MIMO RADAR SIGNAL PROCESSING:MIMO as a Distributed Radar System
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MIMO RADAR SIGNAL PROCESSING:MIMO as a Distributed Radar System
Multiple-input multiple-output (MIMO) radar has been receiving increasing attention in recent years from researchers, practitioners, and funding agencies. MIMO radar is characterized by using multiple antennas to simultaneously transmit diverse (possibly linearly independent) waveforms and by utilizing multiple antennas to receive the reflected signals. Like MIMO communications, MIMO radar offers a new paradigm for signal processing research. MIMO radar possesses significant potentials for fading mitigation, resolution enhancement, and interference and jamming suppression. Fully exploiting these potentials can result in significantly improved target detection, parameter estimation, as well as target tracking and recognition performance.
Here we examine MIMO (multiple-input, multiple-output) as a distributed radar concept in an attempt to understand true performance and system utility and to evaluate novel forms of MIMO. MIMO does not have a strict definition but in essence exploits spatial diversity to obtain performance enhancement. It is possible to conceive of a number of different forms of processing that exploits the spatial diversity offered by a netted or distributed radar system. Therefore the overall aim is to compare the performance, under various practical operating conditions, of different ways of implementing a MIMO radar system. The area of signal processing techniques for radar networks has received increased attention and importance in more recent studies that provide a wide variety of system structures and processing methods. Here we define a radar network as a system made up of more than one transmitter and more than one receiver. Transmitters and receivers are distributed over a geographic area such that it is possible to view targets at different aspect angles.
Definition and Characteristics of MIMO Radar:
The notion of MIMO radar is simply that there are multiple radiating and receiving sites, as shown in the Fig.1. The collected information is then processed together. In some sense, MIMO radars are a generalization of multistatic radar concepts. The underlying concepts have most likely been discovered independently numerous times. While not using the nomenclature MIMO radar, the RIAS and SIAR radars that are experimental systems developed to study air-surveillance technology, are early examples of systems that could be classified as MIMO radars.
Fig.1 Illustration of the basic MIMO radar. By the most general definition, many traditional systems can be considered as special cases of MIMO radars. As an example, SAR can be considered as a form of MIMO radar. Although SAR traditionally employs a single transmit antenna and a single receive antenna, the positions of these two antennas are translated and images are formed by processing all the information jointly. The significant difference between this radar and a typical MIMO radar, which takes full advantage of the degrees of freedom, is that SAR does not have access to channel measurements for all transmitâ€œreceive position pairs. Equivalently, one may say that only the diagonal elements of the channel matrix are measured. Similarly, a fully polarimetric radar, that is, a radar that measures both receive polarizations for each transmit polarization, is an example of MIMO radar. Clearly, it is a MIMO radar with a relatively small dimensionality. Various possible signaling techniques are used for MIMO radar. The transmit antennas radiate signals, which may or may not be correlated, and the receive antennas attempt to disentangle these signals. Uses of MIMO radar: There are a variety of potential advantages to using MIMO radar. For given system design choices, some of these advantages can be traded for others:
Ã‚Â· Improved target detection performance.
Ã‚Â· Improved angle estimation accuracy.
Ã‚Â· Decreased minimum detectible velocity.
In this section the form of the network, the signal model and the system architecture whose performance is to be investigated are described. A radar network is assumed to consist of a number of transmitters (M) and receivers (N) geographically separated in an arbitrary fashion. Each receiver contains M filters matched to a given transmitted signal. Therefore, a total of MN signals are available for processing. Transmitters and receivers are the devices constituting the nodes of the network of the same specification and are separated in space to provide angular diversity. To provide a deeper insight into the operation and performance of the network, we choose the number of receivers and transmitters to be equal (i.e., N=M). In order to simplify the analysis, each pair of these devices is also collocated. In other words, we consider a radar network made up of M radars each transmitting and receiving. Figure 2 shows a schematic example radar network with M = N = 3. Each can receive both its own transmitted signal and the signals transmitted by the other transmitters. To gain a better understanding of the possible variations in performance for a wide range of parameters, M (and N) are varied from 1 (the monostatic case) to 5. Transmitterâ€œreceiver path pairs are termed nodes of the network and the individual transmitterâ€œreceiver pair is a device. As a consequence, the radar networks under investigation are made up of one to five devices and therefore exhibit 1, 4, 9, 16, and 25 nodes, respectively. Hence the number of nodes is the number of signals that it is possible to process. The network operates with a constant ERP. In other words, as the number of transmitters is increased, the individual emitted power of each transmitter is reduced accordingly. This concept is introduced to allow a fair comparison by keeping the total energy in the system constant. Of course, if each transmitter emits the same power, networks with many nodes will clearly have superior sensitivity. It is also assumed that the transmitted waveforms are orthogonal to one another. However, it should be noted that modulation induced by complex target reflection can cause degradation in orthogonality, and therefore this may not exactly be the case on reception. Each antenna points at the target from a different aspect angle, so that the measurement of radar cross section (RCS) into a particular receiver can differ from the other measurements by several decibels (dB) or more; thus, it is assumed that in this way independent spatial samples of the scattering from the target are obtained. Although a robust synchronization may have to be performed and an increased quantity of data may have to be jointly processed, the achievable benefits can be worth the effort. Qualitatively, these benefits are:
1. An improved detection capability due to multistatic scintillation of the target that increases the possibility of obtaining one or more high-value echo from a target.
