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The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We do so deriving Bayesian recursions that describe the evolution with time of a posteriori densities of the unknown parameters and data. Unlike in the above cited paper, wherein one could evaluate the exact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximations for the receivers that are based on Sequential Monte Carlo (SMC) methods ("particle filtering"). Simulation results, referring to a code-divisin multiple-access (CDMA) system, are presented to illustrate the theory. Index Terms--Bayesian recursions, multiuser detection, particle filtering, random-set theory.

In this work we consider a multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) system, which senses multiple spatial directions and serves multiple users. Upon resorting to an orthogonal frequency division multiplexing (OFDM) transmission format and a differential phase shift keying (DPSK) modulation, we study the design of the radiated waveforms and of the receive filters employed by the radar and the users. The approach is communication-centric, in the sense that a radar-oriented objective is optimized under constraints on the average transmit power, the power leakage towards specific directions, and the error rate of each user, thus safeguarding the communication quality of service (QoS). We adopt a unified design approach allowing a broad family of radar objectives, including both estimation- and detection-oriented merit functions. We devise a suboptimal solution based on alternating optimization of the involved variables, a convex restriction of the feasible search set, and minorization-maximization, offering a single algorithm for all of the radar merit functions in the considered family. Finally, the performance is inspected through numerical examples. [ABSTRACT FROM AUTHOR]

The interplay among the rank of optimized space-time code, the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path were explored to gain insight into a multiple-input multiple-output (MIMO) detection problem. The results confirmed the existence of an inherent tradeoff between diversity and integration and absence of uniformly optimum waveform design strategy.

The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair signal-observation forms a hidden Markov model (HMM)), a sequential procedure is proposed, wherein the detection part is a sequential probability ratio test (SPRT) and the estimation part relies upon a maximum a posteriori probability (MAP) criterion, gated by the detection stage (the parameter to be estimated is the trajectory of the state evolution of the system itself). A thorough analysis of the asymptotic behavior of the test in this new scenario is given, and sufficient conditions for its asymptotic optimality are stated, i.e., for almost sure minimization of the stopping time and for (first-order) minimization of any moment of its distribution. An application to radar surveillance problems is also examined. Index Terms--Asymptotic optimality, hidden Markov models (HMM), sequential detection and estimation, sequential probability ratio test (SPRT).

The general problem of joint sequential target detection and estimation is considered for multiframe surveillance radar systems. Numerical experiments are performed in order to understand the interplay between sensor-target parameters and system performances and also to quantify the gain with respect to other fixed-sample procedures.

This paper addresses the problem of early detection of K [greater than or equal to] 1 multiple moving targets in radar systems through the use of track-before-detect (TBD) techniques. At first, assuming prior knowledge of K, a binary generalized likelihood ratio test (GLRT) is derived, which shows that the multi-target TBD problem can be regarded as a K-path trellis search. Since optimal implementation of the GLRT has a nonlinear complexity either in the number of targets or in the number of integrated frames, suboptimum algorithms are investigated which allow to trade better estimation and tracking accuracy for a much lower implementation complexity. Next, the TBD problem with K unknown is discussed and a novel multi-hypothesis test strategy is derived as the solution to a constrained optimization problem, which subsumes the conventional binary GLRT as the special case of known K. Finally, numerical examples are provided to assess and compare the performances of the proposed TBD procedures.

In random-access communication systems, the number of active users varies with time, and has considerable bearing on receiver's performance. Thus, techniques aimed at identifying not only the information transmitted, but also that number, play a central role in those systems. An example of application of these techniques can be found in multiuser detection (MUD). In typical MUD analyses, receivers are based on the assumption that the number of active users is constant and known at the receiver, and coincides with the maximum number of users entitled to access the system. This assumption is often overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of a number of users larger than the real one may impair performance. The main goal of this paper is to introduce a general approach to the problem of identifying active users and estimating their parameters and data in a random-access system where users are continuously entering and leaving the system. The tool whose use we advocate is Random-Set Theory (RST): applying this, we derive optimum receivers in an environment where the set of transmitters comprises an unknown number of elements. In addition, we can derive Bayesian-filter equations which describe the evolution with ti me of the a posteriori probability (APP) density of the unknown user parameters, and use this density to derive optimum detectors. In this paper, we restrict ourselves to interferer identification and data detection, while in a companion paper we shall examine the more complex problem of estimating users' parameters. Index Terms--Multiuser detection, random set theory, Bayesian recursions.

