Mitigating Automotive Radar Interference using Onboard Intelligent Reflective Surface
Shree Prasad Maruthi Karrthik G. K. Vijaya Krishna A. Mahbub Hassan Jinhong Yuan

	
	
	
	
	
	Mitigating Automotive Radar Interference using Onboard Intelligent Reflective Surface

    Shree Prasad Maruthi^*, Karrthik G. K.^**, Vijaya Krishna A.^†, Mahbub Hassan^, Jinhong Yuan^
		^*Dept. of Electrical and Electronics Engineering, WILP Division, BITS Pilani, India 

			^**Charcoal Technologies, Bengaluru, India, ^†Bosch Global Software Ltd., Bengaluru, India 

			^ School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

			^ School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia

			Email: shreeprasadm@gmail.com, karrthik.gk23@gmail.com, A.VijayaKrishna@in.bosch.com, mahbub.hassan@unsw.edu.au,
 j.yuan@unsw.edu.au
		

    
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		The use of automotive radars is gaining popularity as a means to enhance a vehicle's sensing capabilities. However, these radars can suffer from interference caused by transmissions from other radars mounted on nearby vehicles. To address this issue, we investigate the use of an onboard intelligent reflective surface (IRS) to artificially increase a vehicle's effective radar cross section (RCS), or its “electromagnetic visibility." Our proposed method utilizes the IRS's ability to form a coherent reflection of the incident radar waveform back towards the source radar, thereby improving radar performance under interference. We evaluated both passive and active IRS options. Passive IRS, which does not support reflection amplification, was found to be counter-productive and actually decreased the vehicle's effective RCS instead of enhancing it. In contrast, active IRS, which can amplify the reflection power of individual elements, effectively combats all types of automotive radar interference when the reflective elements are configured with a 15-35 dB reflection gain.
	
	
		Intelligent reflective surface (IRS), active IRS, millimeter wave automotive radar, frequency modulated continuous wave (FMCW), radar interference, advanced driver assistance system (ADAS).
	
	

	

§ INTRODUCTION

	Automotive radars are quickly becoming a standard feature in modern cars due to their ability to operate effectively under inclement weather conditions such as fog, snow, and darkness <cit.>. This advantage over LIDARs and cameras has made automotive radar essential for driverless cars and the preferred choice for a range of advanced driver assistance system (ADAS) applications, including active cruise control, blind spot detection, cross-traffic alerts, and parking assist, among others, for existing cars <cit.>.
	
	At present, frequency modulated continuous wave (FMCW) based automotive radar operating in the millimeter wave band is the preferred choice by original equipment manufacturers (OEM) due to its simple hardware implementation <cit.>. However, with the lack of standardization and the anticipated increase in the use of radars in future vehicles, the issue of interference has become a significant concern, as it can increase the noise floor and severely limit radar's target detection performance <cit.>. Numerous techniques for interference mitigation have been proposed, but they often require computationally demanding signal processing tasks, such as digital beamforming, adaptive nulling, and space-time processing <cit.>.
	
	
	
	
	
	
	
	
	
	
	Intelligent reflective surfaces (IRS) <cit.> have emerged as a new paradigm in wireless communication, with the potential to achieve significant performance gains. Their ability to reflect electromagnetic signals in the desired direction helps to overcome typical wireless channel limitations. Active IRS <cit.>, which features reflecting elements that provide amplification (reflection gain), can offer even further performance improvements.
	
	This paper explores a novel approach that utilizes an active IRS array to enhance the target detection performance of automotive radars. Specifically, we propose embedding an active IRS at the rear end of a target vehicle to significantly improve the strength of the backscattered signal in the direction of the radar. Our approach seeks to address the challenge of interference and limitations of radar systems in detecting targets. This paper makes the following contributions:
	
	
	
	
	∙ We propose the use of a rear-mounted onboard intelligent reflective surface (IRS) to artificially increase the effective radar cross-section (RCS) of a vehicle, enabling the detection of target vehicles under interference from nearby radars. To the best of our knowledge, this is the first proposal to combat automotive radar interference using onboard IRS.
	
	
	
	∙ We demonstrate that passive IRS, which does not support reflection amplification, is too weak to combat typical radar interference. In fact, our analysis reveals that covering the rear-end of vehicles with passive IRS would be counter-productive and could reduce the vehicle's effective RCS.
	
