savings due to our
approach. The optimization problem is formulated in terms of the system parameters and includes
the reconfigurable blocks. For the image transmission example, the source codec, channel codec,
RAKE receiver and power amplifier are the potentially reconfigurable blocks. Energy consumption
is minimized by solving an optimization problem which has energy per pixel as the objective
function and constraints on the desired distortion and maximum available bandwidth. The proposed
reconfigurable system is tested via the evaluation methodology in [14].
The rest of the paper is organized as follows. In the next section, we present an overview of
the system. In section 3, we present the optimization for determining the optimal configuration
parameters. In section 4, we present the key ingredients such as energy and performance models.
The simulation setup and results are presented in section 5.
We consider the indoor wireless communication system shown in Figure 2 in which two terminals
communicate with each other. Using DAT and JSCC methods, we formulate the problem of
e#cient image transmission subject to an end-to-end performance requirement. We define (a) an
input state space S, (b) a configuration space C, (c) models for the DSP algorithms in order to
estimate distortion D, and (d) energy models for estimating energy consumption E .
We also make a few assumptions regarding the problem which make our technique more relevant.
We consider a system operating (1) over short distances of less than 100m between the terminals (so
that the processing power is comparable to the transmit power), (2) in slow/block fading channels
(so that the channel impulse response remains constant for the duration of an image), and (3) with a
low bit-rate feedback channel which correctly updates the channel condition and image variabilities
for each image.
In this section, we present S, C, and the energy optimization problem for a wireless image
transmission system. In section 4.2, models are presented for end-to-end system performance, and
energy models are presented for various system components.
2.1 Input State Space
The input state space S is a collection of all input states or scenarios of interest for which reconfiguration
is desired. The size of S depends upon the input variabilities and the granularity of the
reconfigurable hardware. For the problem of wireless image transmission, the inputs which can
a#ect the power consumption or the system performance are the channel response, and the image
variability.
Based on our general approach to optimization of image transmission systems with rate and
energy constraints in [7], we characterize the image variability in terms of the operational rate-distortion
(R-D) curve (see Figure 1(a)). The R-D curve determines the (zero-error) bit-rate necessary
to achieve a particular mean-squared error distortion. Characterizing the image variability in
terms of the source R-D curve enables us to use a general JSCC formulation of the tradeo# between
data and redundancy.
The state vector s for the wireless image transmission system is:
The h i s are the complex gains in the multipath channel impulse response,
is the delay corresponding to the i th path. In addition to multipath, there is typically also
multiuser interference which can be exploited by employing a reconfigurable multiuser receiver. In
Source Rate (bits per pixel)
Average
Distortion
per
pixel
Akiyo Carphone
Coastguard
Bit
Rate
(a) (b)

Figure

1: (a) Source variabilities (rate-distortion curves) and (b) channel variabilities (bit-error-rate
curves).
Images out
Images in
Images out
Images in
Indoor wireless
multipath channel
Feedback
Configurations