This paper considers the problem of multiple-input multiple-output (MIMO) radars employing space-time coding (STC) to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the first is based on the classical Chernoff bound, the second is an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well-known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.

The performance of user cooperation in the uplink of a synchronous direct-sequence (DS) code-division multiple-access (CDMA) cellular network is analyzed by using nonorthogonal spreading codes. A performance assessment is undertaken to analyze the impact of the multiple-access interference on the proposed cooperative strategies under different scenarios and system assumptions.

A new class of receivers based on widely linear data processing is proposed for data detection in communication systems affected by improper complex noise. It is shown that the improved receivers outperform the conventional ones both in terms of the error probability and of the capacity to cope with the power disparities that the fading channel induces on the data streams transmitted by different antennas.

We focus on the synthesis and the analysis of recursive receivers for direct-sequence code-division multiple-access systems aimed at achieving satisfactory performance at the price of a moderate computational complexity. At the analysis stage, some interesting properties shared by the proposed procedures are proven. Finally, the performance assessment shows that the new schemes are superior to the linear detectors, and some of them achieve a bit-error rate close to that of the optimum receiver. Index Terms--Direct-sequence code-division multiple-access (DS-CDMA) systems, iterative detection, multiuser detection.

In this paper we present a family of track-before-detect (TBD) procedures for early detection of moving targets from airborne radars. Upon a sectorization of the coverage area, the received echoes are jointly processed in the azimuth-range-Doppler domain and in the time domain through a Viterbi-like algorithm that exploits the physically admissible target transitions between successive illuminations, in order to collect all of the energy back-scattered during the time on target (TOT). A reduced-complexity implementation is derived assuming, at the design stage, that the target does not change resolution cell during the TOT in each scan. The constant false alarm rate (CFAR) constraint is also englobed in the proposed procedures as well as the possibility of working with quantized data. Simulation results show that the proposed algorithms have good detection and tracking capabilities even for high target velocities and low quantization rates.

Formulas for the modified Cramer-Rao bounds (CRBs) are obtained under the assumption that the spreading codes can be modeled as random nuisance parameters. Numerical examples showing the impact of the training length, signal-to-noise ratio (SNR) and the number of active users on the CRB are also reported and commented upon.

The problem of blind multiuser detection in a direct sequence code division multiple access (DS/CDMA) multiantenna systems is discussed. The design strategy and performance evaluation technique to space-time coded system are proposed.

In iterative data-detection and channel-estimation algorithms, the channel estimator and the data detector recursively exchange information in order to improve the system performance. While a vast bulk of the available literature demonstrates the merits of iterative schemes through computer simulations, in this paper analytical results on the performance of an iterative detection/estimation scheme are presented. In particular, this paper focus is on uncoded systems and both the situations that the receiver and the transmitter are equlpped with either a single antenna or multiple antennas are considered. With regard to the channel estimator, the analysis considers both the minimum mean square error and the maximum likelihood channel estimate, while, with regard to the data detector, linear receiver interfaces are considered. Closed-form formulas are given for the channel-estimation mean-square error and for its Cramer-Rao bound, as well as for the error probability of the data detector. Moreover, the problem of the optimal choice of the length of the training sequence is also addressed. Overall, results show that the considered iterative strategy achieves excellent performance and permits, at the price of some complexity increase, the use of very short training sequences without incurring any performance loss. Finally, computer simulations reveal that the experimental results are in perfect agreement with those predicted by the theoretical analysis. Index Terms--Channel estimation, Cramer-Rao bound (CRB), data detection, multiantenna systems, wireless communication.