	
	∙ Our simulations show that an active IRS with 15-35 dB reflection gain can help achieve a probability of detection greater than 99%. Therefore, even the most basic single-antenna radars can overcome various types of automotive radar interference without requiring complex signal processing tasks.
	
	
	
	The rest of the paper is structured as follows. Related work is presented in Section II. In Section III, the FMCW signal model is described. Section IV describes different interference scenarios. The automotive interference model is presented in Section V, followed by the IRS-assisted target detection in Section VI. Simulation results are presented and discussed in Section VII before concluding the paper in Section VIII. 
	

§ RELATED WORK

	
	Researchers have begun developing techniques to mitigate interference in automotive radars. Existing work in this area can be categorized as signal-processing-based, deep-learning-based, or IRS-based.
	
	Signal processing and deep learning: Due to the lack of standardization and increasing usage of FMCW-based automotive radars for various ADAS applications, the MOSARIM project <cit.> was initiated by the European Commission to study different interference scenarios and suggest countermeasures. Several techniques have been proposed in the literature to combat interference, including repurposing the radar for both communication and sensing <cit.>, conventional approaches based on minimizing interference in the time and frequency domain <cit.>, and adaptive filtering techniques to estimate and cancel the interferer samples <cit.>. Compressed sensing blindly mitigates interference <cit.>, while supervised and unsupervised deep neural network techniques have been proposed <cit.>. However, deep neural network techniques require a large dataset under dynamically varying conditions and may not always provide robust parameter estimates under different types of interference <cit.>.
	
	
	
	
	
	
	Passive IRS: The aforementioned approaches suppress interference and thereby improve the effective SIR. In contrast, an intelligent reflective surface (IRS) improves the SIR by coherently reflecting the signal from the target, thus enhancing its “electromagnetic visibility" or effective RCS. Passive IRS has been investigated for improving the reliability of wireless communication in <cit.>, while passive IRS-assisted radar, where the IRS is embedded in infrastructure, is studied in <cit.> to extend sensing range and suppress interference. In <cit.>, passive IRS embedded on vulnerable road users is shown to improve their visibility when located at short range.
	
	Active IRS: Recently, active IRS, which amplifies reflected signals, has gained attention to further improve performance gains in wireless communication <cit.>. Although active IRS is still in its infancy, it is considered as one of the key technology enablers for mmWave and terahertz communications <cit.>. 
	
	In <cit.>, an active IRS-based approach is proposed to improve radar detection capability under severe path loss. However, the IRS is not embedded on the target. In contrast, the active IRS proposed for automotive radar in this paper is mounted on the target vehicle and is shown to significantly improve the SIR under the challenging scenario of short-range interferer and long-range target.
	

§ FMCW SIGNAL MODEL

	In this section, we present the transmitted and received signals models for the FMCW radar. Notations used throughout this section are summarised in Table <ref>.
	

 §.§ Transmitted FMCW Radar Signal Model

	
	The transmitted waveform by an FMCW automotive radar is a sequence of chirps of the form <cit.>
	
    x_T(t) = √(P_t)∑_l=0^N_f-1s_b(t-lT_r)· a(t)

	where s_b(t) = exp[j2π(f_ct+1/2B_s/T_rt^2)] is a chirp signal, a(t) = rect(t-Tr/2 -lT_r/T_r), P_t is the transmitted power, T_r is the chirp duration, f_c is center frequency, B_s is the sweeping bandwidth, and N_f denotes the number of chirps in a frame. Further, the slope S_V of the chirp signal is defined as B_s/T_r. The target parameters and their resolutions measured by the radar with receiver bandwidth B_c are given as i) Maximum range R_max = B_cc_0/2S_V, ii) Range resolution Δ R = c_0/2B_s, iii) Maximum velocity ν_max = λ/4T_r, and iv) Velocity resolution Δν = λ/2N_fT_r. Here, c_0 and λ respectively denote the speed of light and wavelength.
	