Figure

2: Indoor wireless image transmission system.
this paper, for the sake of simplicity, we exploit only the variabilities due to source and multipath
channels and consider the worst-case multiuser interference.
2.2 Configuration Space
We must define the set of possible adaptations of the system to the variable input. The configuration
space C is the set of hardware configurations for the terminal. The definition of configuration vector
and size of C depends on the DSP algorithms used in the system and the flexibility of the hardware
platform. The maximum benefit of the system optimization approach depends on the size of C.
For the image transmission problem, we consider the reconfigurable system shown in Figure 3.
In this block diagram, the blocks within dotted lines in Figure 3(a) are reconfigurable and the others
are fixed/hardwired. The analog and RF blocks (not shown) would include a CDMA modulator,
an RF modulator and demodulator, square-root raised cosine filters, an analog-to-digital converter,
a digital-to-analog converter and a low-noise amplifier. These blocks are not reconfigurable and are
assumed to have fixed energy consumption. The energy consumption due to these blocks is not
included in the calculations.
The source codec is implemented on a programmable processor and is assumed to have a fixed
energy consumption. All other digital blocks except the source codec are assumed to have an ASIC
implementation in 0.18-m, 2.5V standard-cell CMOS technology.
For the source codec we use the well-known SPIHT coder [13] which has good performance on
natural images. For transform-based source coders such as SPIHT, most of the energy consumption
is due to the frequency transform or subband decomposition, and energy consumption due to
quantization is small. Since the wavelet transform component of the SPIHT coder is fixed, fixed
energy consumption is a good assumption.
For the channel codec, we employ Reed-Solomon block codes to provide error correction for
bursty error channels. In section 4.1, we describe a reconfigurable architecture for the codec in
which the energy consumption is proportional to the redundancy added by the codec.
The power limitations of the terminal depend on whether it is a mobile or a base station. A
mobile utilizes battery power which has limited life, whereas a base has access to a stationary power
source with unlimited life. We assume that both mobiles and bases have a fixed maximum transmit
power. The configuration vectors for the mobile (m) and the base-station (b), respectively, are
defined as follows:
R s is the source rate (in bits per pixel), t enc is the maximum number of correctable symbol
symbols per block at the channel encoder, P t is the transmit power (or output power delivered
by the power amplifier), and c rake is the configuration vector for the RAKE receiver (c
implies that i th finger is powered down). The transmit parameters of the mobile are R s , t enc , and
. The receive parameters of the mobile are the number of protection symbols per block at the
channel decoder t dec , and c rake . The parameter c rake depends on the transmit power of the other
device and the channel condition, and t dec is same as t enc of the other device (either the base-station
or the other mobile). Further, M and B are the configuration-spaces (defined as set of all possible
configuration vectors) for the mobile and base-station, respectively.