In this paper, the problem of subspace-based blind adaptive multi-user detection in multi-rate direct-sequence code-division multiple-access (DS.CDMA) systems adopting short (periodic) spreading codes is considered. The solution that we propose is based on the well-known formulation of the linear minimum mean-squared error and decorrelating detectors in terms of signal subspace parameters. Since in a multi-rate scenario the correlation properties of the observable (and, hence, the signal subspace parameters) are periodically time-varying, classical subspace tracking algorithms, which assume that the subspace to be tracked is time-invariant or slowly time-varying, are shown to be not useful in this situation. A new recursive cyclic subspace tracking algorithm is thus developed. This procedure, which is based on a generalization of the PASTd algorithm, is able to capture the periodical variations of the signal subspace, and thus enables subspace-based blind adaptive multi-user detection in multi-rate CDMA systems. The proposed algorithm has a smaller computational complexity than the recently developed cyclic recursive-least-squares procedure, and, as numerical results confirm, is capable of providing very satisfactory performance. Index Terms--Blind adaptive multi-user detection, cyclic algorithms, direct-sequence code-division multiple-access (DS-CDMA) systems, multi-rate CDMA, subspace tracking.

The problem of blind adaptive joint multiuser detection and equalization in direct-sequence code division multiple access (DS/CDMA) systems operating on fading dispersive channels is examined and discussed.

Recently, a new class of linear multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation has been introduced. Unlike classical decorrelating and minimum mean-square error linear multiuser detectors, the new receivers exploit the information contained in the pseudoautocorrelation of the observables, and are, thus, capable of achieving much better performance. In this letter, we present new results on the performance analysis of this class of new receivers. In particular, with reference to a CDMA system with deterministic spreading codes, we show that the new receivers outperform the classical ones in terms of both error probability and near-far resistance. With regard, instead, to CDMA systems with random spreading, we compute the average system near-far resistance, showing that the new receivers can accommodate twice the number of users accommodated by the classical linear multiuser receivers. Index Terms--Code-division multiple access (CDMA), improper random access, multiuser detection, performance analysis, random code-division multiple access (CDMA).

A reconfigurable intelligent surface (RIS) is a nearly-passive flat layer made of inexpensive elements that can add a tunable phase shift to the impinging electromagnetic wave and are controlled by a low-power electronic circuit. This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar. At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the radar transmitter and one close to the radar receiver) and subsumes both a monostatic and a bistatic radar configuration with or without a line-of-sight view of the prospective target. Upon resorting to a generalized likelihood ratio test (GLRT), the design of the phase shifts introduced by the RIS elements is formulated as the maximization of the probability of detection in the location under inspection for a fixed probability of false alarm, and suitable optimization algorithms are proposed. The performance analysis shows the benefits granted by the presence of the RISs and shed light on the interplay among the key system parameters, such as the radar-RIS distance, the RIS size, and the location of the prospective target. A major finding is that the RISs should be better deployed in the near-field of the radar arrays at both the transmit and the receive side. The paper is concluded by discussing some open problems and foreseen applications. [ABSTRACT FROM AUTHOR]

In this work, we study the joint detection and localization of multiple delay- and Doppler-spread targets through an opportunistic radar exploiting mmWave communication signals. The problem is formulated as the identification of an unknown number of active subspaces in a large family of subspaces, accounting for the possible positions of potential targets in the delay-Doppler domain: the resulting testing problem is composite and multi-hypothesis. At first, we derive a solution based on the generalized information criterion (GIC), whose complexity is however prohibitive; then, we propose an approximated form of the GIC-based receiver and derive two iterative data-adaptive strategies, both extracting and eliminating the superimposed back-scattered subspace signals one-by-one. Leveraging the IEEE 802.11ad standard, a short-range low-mobility application is discussed to validate the merits of the proposed procedures in terms of detection and localization capabilities, robustness to multi-target interference, and achievable resolution. [ABSTRACT FROM AUTHOR]