	

 §.§ Received FMCW Signal Model

	For a target vehicle located at range R and with relative velocity ν, the received  FMCW frame is given as <cit.>
	
    0.9!x_R(t) = √(P_r)∑_l = 0^N_f-1s_b(t-τ_l-lT_r) ·rect(t-τ_l-Tr/2 -lT_r/T_r)+ n(t)

	where τ_l = 2(R+ν t+ν lT_r)/c_0 represents round-trip-time of the l^th chirp signal in the FMCW frame from the target vehicle, n(t) denotes the additive white Gaussian noise (AWGN) and P_r represents the received signal power given as <cit.>
	
    0.310.04P_r = P_tG_tG_rσλ^2/(4π)^3R^4

	here G_t, and G_r respectively denote the gain of transmitting and receiving radar antennas and σ RCS of the target. The received FMCW frame x_R(t) is de-chirped by the following steps i.) Multiplying each received chirp signal with the reference chirp signal x_b(t) and ii.) Low pass filter (LPF) with cut-off frequency B_c. The de-chirped FMCW frame is expressed as <cit.>
	
    0.89!x_V(t) = √(P_r)exp(j4π f_c/c_0)∑_l = 0^N_f-1exp{ j2π(f_bt+f_DlT_r)} + n_V(t)

	where f_b = 2S_V R/c_0 and f_D = 2f_cν/c_0 represent beat and Doppler frequency respectively, and n_V(t) is the noise component at the output of the LPF. 
	The range R and relative velocity ν of the target are determined by the following steps i.) Computing the two dimensional Fast Fourier transform of (<ref>), which is called as the range-doppler (R-D) plot, and ii.) Applying thresholding algorithms such as variants of constant false alarm rate (CFAR) on the R-D to determine the target parameters. It is important note here the CFAR algorithms assume the knowledge of noise statistics <cit.>.
	

§ INTERFERENCE IN AUTOMOTIVE RADAR

	
	Fig. <ref> illustrates the radar interference scenario wherein the victim radar measures the target vehicle parameters in the presence of interferer radar located at range R_I. With lack of standardization and co-ordination, parameters of FMCW based automotive radars vary with OEMs. Hence the interference between automotive radars from different or same OEMs are categorized as <cit.>:
	
	i.) Similar slope interference: This type of interference occurs when both the victim and the interfering radars choose to operate with the same bandwidth and chirp duration leading to identical chirp slopes. However, due to hardware `imperfection', they cannot produce identical slopes in practice. Rather, the slopes are expected to be slightly different and vary within 10%, hence is referred to as the similar slope interference. Fig. <ref> illustrates the similar slope interference scenario with victim and interfering radar operating at slopes S_V and S_I, respectively. Chirp duration of the victim radar is denoted as T_r. From the output of LPF at the victim radar in Fig. <ref>, it is observed that the interference is dominant across the entire chirp duration in certain chirps within the FMCW frame.
	
	ii.) Sweeping interference: This type of interference arises when the victim and the interfering radars are operating with significantly different slopes because they have chosen to operate with different bandwidth and (or) chirp duration. Interference scenario for the victim and the interfering radars operating at different slopes is shown in Fig. <ref>. Here it is observed that interference is present across all chirps but affecting only for a small fraction of the chirp duration. 
	
	In this work, we consider both types of interference when evaluating the performance of the proposed IRS-assisted automotive radar. 
	
	
	

	

§ AUTOMOTIVE RADAR INTERFERENCE MODEL

	Consider an interferer radar chirp signal x_I(t) received at a time offset τ_I with respect to the reference chirp signal of victim radar. The output of LPF x_O_l(t) for the l^th received chirp signal x_V_l(t) from the target is given as <cit.>
	
    x_O_l(t) = {
    			x_V_l(t) + x_I(t);     t ∈ T_u
    x_V_l(t);    Otherwise
    .

	here T_u is the vulnerable time period in which the frequency content ℱ{ x_V_l(t) + x_I(t) } lies within the bandwidth of the LPF. Further, x_I(t) is given as  
	
    0.70.04x_I(t) = √(P_r_I)exp{ j2π[1/2(S_Vt^2 - S_I(t-τ_I)^2)] }

	here S_I is the slope of the interferer radar and P_r_I represents the received interference power and is of the form <cit.>
	
	
	
	
	
	
	
	
		
		
		
		
		
		
		
		
		
		
		
		
		
    0.3250.05P_r_I = P_t_I G_t_I G_rλ^2/(4π R_I)^2

		here P_t_I and G_t_I respectively denote the transmitter power and gain of the interferer radar, and R_I is the range between the interferer and the victim radars. Now comparing (<ref>) and (<ref>), it is observed that interference power P_r_I will be significant as compared to received power P_r from the target for small interferer range R_I and large target range R.
		