Figure

3(b) shows the block diagram of the controller. The controller adapts the system to
the changes in the input by reconfiguring or changing the parameters of the various blocks. The
first block in the controller quantizes the input variabilities as determined by the source coder and
channel decoder. The energy-optimum configuration vectors are either obtained by an optimization
algorithm running in real-time or from a precalculated look-up table.
2.3 Energy Optimization Problem
We develop the energy optimization problem by expressing the total energy consumption and
end-to-end performance of the system in terms of the system configuration and the given input.
We first describe the general optimization problem for terminal to terminal communication, then
follow up with simplifications for di#erent scenarios. The most general problem is two-way mobile-
to-mobile communication, since the configuration vector for the base is a special case of the mobile
configuration vector where the transmit power and number of RAKE fingers are free variables.
2.3.1 General optimization scenario : mobile-to-mobile scenario
Consider two-way mobile-to-mobile communication. The state vectors for the system, s m1 and
s m2 , describe: (1) the rate-distortion points of the image transmitted by mobile 1 , and the channel
response from mobile 1 to mobile 2 , and (2) the rate-distortion points of the image transmitted
by mobile 2 , and the channel response from mobile 2 to mobile 1 , respectively. We determine the
configuration vectors, m1 opt (s m1 ) and m2 opt (s m2 ), which minimize the energy consumption per
pixel at each mobile while satisfying constraints on (1) distortion Dm1 per pixel for the image
transmitted by mobile 1 (distortion is defined as mean-squared error between the original image at
the transmitter input and the reconstructed image at the receiver output) and distortion Dm2 per
pixel for the image transmitted by mobile 2 , and (2) total rate Rm1,tot and Rm2,tot (total rate is
defined as the sum of source and channel bits per pixel) at mobile 1 and at mobile 2 , respectively.
Therefore, the energy optimization problem can be written as
Rm1,tot (m1) # R o1 ,
Rm2,tot (m2) # R o2 , (5)
where E(m1,m2) is the sum of the energy consumption at each mobile
The energy consumption at mobile 1 is given by
fixed are the energy consumption of the RS encoder, RS
decoder, RAKE receiver, power amplifier, and fixed components respectively. The RS encoder
power consumed in the mobile is for encoding the data to be transmitted. The RS decoder power
consumed at mobile 1 is for decoding the received data from mobile 2 . At present, we do not include
fixed due to the source encoder and the other hardwired blocks in the optimization problem.
Any flexibility in these fixed system components would increase the benefits of an optimization
approach. The optimization problem in (5) represents the core of DAT where energy is minimized
subject to a system-level performance constraint. The constraints themselves are satisfied via joint
source-channel coding algorithms.
Assuming that the two users are exchanging independent information, the energy optimization
above can be partitioned into two one-way communication problems, one for each direction. For
the image transmitted from mobile 1 to mobile 2 ,
Rm1,tot (m1) # R o1 . (7)
Mobile 1 receives channel information from mobile 2 and uses it to compute R s , t m1
enc
its own
configuration as well as c rake for mobile 2 . Mobile 2 combines the c rake information transmitted
by mobile 1 with R s , t m2
to obtain its configuration vector. An optimization algorithm for
determining the configuration vectors m1 opt and m2 opt is described in the next section.
A performance criterion which may be more desirable to the end user is the probability of
delivering a particular quality of service. The user may desire that the distortion is above some
level D which is close to zero. The optimization problem then becomes
Rm1,tot (m1) # R o1 ,
Rm2,tot (m2) # R o2 , (8)
This problem separates into an optimization problem for the image transmitted by mobile 1 and an
optimization problem for the image transmitted by mobile 2 , where P (D > D o ) is the probability
that the rate corresponding to the desired maximum distortion D o is successfully decoded. Joint
source-channel coding does not play a significant role in this situation because the source coder
must operate at a specified rate R s (as determined by the rate-distortion points) and the channel
codec is energy-optimized. In this scenario, it is possible that for large values of P the
bandwidth is under-utilized.
2.3.2 Special Case: Mobile-to-Base-Station Scenario
Consider two-way communication between a mobile and a base station. The optimization problem
for the system is just a special case of (5) in which one of the mobiles, say mobile 2 , is a base-
station. As in the mobile-to-mobile scenario, the system optimization divides into two problems,
one for the base station, and one for the mobile. Because the power consumption at the base
station is not considered an issue here, these problems are special cases of the problem in (7)
with
enc ), and E rake (c rake ) at the base station all set to zero. Otherwise, the
optimization problem and the algorithm with solution remain the same as in the general case. So,
for the image transmitted from the mobile over the uplink channel,
R m,tot (m) # R
2.3.3 Optimization Example
To illustrate the necessity of the optimization and to clarify our methodology, we provide the simple
example of one-way mobile-to-mobile communication with a configuration space of three choices.

Figure

4 shows the total energy consumed at distances of 10m and
50m for images "carphone" and "coastguard" by the three di#erent configurations
3 with the parameters listed in Table 1. Note that R s is not listed, since it is related to t enc by
the rate constraint R tot # R
Configuration

Table

1: Configuration space parameters.
Configuration supports a PSNR= 35dB for both images at 10m, but not at 50m. Configuration
supports "coastguard" at 50m and 10m, but does not support "carphone" at either
distance because the rate R tot is too small. Configuration m 3 supports both images at both dis-
tances, but is not energy-e#cient for short distances. Because of image variability and channel
variability, reconfiguration is required for energy e#ciency. Optimal configuration parameters can
be determined either by brute-force search or with an optimization algorithm. When the sizes of
the configuration space and the input state space are small, a brute-force search is feasible; oth-
erwise, an optimization algorithm is required. In this paper, the configuration space has a size of
ENCODER
t dec
components
components
CHANNEL
(RS)
(RS)
CHANNEL
DECODER
DECODER
IN
IMAGES
IMAGES
OUT
ENCODER
RECEIVER
ANTENNA
U
R
POWER
AMPLIFIER
(a)
s
from channel
from source
codec
codec
OPTIMIZATION ALGORITHM
configuration
energy-optimum
(b)

Figure

3: A reconfigurable multimedia system: (a) the transceiver and (b) the controller.
Total Energy (Joules)
PSNR
carphone 10m
coastguard 10m
carphone 50m
coastguard 50m