Abstract The number of active users, their timing offsets, and their (possibly dispersive) channels with the access point are performance-critical parameters for wireless code division multiple access (CDMA). Estimating them as accurately as possible using as short as possible training sequences can markedly improve error performance as well as the capacity of CDMA systems. The fresh look advocated here permeates benefits from recent advances in variable selection and compressive sampling approaches to multiuser communications by casting estimation of these parameters as a sparse linear regression problem. Novel estimators are developed by exploiting two forms of sparsity present: the first emerging from user (in)activity, and the second from the uncertainty on user delays and channel taps. Simulated tests demonstrate a large gain in performance when sparsity-aware estimators of CDMA parameters are compared to sparsity-agnostic standard least-squares-based alternatives.

In this work, we exploit the sector level sweep of the IEEE 802.11ad communication standard to implement an opportunistic radar at mmWaves and derive an adaptive procedure for detecting multiple echoes and estimating their parameters (namely, amplitude, delay, and Doppler shift). The proposed detector/estimator extracts the prospective echoes one-by-one from the received signal, after removing the interference caused by the previously detected (stronger) reverberations from the environment. Examples are provided to assess the system performance, also in comparison with other detectors/estimators and the Cramér-Rao bounds on the localization accuracy. Results indicate that the proposed method is robust against the interference induced by the imperfect ambiguity function and can achieve a delay resolution approximately equal to the inverse of the signal bandwidth, corresponding to a range offset of about 17 cm. Instead, the Doppler resolution is inherently limited by the short duration of the data packet and, in the most favorable case, is approximately 3.26 KHz, corresponding to a relative radial velocity off-set of about 8.16 m/s for a wavelength of 5 mm. [ABSTRACT FROM AUTHOR]

This paper considers the uplink of a massive MIMO communication system using 5G New Radio-compliant multiple access, which has to co-exist with a radar system using the same frequency band. A system model taking into account the reverberation (clutter) produced by the radar system onto the massive MIMO receiver is proposed. In this scenario, several receivers for uplink channel estimation and data detection are proposed, ranging from the simple channel-matched beamformer to the zero-forcing and linear minimum mean square error receivers for clutter disturbance rejection, under the two opposite situations of perfectly known and completely unknown clutter covariance. A theoretical analysis is also provided, deriving a lower bound on the achievable uplink spectral efficiency and the mutual information between the input Gaussian-encoded symbols and the observables available at the communication receiver of the cellular massive MIMO system: regarding the latter, in particular, it is shown that, in the large antenna number regime, and under the assumption of perfect channel state information (CSI), the effect of radar clutter at the base station is suppressed and single-user capacity may be restored. Numerical results, illustrating the performance of the proposed detection schemes, confirm the findings of the theoretical analysis, and permit quantifying the system robustness to clutter effect for increasing number of antennas at the base station. [ABSTRACT FROM AUTHOR]

In this paper, we consider an un-cooperative spectrum sharing scenario, where a radar system is to be overlaid to a pre-existing wireless communication system. Given the order of magnitude of the transmitted powers in play, we focus on the issue of interference mitigation at the communication receiver. We explicitly account for the reverberation produced by the (typically high-power) radar transmitter whose signal hits scattering centers (whether targets or clutter) producing interference onto the communication receiver, which is assumed to operate in an un-synchronized and un-coordinated scenario. We first show that the receiver design amounts to solve a joint (non-convex) interference removal and data demodulation problem. Next, we introduce two algorithms exploiting sparsity of a proper representation of the interference and the vector containing demodulation errors of the data block. The first algorithm is basically a relaxed constrained atomic norm minimization, while the latter relies on a two-stage processing structure and is based on alternating minimization. The merits of these algorithms are demonstrated through extensive simulations; interestingly, the two-stage alternating minimization algorithm turns out to achieve satisfactory performance with moderate computational complexity. [ABSTRACT FROM AUTHOR]