		

§ IRS ASSISTED ENHANCED TARGET DETECTION

		Consider a passive IRS with N elements embedded on the rear side of the target vehicle as shown in Fig. <ref>. Further, the victim radar is assumed to be at azimuth angle θ and elevation angle ϕ from the IRS-assisted target vehicle. For a passive IRS with N elements, the received signal at the victim radar is
			
    x_V^P-IRS(t)  = ∑_k=0^N-1{ h_f,k(t) * x_T(t) * h_r,k(t) }exp(j δ_k)

		 here δ_k denotes the phase shift introduced by each IRS element, the channel impulse response along forward and reflected path is represented as h_f,k(t) and h_r,k(t) respectively and is given as
		 
    h_f,k(t) = √(a_k)δ(t-τ_k-τ_l/2)
 
		 		 
    h_r,k(t) = √(b_k)δ(t-τ_k-τ_l/2)
 
		 here the channel gain along forward path is a_k = √(G_t/4π R^2σ_e),  with σ_e = λ^2G_e^2/4π representing the RCS  of each IRS element and reflection gain of each IRS element G_e = π <cit.>. The time delay τ_k between the k^th and the reference IRS element with position co-ordinates (x_k,y_k) is given as
		 
    τ_k =  1/c_0[x_ksin(θ)cos(ϕ) +y_ksin(θ)sin(ϕ)]

		 Substituting (<ref>) and (<ref>) in (<ref>), the received signal at victim radar can be written as
		 
    x_V^P-IRS(t)  = ∑_l=0^N_f-1∑_k=0^N-1{√(a_kb_k) s_b(t-2τ_k-τ_l-lT_r).

		 
    ×.exp( jδ_k) } + n( t)

		 After de-chirping (<ref>), i.e., the output of LPF x_V_L^P-IRS(t) at the victim radar can be written as  
		 	
    x_V_L^P-IRS(t)  = ∑_l=0^N_f∑_k=0^N-1√(a_kb_k)exp{ 2f_cτ_k + f_cτ_l-1/2S(2 τ_k) ^2.

		 	
    . -1/2Sτ_l^2 +2 S t τ_k+Stτ_l-2Sτ_kτ_l}×exp(jδ_k) + n_V(t)

		 	Since τ_k^2≪ S and τ_l^2≪ S, the terms -1/2Sτ_k^2, -1/2Sτ_l^2 and Sτ_kτ_l can be neglected and (<ref>) is expressed as
		 		
    x_V_L^P-IRS(t)  = ∑_l=0^N_f∑_k=0^N-1√(a_kb_k)exp{4j f_cτ_k + j f_cτ_l.

		 	
    . +S t (1+2τ_k/τ_l)τ_l}×exp( jδ_k) + n_V(t)

		 	As τ_l≫τ_k, (<ref>) can be written as	
		 		 		
    x_V_L^P-IRS(t)  = ∑_l=0^N_f∑_k=0^N-1√(a_kb_k)exp{2 f_cτ_k + f_cτ_l.

		 
    . +S t τ_l}×exp( jδ_k) + n_V(t)

		 Further (<ref>) can be simplified as
		 
    !x_V^P-IRS(t) = exp{j4π f_cR/c_0}∑_l=0^N_f-1∑_k=0^N-1{√(a_kb_k)exp(j4π f_cτ_k).

		
    exp(jδ_k)exp{ j2π(f_bt+f_DlT_r)}+ n_V(t)
 

		Further, due to the very small separation between the IRS elements, we assume a_kb_k = g = P_tG_tG_rG_e^2λ^4/(4π R)^4 for all k. Using (<ref>), the overall RCS^1 of the entire passive IRS is obtained as:
		
		
			
			
		
		
    σ_O^P = σ_e∑_k=0^N-1exp(j4π f_cτ_k)exp(jδ_k)

		
		
			
			
		∙Phase optimization of IRS elements:
		A fundamental goal of using IRS is to coordinate the phase shifts of each individual elements in a way so that the reflections of each element are combined coherently at the receiver for maximum gain. From (<ref>), we can verify^1 that, the optimal phase shift at the k^th IRS element is given as: 
		
    δ_k^* = -j4π f_cτ_k

		Thus, the optimal phase shift depends on the direction of arrival (DOA) angles θ and ϕ of the victim radar which can be estimated by various methods such as by using a planar antenna array at the target vehicle or allowing the victim vehicle to transmit its location to the target vehicle using vehicle-to-vehicle communication.
		