Figure

4: Performance of three configurations defined in Table 1.
corresponding to the variation in protection symbols - variation
in P t - the variation in c rake and the state space has a size of 9 504 - corresponding to
the number of rate-distortion points - the length of the channel response.
3 Optimization Algorithm
All the energy optimization problems described are solved by a feasible directions algorithm [15].
At each step of the algorithm, the gradient #E of the objective function E(t m
respect to t m
enc and P t and a feasible direction chosen so that the objective
function decreases (i.e #Ed # 0). The update at each step is
dt
The derivatives in (11) are computed numerically as dE
dt
E(t,P t +P t,min )-E(t,P t )
, where P t,min is the minimum transmit power. The parameters # > 0, and
determine the stepsize and the angle between the direction and the gradient, respectively.
For the image transmission system studied here, we chose to be a unit
step.
Taking a step in the feasible direction does not guarantee that the distortion constraint is met.
Assuming that we start at an initial state [t m
which satisfies the constraint, at each update,
the distortion is measured and compared to the constraint. If the distortion constraint is not met,
then the update is not taken and the stepsize # is decreased towards zero until the distortion
constraint is met. For the image transmission system studied here, we chose the modification
reset the parameter to for each new gradient computation. Many
variations of this simple feasible directions algorithm are possible.
To determine the optimal c rake , we apply the optimization algorithm for each of the possible
values and choose the best one. To apply the optimization algorithm to the P (fail) case, the
distortion constraint is replaced with the probability constraint
(R < RDo
where R is the number of consecutive bits decoded correctly, and RDo is the rate corresponding to
distortion D determined by the rate-distortion points.
The energy and performance models employed in the estimation of E(m,b), E(m1,m2), D(m, s m ),
and D(b, s b ) are described next.
4 Energy and Performance Models
In this section, we present relationships of the energy consumption and distortion to the configuration
signals. The high-level estimates of the energy consumption are obtained via energy models
for the power-hungry blocks in the RS codec, RAKE receiver, and power amplifier. These models
are obtained via real-delay simulations [16] of the hardware blocks employing 0.18-m, 2.5V
CMOS standard cells obtained from [17]. Similarly, performance models of the source coder and
the channel coder are employed to estimate the average distortion per pixel for the various states
and configurations.
4.1 Energy Models
Energy models are employed to relate the configuration vector to a high-level estimate of the energy
consumption of the algorithm. It is well known that the energy consumption of the digital circuits
is dependent upon the input signal statistics. However, in the case of Galois field multipliers and
adders, it is found that the energy consumption varies by less than 5%, when the correlation of
the input bit-stream is varied from 0.0 to 0.9. This is because when the correlated bit-stream
is converted to Galois field symbols, the correlations among successive bits are lost, thus making
Galois field symbols uncorrelated. Therefore, in the following, we present energy models which are
independent of the input signal statistics, but are functions of input precisions. The energy models
for the RS codec, the RAKE receiver, and the power amplifier are presented next.
1. RS Encoder/Decoder
The complete block diagram of the Galois field components and the RS encoder and decoder are
derived in the Appendix and can also be found in [18]. We summarize the results here to maintain
the flow of the discussion. The energy models for adder, multiplier and inverse blocks over Galois
field are derived by simulating these blocks via a real-delay gate-level simulator MED [16]
and are given by
where m is the number of bits per symbol. These models are employed to obtain an estimate of
the energy consumption of the RS encoder and decoder in di#erent configurations. The energy
consumption of a bit-parallel RS encoder architecture is given by
Energy consumption of the RS decoder is due to the syndrome computation (SC) block,
Berlekamp-Massey (BM) block and Chien-Forney (CF) block and is given by
The energy consumption of the RS codec is obtained as a sum of E rsenc and E rsdec in (16) and
