Target Characterization Using MIMO Radar

Let us consider the radar detection problem at the delay τ as follows (Levanon, 1998; Eran Fishler et al., 2006):

H₀: Fall detection.

Based on the Neyman–Pearson sense, the optimal detector likelihood ratio test (LRT) can be given as (Trees, 1968) follows: (1) T=logfrt|H1frt|H0<H1>H0δth, T = \log {{f\left( {r\left( t \right)|{H_1}} \right)} \over {f\left( {r\left( t \right)|{H_0}} \right)}}\matrix{ { < {H_1}} \cr { > {H_0}} \cr } {\delta _{th}}, where f(r(t)|H₀) and f(r(t)|H₁) are the probability density function of observation corresponding to the radar detection hypotheses and δ_th is a threshold, which is governed by the probability of false alarm. Here, the received signal model is represented by r(t).

For the analysis purpose, in this paper we have considered M and N number of transmitter and receiver antennas. Let x be the output of matched filter banks. Then, the optimal detector is given by the following: (2) T=x2<H1>H0δth. T = {\left\| x \right\|^2}\matrix{ { < {H_1}} \cr { > {H_0}} \cr } {\delta _{th}}.

Now for the MIMO system, the distribution of the test statistic (Levanon, 1998; Eran Fishler et al., 2006) can be represented as follows: (3) x2∼σn22X2MN2H0E2M+σn22X2MN2H1, {\left\| x \right\|^2}\sim\left\{ {\matrix{ {{{\sigma _n^2} \over 2}X_{\left( {2MN} \right)}^2} \hfill & {{H_0}} \hfill \cr {\left( {{E \over {2M}} + {{\sigma _n^2} \over 2}} \right)X_{\left( {2MN} \right)}^2} \hfill & {{H_1}} \hfill \cr } ,} \right. where xd2 x_{\left( d \right)}^2 denotes a χ² random variable having d degrees of freedom, E is the total transmitted energy and σn2 \sigma _n^2 is the noise level per receive element.

The probability of false alarm can be expressed as follows: (4) PrFA=PrT>δth|H0=Prσn22X2MN2>δ=PrX2MN2>2δthσn2. \matrix{ {{P_{rFA}}} \hfill & = \hfill & {\Pr \left( {T > {\delta _{th}}|{H_0}} \right)} \hfill \cr {} \hfill & = \hfill & {\Pr \left( {{{\sigma _n^2} \over 2}X_{2MN}^2 > \delta } \right) = \Pr \left( {X_{2MN}^2 > {{2{\delta _{th}}} \over {\sigma _n^2}}} \right).} \hfill \cr }

The probability of detection is given by the following: (5) PrD=PrT>δth|H1=PrE2M+σn22X2MN2>δth=1−FX2M22δthEM+σn2=1−FX2MN2σn2EM+σn2FX2MN2−11−PrFA. \matrix{ {{{Pr}_D}} \hfill & = \hfill & {\Pr \left( {T > {\delta _{th}}|{H_1}} \right) = \Pr \left( {\left( {{E \over {2M}} + {{\sigma _n^2} \over 2}} \right)X_{2MN}^2 > {\delta _{th}}} \right)} \hfill \cr {} \hfill & = \hfill & {1 - {F_{X_{2M}^2}}\left( {{{2{\delta _{th}}} \over {{E \over M} + \sigma _n^2}}} \right) = 1 - {F_{X_{2MN}^2}}\left( {{{\sigma _n^2} \over {{E \over M} + \sigma _n^2}}F_{X_{2MN}^2}^{ - 1}\left( {1 - {{Pr}_{FA}}} \right)} \right).} \hfill \cr }

As in the study of Trees (1968), the detector's output SNR (β) is defined as follows: (6) β=ET|H0−ET|H1212VarT|H0+VarT|H1. \beta = {{{{\left| {E\left( {T|{H_0}} \right) - E\left( {T|{H_1}} \right)} \right|}^2}} \over {{1 \over 2}\left[ {Var\left( {T|{H_0}} \right) + Var\left( {T|{H_1}} \right)} \right]}}. For MIMO radar, (T/H₀) = NM(σ_n)² and: ET/H1=MNσn2+EM=MNσn2+EN. E\left( {T/{H_1}} \right) = MN\left( {\sigma _n^2 + {E \over M}} \right) = MN\sigma _n^2 + EN. And also: VarT/H0=MNσn22=NMσn4 Var\left( {T/{H_0}} \right) = MN{\left( {\sigma _n^2} \right)^2} = NM\sigma _n^4 and: (7) VarT/H1=MNσn2+EM2=MNσn4+E2M2+2.σn2EM. \matrix{ {Var\left( {T/{H_1}} \right)} \hfill & = \hfill & {MN\left\{ {{{\left( {\sigma _n^2 + {E \over M}} \right)}^2}} \right\}} \hfill \cr {} \hfill & = \hfill & {MN\left( {\sigma _n^4 + {{{E^2}} \over {{M^2}}} + 2.\sigma _n^2{E \over M}} \right).} \hfill \cr }