Increased amounts of bandwidth are required to guarantee both high-quality/high-rate wireless services (4G and 5G) and reliable sensing capabilities, such as for automotive radar, air traffic control, earth geophysical monitoring, and security applications. Therefore, coexistence between radar and communication systems using overlapping bandwidths has come to be a primary investigation field in recent years. Various signal processing techniques, such as interference mitigation, precoding or spatial separation, and waveform design, allow both radar and communications to share the spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we consider a pulse radar and study the tradeoff between integration time and scan rate for diverse target scattering models. At the design stage, we optimize the available degrees of freedom (namely, pulse train length and detection threshold) so as to maximize the detection rate, defined as the average number of detections from the target per unit of time, subject to a constraint on the false alarm rate, which is the average number of false alarms from the monitored area per unit of time. This objective function allows to carefully balance the contrasting needs for a large probability of detection (achievable through a large dwell time) and a short scan time. Closed-form solutions are provided for Swerling's Cases 1 and 3 target fluctuation and for the Marcum nonfluctuating model, while, for the Swerling's Cases 2 and 4, the solution is found with the aid of computer simulation. A thorough performance analysis is given to show the achievable tradeoffs among the principal system parameters under the different target models. [ABSTRACT FROM AUTHOR]

This paper handles the problem of optimizing the scanning policy of a surveillance system in the presence of Rayleigh targets in a mixture of K-distributed clutter and Gaussian noise. Adopting the detection rate (DR) and false alarm rate (FAR) as performance measures, we show that the said optimization amounts to solving a constrained DR maximization, wherein the free parameters are the transmit beamwidth, the dwell time, and the detection threshold, whereas the constraints concern the maximum FAR and time on target. A thorough performance assessment is offered, aimed at eliciting the influence of the signal-to-noise and clutter-to-noise ratios, the clutter shape parameter, and the rate of change of the target response. The results indicate that, although a uniformly optimum transmit policy does not exist, some trends can be devised, which appears of particular relevance especially for systems that can avail themselves of some degree of cognition. [ABSTRACT FROM AUTHOR]

This paper considers the joint design of a multiple-input multiple-output (MIMO) radar with co-located antennas and a MIMO communication system. The degrees of freedom under the designer's control are the waveforms transmitted by the radar transmit array, the filter at the radar array and the code-book employed by the communication system to form its space-time code matrix. Two formulations of the spectrum sharing problem are proposed. First, the design problem is stated as the constrained maximization of the signal-to-interference-plus-noise ratio at the radar receiver, where interference is due to both clutter and the coexistence structure, and the constraints concern both the similarity with a standard radar waveform and the rate achievable by the communication system, on top of those on the transmit energy. The resulting problem is nonconvex, but a reduced-complexity iterative algorithm, based on iterative alternating maximization of three suitably designed subproblems, is proposed and analyzed. In addition, the constrained maximization of the communication rate is also investigated. The convergence of all the devised algorithms is guaranteed. Finally, a thorough performance assessment is presented, aimed at showing the merits of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the feasibility of an opportunistic radar, which exploits the probing signals transmitted during the sector level sweep of the IEEE 802.11ad beamforming training protocol. Several solutions are presented to detect the presence of prospective obstacles and estimate their position, radial velocity, and backscattered signal amplitude, which differ in the amount of prior information as to the transmitted signal and the channel fluctuation. Also, we derive the Cramér–Rao bound as a benchmark for the proposed estimators: The derivation of these bounds is per se relevant, as it generalizes classical results to the case where the echo is not entirely contained in the observation window. Numerical examples are provided to assess performance of the proposed solutions. The results indicate that the close-to-one detection probability is achievable up to 90 m with a probability of false alarm of 1e-4 and Swerling-I target fluctuation; in this region, the target delay is estimated with an accuracy smaller than the symbol interval (corresponding to a range resolution smaller than 10 cm) with probability close to one, while the velocity estimate is generally quite poor as a consequence of the very short duration of the probing signal. [ABSTRACT FROM AUTHOR]