(17) as follows:
2. RAKE Receiver
Energy consumption of the RAKE receiver in Figure 5(a) is dependent upon the powered-up
fingers (i.e., taps for which c rake,i = 1). Figure 5(b) shows the architecture of a finger in a RAKE
receiver. The received signal r[n] is correlated with the delayed spreading sequences s
and then multiplied by a complex gain h # i . The outputs from all the fingers are added together and
passed to the slicer to obtain the bits. If L is the number of fingers, then the energy consumption
of the RAKE receiver is given by
is the energy consumed by the i th finger of the RAKE receiver. The adder and
multiplier energy models [5] are obtained via real-delay gate-level simulations of the blocks designed
for 0.18-m, 2.5V CMOS technology from [17].
3. Power Amplifier
Energy consumption of the power amplifier is characterized by its power-aided-e#ciency (PAE)
# (defined as the ratio of the output power P t to the power drawn from the supply). Power
amplifiers are typically designed to maximize # at the maximum output power P t,max , with # being
a decreasing function of P t . The functional relationship between # and P t (also called a power-
aided-e#ciency curve) is usually provided in vendor data-books. For the digitally-programmable
power amplifier in [19], the e#ciency #(P t ) of this power amplifier can be approximated as follows:
where # max is the maximum e#ciency, and P t,max is the maximum transmit power. If f bit is the
bit-rate, then the power amplifier energy consumption per bit E pa is given by
4.2 Rate Models
Performance models are employed to relate the configuration vector to the performance metrics such
as distortion, bit error rate (BER) or signal-to-noise ratio (SNR). In the following, we present
performance models for the source coder, channel coder, RAKE receiver and power amplifier.
1. Source Coder
The performance metric for the image transmission system is the end-to-end average distortion
per pixel. The SPIHT source coder produces a progressive bitstream which improves the quality of
the decoded image as more bits are received correctly. When a bit error occurs in the transmission,
all future bits are lost due to an embedded property of the bitstream. So, the end-to-end average
distortion per pixel can be computed [7] as follows:
where M is the number of codewords transmitted per image, D(i) is the distortion value if only
the first i codewords are correctly received, p(i) is the probability of receiving the first i codewords
correctly and the (i +1) th codeword in error, and D(M) is the residual distortion because of a finite
source rate R s . The D(i) values are obtained from the image-specific operational rate-distortion
curve of the SPIHT coder. The p(i) values are obtained from the error probability of the channel
code. For block-error codes, the probability of receiving i consecutive blocks correctly is given by:
where p e,c is the probability of error for the channel code.
2. Source Estimation: Operational Rate-Distortion
The variability in the input data is captured by operational rate-distortion points. There are
several ways of estimating these rate-distortion points. The straight-forward approach is to apply
the source encoder and decoder at various rates, calculate the distortion between the original and
decoded images, and interpolate between these (r, d) points. In [20], Lin et al. use a cubic spline
interpolation to get smooth rate-distortion curves for gradient-based optimization algorithms. Since
multiple (r, d) points must be measured by encoding and decoding at these rates, the processing
power required for the computation is significant.
We consider some simplifications and special cases. For transform-based source coders such as
SPIHT and JPEG, the error in the encoded image is primarily due to quantization, especially at
high rates. The transform-domain quantization error energy at various rates provides an estimate
of the operational rate-distortion points. In the SPIHT coder, wavelet transform coe#cients are
encoded hierarchically according to bit-planes, starting from the most significant bit-plane. The
compressed bitstream has the embedded property of containing all the lower rates. Due to the
embedded nature of this compressed bitstream, shortening the compressed bitstream is the same
as compressing to the lower rate. In terms of estimating the (r, d) points, this implies that the
encoder need only be run at the maximum rate.
We can compute the error energy at the encoder progressively from lower rates to higher rates