Therefore, using Equation (5), the output SNR level can be calculated as follows: (8) βMIMO=ET/H0−ET/H1212VarT/H0+VarT/H1=EN2122MNσn4+E2/M2+2σn2E/M,=ρ2NM1+ρ2/2M2+ρ/M \matrix{ {{\beta _{MIMO}}} \hfill & = \hfill & {{{{{\left| {E\left( {T/{H_0}} \right) - E\left( {T/{H_1}} \right)} \right|}^2}} \over {{1 \over 2}\left[ {Var\left( {T/{H_0}} \right) + Var\left( {T/{H_1}} \right)} \right]}}} \hfill \cr {} \hfill & = \hfill & {{{{{\left( {EN} \right)}^2}} \over {{1 \over 2}\left[ {2MN\sigma _n^4 + \left( {{E^2}/{M^2}} \right) + 2\left( {\sigma _n^2E/M} \right)} \right]}},} \hfill \cr {} \hfill & = \hfill & {{{{\rho ^2}N} \over {M\left( {1 + \left( {{\rho ^2}/2{M^2}} \right) + \left( {\rho /M} \right)} \right)}}} \hfill \cr } where the SNR is denoted by ρ as the ratio between the total transmitted energy and the noise level per receive element and can be defined as ρ=E/σn2 \rho = E/\sigma _n^2

In this section, we consider different configurations of the MIMO system to analyze the system performance. All the simulation results have been done using MATLAB software. Here, the probability of the detection (P_d) and the output signal SNR after the MIMO signal processing have been studied.

Figures 1 and 2 show the performance of a MIMO radar with the change in the number of antennas in the transmitter and receiver section. As shown in the figure, there is an improvement in the radar performance with the increase in the number of the antennas. To simulate the result of Figure 1, the authors have taken the probability of false alarm (Pfa) = 10e−6. For quantitatively analyzing the result as in Figure 1, let us consider that the required SNR for the SISO system is 18 dB. Similarly, the required SNR for the MIMO system having configuration 2 × 2, 4 × 4×, 8 × 8 is 12.3 dB, 9.8 dB, 8 dB, respectively. This indicates the tremendous performance improvement due to the increase in the number of antennas. The same is true for the post-processing SNR for the MIMO system as indicated in Figure 2.

Figure 1:

Figure 2:

Therefore, from these two numerical results, one can conclude that diversity order plays an important role in enhancing the performance of a MIMO system. MIMO radar exploits the target angular spread to combat target fading. MIMO radar observes a different aspect of the target, enabling the MIMO radar to exploit spatial diversity to overcome target fading. The diversity order is directly proportional to the number of the antennas and the same is visible here in the results.

It is reasonable to point out that although MIMO radar offers many advantages, but from the point of view of the implementation, MIMO radar is considerably more complex and costly than the monostatic radar. Therefore, this puts some limitations on the number of antennas that can be used.

The authors have taken the double-folded approach for the development of the radar setup. First, the authors have taken stand-alone hardware such as arbitrary waveform generator (AWG), vector signal analyzer (VSA) for the design of the transmitter and receiver section. And the vector signal generator (VSG) is used as RF frequency generator. Second, after parameter finalization through the rigorous experimentation, the total system has been realized in the miniaturized version using the SDR platform with multiple antennas.

In the stand-alone approach as in Figure 3, as the baseband signal generator, AWG has been used to generate P4 coded signal with 5 MHz bandwidth. The authors have used 70 MHz as the IF frequency. The VSA used in this experiment has 14 bits resolution and it can support the maximum sampling rate up to 250 MHz. Now higher IF leads to the increased possibilities of the clock jitter. As our system is based on the correlation processing, proper synchronization is very much required, and therefore we cannot afford the clock jitter. However, very low IF makes the system more susceptible to electromagnetic noise. This leads to the choice of IF frequency as 70 MHz. Also, the authors want to have a flexibility of having the baseband signal bandwidth up to 100 MHz and this is one of the reasons for choosing IF frequency as 70 MHz. However, here we have taken a signal bandwidth of 5 MHz only.

Figure 3:

The baseband signal has the following specifications: No. of bits: 25 bits P4 code; Duty cycle: 35%; Ton = 5 micro sec; Toff = 9.28 micro sec. Then the IF signal is upconverted to the RF frequencies (0.3–3.0 GHz) by using a vector signal generator (VSG) as RF frequency generator. For the transmission and reception, Horn antenna has been used. The target under the test (TUT) is placed on a three-axis rotating pylon. At the receiver side, all the radar signal processing algorithms have been performed in VSA. Here, the authors have used two-channel VSA; one channel is used to take the reference signal and another channel is used for the received signal. In VSA, with the help of the correlation processing between the received and reference signal, the target detection has been carried out. The entire system is designed in LabView platform.