		
			
			
			
		Hence, by appropriate adjustment of the IRS element phases at the target vehicle, the received signal power at the victim radar can be improved by a factor of N and the optimised RCS of a passive IRS-assisted target vehicle is computed as: 
		
    σ_O^P^* = Nσ_e

		∙RCS of active IRS:
		It will be shown later in the results section, that passive IRS is not a practical option for improving the effective RCS of the target vehicle. However, by considering active IRS, i.e., by providing a reflection gain, Γ, at each IRS element, the effective RCS can be increased to: 
		
    σ_O^A^* = Γ Nσ_e

		
		
		The output of LPF due to the signal reflected by active IRS-assisted target vehicle is obtained as:  
		
    !x_V^A-IRS(t) = exp{ j4π f_cR/c_0}∑_l=0^N_f-1∑_k=0^N-1{Γ √(g_k)exp(j2π f_cτ_k)·.

		
    . exp(jδ_k)exp[ j2π(f_bt+f_DlT_r)]+ n_A_k( t )} +n_V(t)

		where the component n_A_k( t ) arises due to noise introduced by each active IRS element to its reflected signal <cit.>. The optimal phase shift δ_k at each element is determined according to (<ref>). 
		
		∙Signal-to-interference ratio (SIR):
		The ultimate goal of using the IRS in the target vehicle is to improve the SIR at the victim radar, which in turn can help improve the detection probability. 
		The SIR due to active IRS-assisted target is given as <cit.>:
		
    0.50.04SIR [dB] = 10log_10(G_PP_a/P_r_I)

		where P_a = NΓ g^2 represents the received signal strength and G_P = T_rB_cN_f denotes the processing gain <cit.>.
		

§ RESULTS

		In this section, we first compare the effective RCS of a typical vehicle when fitted with a passive vs. active IRS. This exercise reveals the interesting insight that the use of passive IRS would actually reduce the vehicle RCS instead of improving it and in turn motivates the need for using active IRS. We then simulate the typical automotive radar interfering scenarios to obtain the reflection gain (Γ) that would be required for the active IRS to enable reliable target detection under automotive radar interference. 
		
		

 §.§ Effective RCS: Passive vs. Active IRS

		In <cit.>, the RCS of typical sedan cars is experimentally determined as σ = 10 dBm^2, which will be used as the baseline RCS and referred to as the non-IRS scenario in this paper. It can be assumed that the useful reflections from the target vehicle actually comes from the metals at the rear of the vehicle covering an area of 1m × 1m, approximately. If this area is covered with an IRS, we could fit about 256× 256 = 65,536 IRS elements [Assuming each element has a size of λ/2 m×λ/2 m and a spacing of λ/2 m between the elements, where λ = 3.89mm for 77GHz radars.]. Thus, the effective RCS for passive IRS can be computed as 0.78sm or -1.079 dBsm according to Eqn. (<ref>). 
		
		This interesting result shows that simply covering the rear of the vehicle with a passive IRS will not be effective and would actually significantly reduce the RCS of the vehicle from its baseline value. This result further motivates us to consider active IRS, which holds the promise to increase the RCS beyond the baseline by configuring adequate reflection gain (Γ) for the IRS elements. For an active IRS, the improvement in effective RCS as a function of Γ is shown in Fig. <ref>. We find that active IRS can overcome the baseline RCS with Γ > 10 dBm^2. 
		
		Improvement in RCS will result in improvement in SIR, which in turn will improve the detection probability. Therefore, from Fig. <ref>, we can deduce that active IRS can potentially improve the detection probability compared to the non-IRS case if it is configured with Γ > 10 dBm^2.  However, we still do not know the required value of Γ that will enable highly reliable detection with a detection probability close to 100%. In the following, we conduct simulations to evaluate the probability of detection as a function of Γ to find this answer for different types of FMCW interference, i.e., similar slope vs. sweeping slope.
		