as follows. Let {c 0
D } be the set of original wavelet coe#cients, where D is the number of
pixels in the image. Let n be the number of bits to encode the largest coe#cient. At zero source
rate, the distortion energy
is the total energy in the wavelet coe#cients. When
the most significant bit-plane is encoded, the new distortion energy
where the
coe#cients are
The indicator function I(c) just determines whether the particular coe#cient c has a 1 in the
most-significant bit-plane. By expanding and collecting terms, we can write
is the number of coe#cients with a 1 in the most-significant bit-plane.
For the coe#cients not being updated, so the summation is over relatively few values.
The summation can easily be computed by shifting the coe#cients being updated, masking o# the
error, and accumulating (M does not have to be computed explicitly). For the next most significant
bit-plane, we update E 1 based on the number of coe#cients with 1 at this bit-plane and so on.
The introduction of this calculation does not require any additional memory, since only the original
coe#cient values need to be accessible. To convert error energy to distortion, we simply divide by
the number of total image pixels. The rate at which a particular distortion occurs is known as a
consequence of the encoding (length of the output bu#er). We also point out the update above can
occur at finer steps than at each bit-plane. So, the complete rate-distortion curve can be found
using this technique in real-time to progressively update the error energy as more significant bits
are encoded.
3. Channel Coder
The performance metric for the channel coder is the probability of error p e,c . For a Reed-Solomon
code with codeword length of 2 m
correction capability of t symbols,
we have [21]
where p e,s is the symbol error probability and is computed as:
where p e,b is the uncoded bit error probability computed as (for AWGN channels and binary phase
shift signaling scheme) [22]
where SNR o is the signal-to-noise ratio at the output of the RAKE receiver, and Q[x] is the
probability that a standard Gaussian random variable has value greater than x.
4. Power Amplifier and RAKE Receiver
The performance for the power amplifier and RAKE receiver is defined by SNR o and is computed
as:
c rake,i |h i | 2 , (30)
are the transmit power and noise power, respectively, PL(d) is the propagation
loss for distance d between the transmitter and receiver, L is the number of fingers in the RAKE
receiver, c rake,i is the configuration signal for i th RAKE finger, and h i is the channel coe#cient for
the i th path.
5 Application to Indoor O#ce Channels
In this section, we simulate the proposed reconfigurable multimedia system in an indoor o#ce
environment. Our goals are to determine the improvement obtained in a realistic setting using
our total system optimization. We compare with both conventional worst-case fixed design and
a system employing power control. We find that significant power reduction is possible in the
short range. These results are understood better by studying more detailed behavior such as
comparing the power amplifier power consumption with the power consumption of the digital
blocks, power consumption of the individual blocks, and the variability of the optimal parameters
over the images and over distance. Section 5.1 presents the simulation setup and simulation results
follow in section 5.2.
5.1 Simulation Setup
The proposed receiver is simulated for an indoor o#ce environment. The propagation models
for indoor o#ce channels are obtained from the IMT-2000 evaluation methodology [14]. In these
models, the propagation e#ects are divided into two distinct types: (1) mean path loss and (2)
variation in the signal due to multipath e#ects. The mean path loss PL for the indoor o#ce
environment is modeled as follows:
where d is the transmitter and receiver separation (in meters) and q is number of floors in the path.
This represents a worst-case model from an interference point of view. We assume that distance d
can vary from 2m to 100m.
The multipath e#ect is modeled via a channel impulse response which is characterized by a
delay-line model given in (2). The mean values of the relative delays
are specified in Table 2 [14]. Channel models A and B are the low delay spread and median
delay spread cases, respectively. Each of these two channels can occur in an actual scenario with
probability of
Path Channel A Channel B
Relative delay (ns) Average power (dB) Relative delay (ns) Average power (dB)