2. A joint estimation of target position.
3. The capability of resolving multiple targets (as a consequence of benefit 2, above)
4. Increased information in the same bandwidth occupation.
5. An increased electronic countercountermeasures (ECCM).
Fig.2 MIMO spatialdiversity and netted radar configuration Spatial
The MIMO spatial diversity model described below has the conventional form of MIMO that has appeared in the literature [1â€œ 3]. This form of MIMO radar system exploits measurements of independent samples of target scattering as the basis for improving the probability of detection. Here, this processing approach is termed spatial MIMO or, simply MIMO. Data samples are processed incoherently and in a centralized architecture; that is, there is a central processing unit collecting the receiver outputs from all the nodes and returning a decision about the presence or absence of a target. A decision is determined by
and arises from the likelihood ratio test (LRT) for this form of processing , where is an appropriate threshold. The RCS of the target is assumed to have a Swerling II distribution, which corresponds to a Swerling I distribution when only one pulse is integrated. Netted Radar Systems: The second and third models that have been developed have the same physical layout as the spatial diversity MIMO, but instead use conventional coherent processing. In this approach the received signals are processed through the bank of matched filters, after this the coherent summation is performed. As the model of the received signal is the same as represented by
the results of processing after the filtering are the same as in Eq. (8.4). Two different forms of netted radar may be formulated: (1) coherent netted radar (NR) and (2) rephased coherent netted radar (RPCNR). Coherent Netted Radar (NR): This processing approach uses the same samples as for the case of the spatial MIMO radar system, but it sums them coherently. This is not the same as the MIMO concept but provides a valuable means of comparison. The phases of the incoming signals are highly correlated as they
Fig.3 The coherent netted radar integration depend on the targetâ„¢s position and the geometry of the system. However, it is well known that the phase wraps every halfwavelength, so, given that the position of the target cannot be measured with this degree of accuracy, the signals appear to have uncorrelated phases uniformly distributed between Figure.3 shows what happens if four signals are coherently summed without preprocessing the phases to align them. In this case the phases will be uniformly distributed and the overall coherent sum will be a signal whose amplitude is much smaller than the sum of the amplitudes of the single elements. In the extreme case, when the amplitude is constant and the sum of the phases is it is possible to cancel the signal completely. In such conditions this processing will provide the lower bound limit for the performance, as its SNR after integration will be statistically the same as for the single-pulse case. In NR processing the same samples used for the MIMO case are summed coherently and their power compared with the threshold. In this case the detection decision is now given by
The Rephased Coherent Netted Radar (RPNR): This system again uses the same samples as the previous cases, but performs a rephasing of the vectors according to the exact position of the target in order to maximize the SNR (Fig. 4) and subsequently the achieved performance. In other words, the phases of the signals in Fig.3 have been appropriately realigned, so the amplitude of their sum is as great as possible. This approach is extremely challenging and perhaps impossible in practice as it exploits a priori information about the exact location of the target (assumed to be pointlike); however, it provides the upper bound limit for the performance as it maximizes the SNR. The decision rule in
Fig.4 The rephased coherent netted radar integration. this case is
therefore where is the phase of the desired signal only, when present. This system approach is examined as it provides a reference against which the losses of the other systems can be compared and hence may be regarded as an upper benchmark. Decentralized Radar Network (DRN): In this section a different suboptimum algorithm is applied to the same distribution of nodes in the radar network. The algorithm is characterized by a double threshold for detection. This is a two-stage approach to detection and is termed a decentralized radar network (DRN). The use of this form of processing technique represents an alternative to MIMO processing for radar networks. The radar network operates with the same geometry as the MIMO and NR systems. This is a suboptimum way of processing the incoming signals, where the radar network is assumed to consist of all the possible mono/bistatic radars working separately in the initial stage and where all results are subsequently fused together. The processing therefore consists of two parts: (1) detection is extracted from the signals for each of the mono/bistatic cases (i.e., in decentralized preprocessing), and (2) all the decisions are jointly fused, so the system can provide a final output.
False-Alarm Rate (FAR): Here we considered the case where the probability of false alarm (Pfa) is evaluated as a function of threshold value for the case where only white Gaussian noise with zeromean value and normalized variance is input to the receivers. In the systems under investigation there is a false alarm when
in the MIMO case in the NR and RPNR cases, and
in the DRN case, where
From a mathematical perspective, it is then clear that, even if the MIMOâ„¢ and NRâ„¢ noise samples have the same mean values, an extra variance has to be considered in the probability density function (pdf) of the noise power for the NR. This extra variance leads to poorer performance of the NR systems for a given FAR. The DRN cannot be compared directly since its processing provides a thresholding at the output of each single node only. Figures 5â€œ6 show the threshold required to achieve a chosen FAR for a numbers of processed signals. The advantage achieved by incoherent systems is due to reduction in the variability in the total received signal, hence enabling a lower threshold to be set; in other words, the total noise power contributing to the detection decision is lower in the incoherent systems than in the coherent ones (e.g., they require a threshold of an additional 3â€œ8 dB to achieve a performance level equivalent to that of MIMO). The reduced threshold set with incoherent processing provides, as seen in the next section, an increased sensitivity when used for detection. It is also evident that for MIMO and NR systems, the higher the number of nodes, the higher the threshold, the opposite occurs when using a decentralized algorithm. Note that for the decentralized case the threshold is set at the single node, while in the centralized case it is determined for the overall set of received signals.
