Target Localization in Distributed MIMO OFDM Radar

Target Localization in Distributed MIMO OFDM Radar Leonardo Leyva∗, Joumana Kassam∗, Daniel Castanheira∗, Ad˜ ao Silva∗, and At´ ılio Gameiro∗ Instituto de Telecomunicac¸ ˜ oes (IT), and DETI, Universidade de Aveiro, Aveiro, Portugal E-mails: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract—Radar systems have evolved to meet the growing demand for high-precision and reliable target detection under diverse environmental conditions. This paper proposes a multiple-input multiple-output (MIMO) radar system with widely distributed antennas that leverages interleaved orthogonal frequency division multiplexing (OFDM) for enhanced sensing capabilities. This paper proposed an algorithm for MIMO radar system with widely distributed antennas. The processing is done at the central processing unit (CPU) for joint localization. The system is evaluated for different scenarios, demonstrating its capability to accurately localize multiple targets while minimizing ambiguities, showing improved detection performance. Index Terms—MIMO radar, localization, target detection, interleaved OFDM. I. INTRODUCTION Multiple-input multiple-output (MIMO) radar systems represent a significant evolution in radar technology, that uses multiple spatially distributed transmitters and receivers to enhance target detection and system performance [1]. Unlike conventional phased-array radars that transmit scaled versions of a single waveform, MIMO radars can transmit multiple waveforms through their antenna arrays, offering unprecedented waveform and spatial diversity. This diversity enables two primary configurations: widely separated antennas [2] for capturing the spatial diversity of a target’s radar cross-section (RCS) and colocated antennas [3] for leveraging waveform diversity. Therefore, MIMO radar can be seen as a specific implementation of a multi-static radar system, which consists of several radar pairs, including collocated monostatic and separated bistatic pairs. Information from these pairs is sent to a central processing unit (CPU) that estimates target positions, thus enhancing detection performance while requiring robust data fusion techniques. Emerging MIMO radar with advanced techniques like orthogonal frequency division multiplexing (OFDM) [4], including interleaved OFDM [5], can enhance spectral efficiency and robustness by minimizing interference and improving detection accuracy. Interleaving subcarriers may ensure better bandwidth usage while maintaining orthogonality, making it particularly suitable for systems where spectrum sharing is critical. These advancements are driving MIMO radar’s evolution into a more reliable multi-functional technology for sensing and communication. However, like multi-static radars, MIMO radar faces challenges in transferring data to the CPU and defining effective fusion rules, which are crucial for integrating information from multiple sources to enhance target detection, localization, and tracking [6]. Fusion occurs at two main levels either low-level (data) fusion or high-level (parametric) fusion. The high-level fusion can use soft methods (weighted combinations) or hard methods (unweighted aggregations), balancing performance and data efficiency. In [7], the authors proposed a data-level fusion methodology with limited data transfer and computational complexity based on the maximum likelihood estimation (MLE) for joint angle of departure (AoD) and angle of arrival (AoA) localization of Ktargets using a multi-static OFDM radar system. In [8], a novel algorithm for multiple moving target detection in multi-static radar systems was proposed, addressing the challenge of unknown target velocity or position. Herein, to detect targets with few false alarms, a generalized likelihood ratio test (GLRT) detector was modified based on MLE by eliminating the interference components in the observation matrix, thus suppressing “ghost targets” caused by registration errors. Therefore, designing an efficient fusion method that balances performance and data transmission is essential for achieving optimal results in radar applications. In this work, we propose a novel algorithm for MIMO radar system with distributed antennas. The signals collected by the multiple access points (APs) are transmitted to a CPU, where joint localization tasks are performed. The algorithm is designed to extract delay information locally and the information is fused at the CPU. Results show the system’s ability to effectively detect and localize multiple targets. The rest of the paper is organized as follows: Section II describes the system model of MIMO radar CF-based system. Section III presents the proposed distributed algorithm for target localization. Then, the numerical results are outlined in Section