Table

2: Indoor o#ce multipath channels [14].
We assume that we are transmitting a database of images with 176 - 144 pixels per frame in
quarter common intermediate format (QCIF) obtained from [23].
It was found that a PSNR of 35dB provided a desirable level of visual quality and a total rate
R o of 3 bits per pixel (bpp) is su#cient to obtain this PSNR. Some other system parameters are
given in Table 3.
Rates Bit rate 760.32 kbits/sec (binary phase shift keying)
Chip rate 12.16 Mchips/sec (length spreading sequences)
Power Maximum e#ciency Low Power: P
Amplifier
RAKE receiver and 0.18-, 2.5V
Channel Codec CMOS Technology
Low-noise amplifier Noise figure=5 dB, B.W.=12.16 MHz
Constraints D (in terms of PSNR)
bits per pixel (bpp)

Table

3: System parameters.
5.2 Simulation Results
The real novelty/impact of the work is shown by the di#erence in power consumption between
optimized and fixed systems. The energy savings are obtained by reconfiguring the system to
take advantage of image and channel variabilities. The contribution of the input variability to the
reconfiguration is shown in the variation of the parameters in the configuration vector.
The proposed mobile-to-mobile image transmission system is tested for distances from 2m to
100m, multipath channels A and B described in the previous subsection, QCIF images "akiyo",
"carphone", "claire", "coastguard", "container", "hall objects", "mother and daughter" and
"silent", total rate R o of 3 bpp, and PSNR of 35dB.
To show the overall impact of the optimization approach, we compare the optimized system
to two fixed systems for the end-to-end distortion criterion and the P (fail) criterion. Then, the
contribution of each component of the system is analyzed in detail to show the origin of the power-consumption
savings.
1. Comparison with Fixed Systems

Figure

6 shows a comparison between the long-range optimized system and the long-range
transmit-power-controlled system (averaged over both channels, all the images, and both PSNR
constraints) where both systems employ the high-power amplifier designed for long distances. A
significant point is that the fixed system is not a worst-case comparison. The fixed system utilizes
the feedback channel to account for the variation of transmit power over distance but does not
account for the variation in the digital block parameters (as in the optimized system). The average
total power savings of 15.6% between the two systems arises due to reconfiguration of the source
rate, RS coder, and RAKE fingers.
The power amplifier at the transmitter is a significant component of the power consumption in
the image transmission system. The e#ciency of the power amplifier ranges from 2.2% at the lowest
transmit power to its highest e#ciency of # 50% at the maximum transmit power, P t,max .
When operating the system over distances from 2m to 100m, the significant variation in transmit
power from 10-W to 5mW lowers the e#ciency of the entire system. A plausible alternative is to
use a low-power amplifier for short distances and a high-power amplifier for longer distances.

Figure

7 shows a comparison between the short-range optimized system and the short-range
transmit-power-controlled system. The average total power savings due to optimization is 49.4%.
Comparing Figure 7 with Figure 6, we see that the low-power transmission system consumes less
than one-third of the total energy consumed in the original system designed for longer distances.
For this particular system, the choice of the power amplifier plays the most significant role in the
e#ciency of the transmission system.
Now, we compare the optimized system to a worst-case system which does not employ power
FINGER L
re(h
im(h
re(s
im(s
im(s
im(r[n])
re(r[n])
re(s
(a) (b)

Figure

5: The RAKE receiver: (a) block diagram and (b) architecture of a finger.
Distance (meters)
Total
Energy
(Joules)
Optimized System
Fixed System

Figure

Comparison between transmit-power-controlled system and optimized system over long
range.
Distance (meters)
Total
Energy
(Joules)
Optimized System
Fixed System

Figure

7: Comparison between transmit-power-controlled system and optimized system over short
range.
control. Figure 8 shows a comparison of the PSNR (averaged over both channels and all the images)
in the optimized system designed for 30dB and 35dB and a fixed system designed for the worst-case
image, maximum distance, and worst-case channel. The fixed system has constant performance
of at least 0.7dB above the optimized system, which achieves the PSNR constraint nearly with
equality. Although the fixed system performs slightly better than the optimized system in terms
of PSNR, it consumes three times more energy.
2. Fraction of total energy consumed in each component
The fraction of energy consumption in each component of the transmission system is shown
in

Figure

9. At short distances, the RAKE receiver and transmit power are the most significant
since the BERs at this distance are relatively low so as to not require additional channel coding.
At a distance of 20m, the fraction of digital energy reaches a peak of 29%, where the RS coder is
able to lower BERs by introducing channel coding. At distances over 20m, the fraction of digital
energy decreases since more transmit energy is required to compensate for path loss. More complex
channel coding techniques such as convolutional coding for the inner system may be used to increase
the range of distances over which digital power consumption is significant and hence benefit from
the techniques presented here.
3. Variation of t and P t