Fig.5 MIMO Pfa performance.
Fig.6 NR Pfa performance.
Probability of Detection ( P d ) : In this section the performance of MIMO processing in detection is analyzed and compared to those of the other systems. The detection probability is computed for a number of multistatic RCS models so as to obtain a range of performances that might be expected for a variety of scenarios. The target models employed are (1) Swerling II, (2) Swerling IV, (3) Ricean, and (4) a perfectly conducting sphere. The latter model can be considered to be a Swerling 0 model for the case of relatively closely located nodes. When a only single pulse is considered, the two Swerling models become the Swerling I and III cases, respectively. The model used for the target RCS takes into account the degree of independence in the acquired samples at differing viewing angles, which may be separated by perhaps only a few milliradians . As a consequence, the target RCS at a particular receiver can differ from that at the other nodes by several decibels. This characteristic can be a significant factor in determining the resulting detection performance, which will also depend on the processing approach employed. The results are presented in two ways: (1) maintaining the RCS model constant and therefore showing the difference in detection between the systems and the number of nodes in the systems (keeping the ERP constant) and (2) maintaining the number of nodes fixed while varying the RCS model as well as the processing approach. In all the results we keep the FAR equal to for the overall system. Jamming Tolerance: In this section the effects on performance are considered when one of the receivers of the network is jammed with a fully matched transmission, that is, when the received signal at the qth receiver is expressed as
and is the threshold after matched filtering of for the mth waveform at the qth receiver. This represents something of a worst-case scenario but is a useful and illustrative benchmark. Figures 7 and 8 show the FAR performance when one of the N receivers is jammed. This means that, due to the collocation of transmitters and receivers, M nodes (from one to five, respectively) are being jammed. The jammer is here assumed to be 40 dB over the noise level. No ECCM has been considered and thresholds are kept fixed at nodes, so applying any sort of ECCM algorithm will provide a higher level of tolerance. These losses are almost of the same magnitude as that of the jammer, and a reduction in performance under jamming is evident for all the cases considered. This drop is particularly severe in all the centralized processing systems, and it is necessary to increase the threshold of the jamming power to ensure the same FAR performance. In each case the detection performance will be severely degraded. However, Fig. 9 shows that for DRN using a 50% criterion it is sufficient to increase the (single-node) threshold of just a few decibels to recover the loss in performance. This is due to the decentralized processing where the rest of the nodes of the network are in effect used to mitigate the jamming. Finally, Figs. 10 and 11 show that the minimum loss criterion performs much worse than the 50% criterion, especially in networks consisting of a large number of nodes.
Fig.7 MIMO false-alarm rate (FAR), one jammed receiver.
Fig.8 NR FAR, one jammed receiver.
Fig.9 DRN FAR, one jammed receiver, 50% criterion.
Fig.10 DRN global versus single-node FAR, one jammed receiver, 50% criterion.
Fig.11 DRN global versus single-node FAR, one jammed receiver, ML criterion.
In this section the sensitivity of each processing approach and subsequent coverage is computed as a function of the number of nodes in the radar network. Therefore, the received power and the SNR levels for a target in a particular geometry can be examined. It is recalled that a constant ERP is supplied to the radar network regardless of the number of transmitters. This allows for a straightforward comparison of performance.
In this chapter the properties and the characteristics of four processing approaches using different algorithms for data processing in a radar network have been examined. The processing approaches exhibit considerable variability in performance with respect to FAR, detection, jamming tolerance, and coverage. Incoherent systems have an advantage over coherent systems as they reduce the overall power of noise after processing due to the beneficial effect they have on the statistical distribution of the noise model chosen for clutter. The decentralized radar networks show increased tolerance to jamming without any of the countermeasures commonly adopted. These systems have also an advantage over the centralized systems since they require a smaller bandwidth for transmitting the information to the decision unit, and this is an important implementation consideration. It has been shown that the performance of radar networks can be superior to that of the monostatic case, when compared on a fair basis of constant transmit power for a variety of processing approaches. In addition, these processing approaches have their own varying performance levels. For example, when working incoherently, they can outperform a simple coherent approach. This is because the phases of the incoming signals are totally uncorrelated and hence the coherent sum is a statistically disruptive event. This is true not only for noise-like targets, such as the Swerling models, but also for targets with a constant amplitude and random phase, as in the case of a sphere. In addition, they perform at a level that is a few decibels poorer than the theoretical upper bound limit and therefore are a valid alternative for implementation in real systems. They are also attractive as they have simpler hardware and processing requirements.
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