IV, followed by the main conclusions in Section V. II. SYSTEM MODEL This work considers a distributed MIMO radar system, as illustrated in Fig. 1. The system is designed for environment sensing using an interleaved OFDM waveform to enable sensing functionalities. The radar system consists of M transmitting antennas located at coordinates Tm= [xtm;ytm] for m= 1, . . . , M and Nreceiving antennas positioned at Rn= [xrn;yrn]for n= 1, . . . , N. The signals from these antennas are transported through a fiber-based fronthaul to a CPU where full or partial signal processing is performed. Fig. 1: Distributed MIMO radar with Mtransmitting, and N receiving antennas, and Qpoint-like targets. A. Transmitted signal The time-domain OFDM signal transmitted by the mth transmitter AP is expressed as xm=FHbm,(1) where bm∈CKrepresents the interleaved OFDM data vector, and F∈CK×Kis the discrete Fourier transform (DFT) matrix, where Kdenotes the number of subcarriers. In the interleaved OFDM scheme, each AP transmits on a unique subset of subcarriers. As a result, the signals satisfy the orthogonality condition, i.e., xH ixm= 0,∀i=m, which is due to the non-overlapping subcarrier allocation across the M transmitter antennas. B. Received signal The signals transmitted by the Mantennas illuminate Q targets. After applying the DFT, the frequency-domain signal at the nth receiver is expressed as rn= M X m=1 Q X q=1 γm,n,qDm,n,qbm+nn,(2) where γm,n,q denotes the RCS of target qas observed by the (m, n)transmitter-receiver antenna pair. The term Dm,n,q = diag{am,n,q} ∈ CK×Krepresents the frequencydomain channel, and nnrepresents additive white gaussian noise (AWGN) with zero mean and variance σ2 nat the nth receiver. The kth element of the frequency-domain channel vector is given by am,n,q(k) = exp{−j2π∆fτm,n,qk},(3) where ∆fdenotes the subcarrier spacing, and τm,n,q =τm,q + τq,n represents the total path delay. More specifically, τm,q and τq,n are the propagation delays between the mth transmitter and the qth target, and between the qth target and the nth receiver antenna, respectively. III. DISTRIBUTED ALGORITHM This section presents a distributed algorithm for target localization. Specifically, the Nreceiver APs estimate the Q delays for each transmitter-receiver pair. The estimated delays are then offloaded to the CPU for joint target localization. The distributed algorithm is illustrated at a glance in Fig. 2. Fig. 2: Schematic illustration of the proposed distributed algorithm for target localization. A. Signal Processing at the nth Receiver At the nth receiver, the data vector, b=PM m=1 bm, is first removed using element-wise division [9]. The signal after data removal is given by ˆrn= M X m=1 Q X q=1 γm,n,qˆam,n,q +wn,(4) where ˆam,n,q represents the interleaved version of the frequency-domain channel vector, derived from Dm,n,qbm. According to (4), the inverse discrete Fourier transform (IDFT) performed on the interleaved subcarriers corresponding to the mth transmitter yields the delay estimates τm,n,q for all q. B. Signal Processing at the CPU The previous delay estimates are used to reconstruct the received signal. Let the reconstructed signal for the (m, n) transmitter-receiver pair be denoted as ˜rn,m for all mand n, which can be obtained as ˜rm,n =X q exp (−j2π∆fˆτm,n,qkm),(5) where kmcontains the set of subcarrier indices assigned to the mth transmitter. Target localization is then achieved by applying a matched filter (MF) between the reconstructed signals and the hypothesized responses for each possible target position. The radar imaging function is computed as P(x, y) = N X n=1 M X m=1  ˜rH m,nhm,n(x, y)  2,(6) where hm,n(x, y)represents the codebook entry corresponding to the (x, y)position. IV. NUMERICAL RESULTS The section evaluates the proposed distributed localization algorithm. using a system configuration with a bandwidth of 800 MHz. The scenario considers a distributed MIMO radar system with four widely separated transmit and four receive antennas, operating over a bandwidth of 800 MHz. For the radio-sensing channel, three targets are located at coordinates [-1, -2], [0, 0], and [3, 3] meters. Unless otherwise stated, the following results were obtained for an signal-to-noise ratio (SNR) of 20 dB. The following presents an experimental investigation into the influence of antenna deployment geometry on radar imaging performance. We compared two distinct antenna arrangements: a regularly deployed grid pattern and a randomly distributed configuration. The study employed Monte Carlo simulations with 500 realizations to assess localization accuracy, quantified via root mean squared error (RMSE). Fig. 3 shows the radar image obtained using an interleaved OFDM signal with 256 subcarriers. The transmitter antennas were uniformly deployed along the x-axis