As a part of system validation, initially, only the range imaging has been considered. As we know that the range resolution depends on the signal bandwidth, here, we have considered a swept bandwidth of 1 GHz for having the resolution of 0.15 meter. Now, to have the swept bandwidth of 1 GHz, we have swept the RF frequency from 1.5 GHz to 2.5 GHz. For the experimentation purpose, the target is kept at a distance of 162 meters. The Tx and Rx antenna height is 18 feet and Pylon height is 16.5 feet.

Figures 4 and 5 represent the signals at the VSA end. These received and reference signals are used for the correlation processing for target detection. Figure 4 represents the reference signal taken directly from the AWG. Figure 5 represents the received signal. The multipath effect of the channel is clearly visible in Figure 5 and is also visible in the range imaging as presented in Figure 7.

Figure 4:

Figure 5:

Figure 6A shows the test bed for radar measurements. As it is clearly shown in the figure, the test bed is surrounded by trees and these are responsible for the unwanted reflection. These reflections produce multipath dispersion over the actual target response. And that puts lots of challenges for the radar designer. Now, with the spread spectrum radar and with swept bandwidth of 1 GHz, a target can be precisely located, and thereby pinpoint characterization of the target is possible under such severe channel condition. To analyze the performance of the radar, a standard flat plate has been used as shown in Figure 6B.

Figure 6:

Figure 7 shows the radar performance in terms of range imaging. Here, a single flat plate of dimension 0.9 m × 0.9 m has been put over the pylon for the detection purpose as shown in Figure 6B. Then the range imaging has been carried over a swept bandwidth of 1 GHz. As shown in the figure, along with the desired target peak, there are some additional peaks throughout the test range, which are due to nearby obstacles such as trees and boundary walls (as in Figure 6). The objective of these experiments is to analyze the detectability performance of the radar system and also accurately point out the target location under severe multipath channel condition. These experiments help us during the characterization of the target through the aspect angle pattern.

Figure 7:

As mentioned in the introduction section, MIMO exploits the spatial diversity to combat the channel fading effect, thereby enhancing the system performance. Therefore, as its extension, the authors have implemented the MIMO radar and the performance of the same has been tested in the same open range, as presented in the next section.

Here, as reconfigurable hardware, Wireless-Access Research Platform (WARP) SDR is used, which has a Xilinx Xilinx Virtex-6 LX240T FPGA along with 2 Radio daughter Cards. Dual-band RF option (2,400–2,500 MHz, 4,900–5,875 MHz) is available, and 2.4 GHz is selected as the carrier frequency for this radar development. The maximum available RF bandwidth is 40 MHz. Available TX power is 30 dB and the Rx gains’ control range is 93 dB. This board can be interfaced with Laptop using a LAN protocol. The baseband P4 code generation, data transmission, data reception and WARP board control code are written in MATLAB. And after receiving the signal, all the receiver signal processing algorithms have been performed in the MATLAB environment (Fig. 8).

Figure 8:

Here, the authors have used two SDR platforms in order to design a 2 × 2 MIMO system; one SDR platform has been used to design the transmitter section with two transmitting antennas, and the other one is used to design two channel MIMO radar signal processing. At the receiver side, two signals are coherently added and then passed through the correlation processing for the detection and characterization purpose. A typical radar setup with the SDR kits is shown below. As in the figure, we have used two horn antennas (frequency of operation: 1.7 GHz–2.7 GHz) both at the transmitter and the receiver section (Fig. 9).

Figure 9:

Figure 10A, B represents the transmitted and received signal at the transmitter section SDR and the receiver section SDR platform, respectively. It is basically a 25 bits P4 coded signal. After the reception of the reflected signal, it has been passed through the correlation processing for the detection purpose. After the successful detection of the target, the correlation peak values are plotted against the azimuth rotational angle of the target to get the aspect angle pattern of the desired target. The same procedure has been followed to have the result as in Figure 11.

Figure 10:

Figure 11:

Figure 11 shows the flat plate pattern using 2 × 2 MIMO radar. Here, in this experiment, 0.98 m × 0.68 m flat plate has been used as target. The RF frequency for this experiment is kept fixed at 2.4 GHz. The above figure depicts that the experimental result is able to achieve almost the same main lobe beam width as per the theoretical calculation. This shows almost equal performance of the MIMO radar system with respect to the theoretical calculation. One important observation is that there is a slight deviation in null formation in the pattern, which is due to the multipath fading effect. This can be improved if we increase the number of antennas, which is the future work corresponding to this project.

This paper deals with the development of the MIMO radar. As presented here, the diversity order increases with the increase in the number of antennas, and this leads to an increase in the probability of detection and also the post-processing SNR level of the received signal. Therefore, one can conclude that MIMO radar significantly improves radar performance. In order to have an intuitive aspect of the performance of the MIMO radar, the experimental result has been presented in terms of the flat plate pattern, where the experimental pattern is nearly identical to the theoretical pattern.