Figures

show the variation of the optimal parameters for the reconfigured system
over distance and over the various images. The significant variation of the t and P t parameters at
large distances shows the necessity of an optimization algorithm for those parameters. The optimal
number of RAKE fingers is found to be either 1 for short distances or 2 for long distances. The
number of RAKE fingers makes a significant impact on the total power consumption since the
RAKE consumes significant power. In addition, the variation of the number of RAKE fingers also
a#ects the Energy/bit and consequently the other parameters.
4. P (fail)-Optimized Systems
The energy consumption due to the various blocks is shown in Figure 12 for the constraints
averaged over all the images for R Channel A. The energy consumption of the RAKE
receiver is the same for all the four constraints and constant over the short distances (less than
15m) and long distances (over 15m). For the PSNR= 35dB constraint, the energy consumption in
Distance (meters)
PSNR
fixed system
optimized system
fixed system
optimized system

Figure

8: Comparison between fixed system and optimized system performance.
1000.10.30.50.70.9Distance (meters)
Fraction
of
Energy
Consumption
in
Various
Blocks

Figure

9: Fraction of energy consumed in each component.
Distance (meters)
Protection
Akiyo
Carphone
Claire
Coastguard
Container
Hall objects
Mother and daughter
Silent
1000.20.611.41.8Distance (meters)
Number
of
fingers,
|c
rake
|
Akiyo
Carphone
Claire
Coastguard
Container
Hall objects
Mother and daughter
Silent
(a) (b)

Figure

10: Optimized system parameters: (a) protection symbols and (b) RAKE fingers.
Distance (meters)
Transmit
Power,
Pt
Akiyo
Carphone
Claire
Coastguard
Container
Hall objects
Mother and daughter
Silent

Figure

11: Transmit power consumed in the optimized system.
Distance (meters)
Energy
consumption
in
various
blocks

Figure

12: Energy consumed in each component.
the RS codec is smaller than for the PSNR= 30dB constraint at distances over 45m. The higher
source rate required to achieve the larger PSNR lowers the channel coding rate. At both PSNRs,
the energy consumption of the system achieving the lower P probability is only slightly
larger than the system achieving P due to the threshold characteristic of the RS coder.
The BER of the RS coder as a function of the SNR has a fast transition from
with only a small change in the SNR.
6 Conclusion
Total-system-energy minimization of a wireless image transmission system is achieved by dynamically
reconfiguring the architecture to exploit the variabilities in the image data and the multipath
wireless channel. The optimal configuration parameters for the reconfigurable system are chosen to
performance constraints by trading o# the energy consumption of the digital blocks and the
power amplifier. Application of the optimization techniques to the indoor o#ce environment shows
that the fraction of digital energy consumption to the total energy consumption in the optimized
system can range from 29% at a distance of 20m to 14% at 100m. The reduction in total energy
consumption in the optimized system averaged (equiprobably) over channels A and B, all distances,
both PSNR constraints, and both rates, is 53.6% and 67.3% for a short-range system (under 20m)
and long-range system (over 20m), respectively, over a fixed system designed for the worst-case
image, distance, and channel. In comparison to a fixed system employing power control to change
transmit power, but with fixed digital power, the reduction in total energy consumption drops to
49.4% and 15.6%, respectively, for the short-range and long-range systems. The most significant
part of the energy consumption was due to the ine#ciency of the power amplifier at short dis-
tances. Using a power amplifier with a lower maximum transmit power P decreased
the energy consumption of the system by 60%. Future work on reconfigurable architectures for
source coders (especially video coders) and more complex channel coders such as rate-punctured
convolutional coders (RCPC) will increase the power consumption of the digital blocks and increase
the benefits of a total-system-energy minimization approach.



--R



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--TR
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energy minimization;low power;joint source-channel coding;indoor wireless transmission