from 0 to 5 meters, with the y-coordinate fixed at 5 meters. Conversely, the receiver antennas were placed along the y-axis from 0 to 5 meters, with the x-coordinate fixed at 5 meters. -5 0 5 x-axis (m) -5 -4 -3 -2 -1 0 1 2 3 4 5 y-axis (m) Tx antennas Rx antennas Real target position Fig. 3: Radar imaging for a scenario in which antennas are regularly deployed along the xand y-axes. From Fig. 3, we can observe how the sidelobes are formed by the intersection of the ellipses generated by each transmitter–receiver pair. These sidelobes tend to concentrate in specific regions, leaving other areas relatively free of interference. Additionally, the resolution and the overall sidelobe structure are shaped by the regular deployment of the antennas. Similar to Fig. 3, Fig. 4 illustrates the radar image obtained using an interleaved OFDM signal with 256 subcarriers. However, in this case, the transmitter and receiver antennas are randomly deployed across the entire area. Specifically, each (x, y)coordinate is drawn from a uniform distribution over the range [−5,5] meters. Fig. 4 shows that, compared to the radar imaging in Fig. 3, the random deployment results in more pronounced sidelobe -5 0 5 x-axis (m) -5 -4 -3 -2 -1 0 1 2 3 4 5 y-axis (m) Tx antennas Rx antennas Real target position Fig. 4: Radar imaging for a scenario in which antennas are randomly deployed within an area of 100 m2. levels. Specifically, in this case, the sidelobes are spread across the entire area. This spread is due to the diversity in the antenna positions, unlike the regular deployment, where the antennas follow a well-defined pattern. Additionally, it can be observed that for some targets, such as the one located at coordinate [3,3], the resolution improves, which may lead to better accuracy. Building on this observation, the next figure investigates the accuracy of the proposed system for different values of SNR and varying OFDM parameterizations. Fig. 5 shows the RMSE of the localization for a single target, evaluated over SNR values ranging from −30 to 10 dB. The result was obtained from Monte Carlo simulations with 500 realizations. In each Monte Carlo realization, the target is randomly placed following a uniform distribution for both the x-axis and y-axis. Specifically, Fig. 5 presents the results obtained for the regular deployment depicted in Fig. 3 and the random deployment shown in Fig. 4, for OFDM configurations with 64 and 256 subcarriers, respectively. The RMSE is computed using the following formula RMSE =v u u t 1 n n X i=1 ((xi−ˆxi)2+ (yi−ˆyi)2), where (xi, yi)represents the true position, (ˆxi,ˆyi)represents the estimated position, and nis the total number of realizations. The results in Fig. 5 reveal two key trends. First, increasing the number of subcarriers from K= 64 to K= 256, while keeping the total bandwidth fixed, improves localization accuracy in the low SNR regime. This improvement is due to the increased maximum unambiguous range provided by the finer subcarrier spacing at higher K, which helps mitigate range ambiguities. For instance, the RMSE starts to decrease at approximately −21 dB for K= 256, while for K= 64 the improvement begins around −16 dB. -30 -25 -20 -15 -10 -5 0 5 10 SNR (dB) 10-2 10-1 100 101 RMSE (m) regular deployment, K = 64 regular deployment, K = 256 random deployment, K = 64 random deployment, K = 256 Fig. 5: SNR versus RMSE for regular and random deployments, considering K∈ {64,256}. Second, for SNR values greater than roughly −5dB, the RMSE plateaus and becomes primarily influenced by the spatial geometry of the antenna deployment rather than the noise level. In this regime, random deployments consistently outperform regular ones due to their enhanced geometric diversity, which helps reduce ambiguities and improve resolution. Conversely, the structured layout of the regular deployment results in more pronounced sidelobes and limits its localization accuracy. V. CONCLUSIONS This paper presented a distributed MIMO interleaved OFDM radar system for target localization. A novel approach was proposed in which each receiver estimates propagation delays locally before forwarding them to the CPU for joint localization. The simulation results demonstrated the effectiveness of the proposed approach in accurately detecting and localizing multiple targets while also highlighting the impact of antenna deployment strategies and OFDM configurations on system performance. ACKNOWLEDGMENT This work has received funding from the FCT - Fundac¸˜ ao para a Ciˆ encia e a Tecnologia under the PhD Research Studentships 2022.12379.BD and REVOLUTION project 2022.08005.PTDC, and from FCT/MCTES through national funds and when applicable co-funded EU funds under the project UIDB/50008/2020-UIDP/50008/2020. 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