This paper proposes computationally efficient algorithms to maximize the energy efficiency in multicarrier wireless interference networks, by a suitable allocation of the system radio resources, namely, the transmit powers and subcarrier assignment. The problem is formulated as the maximization of the system global energy efficiency subject to both maximum power and minimum rate constraints. This leads to a challenging nonconvex fractional problem, which is tackled through an interplay of fractional programming, learning, and game theory. The proposed algorithmic framework is provably convergent and has a complexity linear in both the number of users and subcarriers, whereas other available solutions can only guarantee a polynomial complexity in the number of users and subcarriers. Numerical results show that the proposed method performs similarly as other, more complex, algorithms. [ABSTRACT FROM PUBLISHER]

Most existing approaches to coexisting communication/radar systems assume that the radar and communication systems are coordinated, i.e., they share information, such as relative position, transmitted waveforms, and channel state. In this paper, we consider an uncoordinated scenario where a communication receiver is to operate in the presence of a number of radars, of which only a subset may be active, which poses the problem of estimating the active waveforms and the relevant parameters thereof, so as to cancel them prior to demodulation. Two algorithms are proposed for such a joint waveform estimation/data demodulation problem, both exploiting sparsity of a proper representation of the interference and of the vector containing the errors of the data block, so as to implement an iterative joint interference removal/data demodulation process. The former algorithm is based on classical on-grid compressed sensing, whereas the latter forces an atomic norm (AN) constraint: In both cases the radar parameters and the communication demodulation errors can be estimated by solving a convex problem. We also propose a way to improve the efficiency of the AN-based algorithm. The performance of these algorithms are demonstrated through extensive simulations, taking into account a variety of conditions concerning both the interferers and the respective channel states. [ABSTRACT FROM PUBLISHER]

The focus of this paper is on coexistence between a communication system and a pulsed radar sharing the same bandwidth. Based on the fact that the interference generated by the radar onto the communication receiver is intermittent and depends on the density of scattering objects (such as, e.g., targets), we first show that the communication system is equivalent to a set of independent parallel channels, whereby precoding on each channel can be introduced as a new degree of freedom. We introduce a new figure of merit, named the compound rate, which is a convex combination of rates with and without interference, to be optimized under constraints concerning the signal-to-interference-plus-noise ratio (including signal-dependent interference due to clutter) experienced by the radar and obviously the powers emitted by the two systems: the degrees of freedom are the radar waveform and the aforementioned encoding matrix for the communication symbols. We provide closed-form solutions for the optimum transmit policies for both systems under two basic models for the scattering produced by the radar onto the communication receiver, and account for possible correlation of the signal-independent fraction of the interference impinging on the radar. We also discuss the region of the achievable communication rates with and without interference. A thorough performance assessment shows the potentials and the limitations of the proposed co-existing architecture. [ABSTRACT FROM AUTHOR]

In this paper, we consider a surveillance radar equipped with an electronically scanned antenna and study the performance of a two-step sequential detection procedure, where, for each resolution cell, a second observation is taken if a reliable decision cannot be made after the first one. At the design stage, we optimize the available degrees of freedom (namely, dwell time and detection thresholds) so as to maximize the detection rate (DR), defined as the average number of detections from a target per unit of time, under a constraint on the false alarm rate (FAR), which is the average number of false alarms per unit of time from the inspected area. This is motived by the fact that DR and FAR, beside of being per se meaningful figures of merit for parameter tuning, allow a fair performance comparison among detection strategies with different scanning policies. Examples are presented to illustrate the effects of this design philosophy under the two relevant situations of a slowly fluctuating and a fast-fluctuating target response, also in the presence of clutter. [ABSTRACT FROM AUTHOR]