		
		
		
		

 §.§ Simulation Parameters and Performance Metrics

		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		The parameters considered in the simulation are shown in Table <ref>. Cell averaging-CFAR detector (CA-CFARD) which is the basic version of CFAR is employed for detecting the target parameter from the R-D plot. The noise power at victim receiver is ρ = kT_0B_cF_n where k is Boltzmann's constant and noise power at each active IRS element is ρ_A = kT_0B_sF_n.
		
		The performance of target detection using active IRS is analysed in terms of probability of detection P_D, which is derived as the fraction of the total number of simulation trials that detected the target parameters correctly. The reflection gain of the active IRS, Γ, was increased in steps of 1 dB where 1000 trials were simulated for each Γ by varying certain parameters randomly in each trial.  
		
			
			
		
		

 §.§ Detection Performance for Similar Slope Interference

		
		Fig. <ref> plots the detection probability for an active IRS assisted target as a function of the reflection gain, Γ, when the interfering radar is located at range R_I = 50 m (more aggressive interference) and R_I = 100 m (less aggressive interference). In the simulation, the slope of the interfering radar is randomly varied within the ±10% of the victim radar and the time offset, τ_l, is randomly varied between 0 and the chirp duration T_r. 
		
		We make the following observations: i) The detection probability increases with the increase in reflection gain as expected, ii) target detection performance is significantly better when the interfering radar is located at a longer distances from victim radar (less aggressive interference), which is again expected, iii) For R_I = 50 m and R_I = 100 m, P_D=100% is obtained for gain values 35 dB and 33 dB respectively, iv) for Γ < 10 dB the target detection performance deteriorates compared to the non-IRS assisted target, which is due to the effective RCS being smaller than the RCS of non-IRS assisted target (See Fig.<ref>), v) the P_D of the non-IRS target is very similar (the two lines coincides in Fig. <ref>) for R_i = 50 m and R_i = 100 m [A possible reason for this outcome is because the detection performance depends on the number of samples affected by the interference. In case of similar slope interference, we have found that the significant number of samples in the entire frame are affected by the interference.]. 
		
		The reason for improvement in detection performance with increasing Γ is further explained using Fig. <ref>, which shows the R-D plot and the corresponding CA-CFARD output for a single simulation trial. For Γ = 33 dB, we observe a clear peak and hence CA-CFARD is able to detect the target parameters. However for a smaller Γ, the interference will dominate and thereby CA-CFARD fails to detect the presence of the target. The reason for the peak (corresponding to target parameter) in the R-D plot becoming more prominent with increase in Γ is investigated in Fig. <ref>, which shows that increase in Γ significantly improves the SIR and this in turn results in a prominent peak at the target parameter location in the R-D plot. 
		
		

		

 §.§ Detection Performance for Sweeping Slope Interference

		Performance of IRS assisted target detection under sweeping slope interference with slope 40.90 MHz/μ s is shown in Fig. <ref>, where the time offset τ_I is randomly varied between 0 and the chirp duration T_r. Here it is observed that 100% target detection is achieved for reflection gain of 10 dB earlier when to compared to similar slope interference. A possible reason for this outcome is due to only smaller fraction of victim chirp samples affected by interference (see Fig. <ref>). Further, for R_i = 50 m and R_i = 100 m, P_D=100% is obtained for gain values 20 dB and 15 dB respectively.
		
		

		

§ CONCLUSION

		

		This paper has proposed a novel solution for enhancing the performance of automotive radars under interference from other nearby radars. We have shown that an active onboard IRS can significantly increase a vehicle's RCS, thereby improving the strength of backscattered signals in the direction of the radar. Our simulations demonstrate that an active IRS with a reflection gain of 15-35 dB can achieve a probability of detection greater than 99%, enabling even the most basic single-antenna radars to overcome various types of automotive radar interference. This paper also highlights the limitations of passive IRS, which could actually reduce the vehicle's effective RCS. Our findings have important implications for the design and development of automotive radar systems, and we believe that this proposed approach has the potential to revolutionize the field of vehicular sensing and communication. Future work will consider use of multi-antenna radars to further reduce the required reflection gain of the active IRS.
		

		
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