Generalized Likelihood Ratio Test Receiver Research Articles

Design of Optimal Noncoherent Constellations for SIMO Systems

In this paper, we consider a single-input multiple-output (SIMO) system, in which a single-antenna transmitter communicates with a receiver having multiple antennas. It is assumed that the channel coefficients keep constant during two consecutive time slots, after which they become new independent values. For such a system, we focus on the concept of uniquely factorable constellations (UFCs) in the design of noncoherent coding schemes under two communication scenarios. The first scenario is the massive SIMO system, in which only the first and second order channel statistical information is available. The second is the traditional Rayleigh fading SIMO system. First, parameterized massive UFC (MUFC) and unitary UFC (UUFC) are designed for each scenario. It is proved that these designs ensure the unique identification of the transmitted signals when there is no additive Gaussian white noise. Second, using the Riemannian distance (RD) metric for the RD-based detector and coding gain criterion for generalized likelihood ratio test receiver, the optimal MUFCs and UUFCs of various sizes are constructed, respectively. Finally, we exploit the structures of our proposed designs to reduce the decoding complexities compared to the exhaustive search methods. Comprehensive computer simulations show that our proposed schemes outperform the current designs in literature.

New insights into time synchronization of MIMO systems without and with interference

Abstract The time synchronization of (M × N) MIMO systems has been studied this last fifteen years, for both single-carrier (SC) and multi-carriers links. Without any interference, most of the available receivers assume orthogonal sequences. With interference, the current most powerful receiver is a generalized likelihood ratio test (GLRT) receiver, assuming unknown, stationary, circular, temporally white and spatially colored Gaussian noise. However, this receiver is more complex than its non-GLRT counterparts, which, unfortunately, do not perform as well in most cases. In this context, the purpose of this paper is to get new insights into the time synchronization of SC MIMO links, both without and with interference, in order to overcome the limitations of the available receivers. In the absence of interference, the MIMO GLRT receiver is computed and compared to the existing ones in a unified framework, enlightening its better performance. In the presence of interference, as the complexity is an important issue in practice, several ways to decrease the complexity of the available GLRT receiver while keeping its performance are proposed, enlightening the great practical interest of the proposed schemes. Finally, the optimization of the number of transmit antennas is investigated, enlightening the existence of an optimal value of M depending on the channel matrix.

GLRT Detector in Single Frequency Multi-static Passive Radar Systems

The target detection problem in multi-static passive radar systems (MS-PRS) is investigated, where multiple transmitters operate at a single frequency and a single multi-antenna radar receiver processes the received signals. In contrast to multi-frequency MS-PRS, the detector design is challenging due to the fact that the detector sees a mixture of transmitted signals which may not be separately treated. We propose the design of generalized likelihood ratio test (GLRT) receivers to optimize the detection performance. The beamformers at the radar receiver are optimized so that the received signals can be seen as statistically independent signals from multiple reference channels and a surveillance channel. The detector optimization problem is accurately approximated with a convex optimization algorithm. It is analytically shown that the performance of the proposed GLRT receiver approaches that of the active radar. Computer simulations verify the analytical results.

Least Square Error Detection for Noncoherent Cooperative Relay Systems

In this paper, noncoherent cooperative amplify-and-forward (AF) half-duplex relay systems are considered. For such systems, an asymptotic formula of pairwise error probability (PEP) for the least square error (LSE) detector is derived by using the perturbation theory on the eigenvalues. The result shows that the full-diversity-gain function mimics coherent cooperative AF half-duplex relay systems, whereas the coding gain function mimics noncoherent multiple-input-multiple-output (MIMO) systems. In addition, it is proved that, for any given nonzero received signal, the unique blind identification of both the equivalent channel and the transmitted signals in a noise-free case is equivalent to full diversity with the LSE detector in a Gaussian noisy environment. In particular, for the noncoherent AF half-duplex protocol with three nodes, a full-diversity unitary diagonal distributed space-time block code (STBC) is designed by utilizing the full-diversity criterion established in this paper and recently developed uniquely factorable constellation. Furthermore, the generalized likelihood ratio test receiver is derived for this specific coded protocol. Simulation results show that the code presented in this paper substantially outperforms the differential code and the optimally precoded training scheme in the current literature.

Non-Coherent Amplify-and-Forward Generalized Likelihood Ratio Test Receiver

This paper proposes a simple non-coherent amplify-and-forward receiver for the relay channel and evaluates its diversity performance for Rayleigh fading channels. We use the generalized likelihood ratio test to obtain the decision rule in closed form, independent of the fading distribution. The receiver is developed for M-ary orthogonal signals and multiple relays. The only side information required at the destination is the average noise energy at the receiver; no statistical knowledge of the channel gains is needed. We develop closed-form upper and lower bounds on the probability of error of this receiver for the case of binary signaling with a single relay and show that this receiver achieves near full diversity, with the probability of error decreasing with increasing signal-to-noise ratio (SNR) as log2(SNR)/ SNR2 for large SNR. Additional results obtained by simulation demonstrate increasing diversity gain with additional relays.

Noncoherent Communication in Multiple-Antenna Systems: Receiver Design and Codebook Construction

In this paper, we address the problem of space-time codebook design for noncoherent communications in multiple-antenna wireless systems. In contrast with other approaches, the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter, and the Gaussian observation noise is allowed to have an arbitrary correlation structure, known by the transmitter and the receiver. In order to handle the unknown deterministic space-time channel, a generalized likelihood ratio test (GLRT) receiver is considered. A new methodology for space-time codebook design under this noncoherent setup is proposed. It optimizes the probability of error of the GLRT receiver's detector in the high signal-to-noise ratio (SNR) regime by solving a high-dimensional nonlinear nonsmooth optimization problem in a two-step approach. First, a convex semidefinite programming (SDP) relaxation of the codebook design problem yields a rough estimate of the optimal codebook. This is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the space-time codewords. The results obtained through computer simulations illustrate the advantages of our method. For the specific case of spatio-temporal white observation noise, our codebook constructions replicate the performance of state-of-the-art known solutions. The main point here is that our methodology permits extending the codebook construction to any given correlated noise environment. The simulation results show good performance of these new designed codes in colored noise setups.

Generalized UWB transmitted reference systems

Maximum-likelihood (ML) and generalized likelihood ratio test (GLRT)-based data detection schemes for an ultra-wideband communication system are proposed and compared with the training-based (TB) transmitted reference (TR) receiver. The exact probability of error for the TB receiver and a lower bound for the ML and the GLRT receiver are provided in terms of a doubly noncentral F-variate. An optimization with respect to the integration interval length and the energy allocation between the training and the data symbols is investigated. Analytical and simulation results reveal that the proposed detection schemes provide significant performance improvements in terms of bit-error rate over the TB receiver structure.

Suboptimal, partially coherent detection over multipath/multichannel rayleigh fading

AbstractPartially coherent detection is studied as a problem of detection over diversity channels with unknown amplitudes, and known or perfectly estimated phases. The optimum composite hypothesis receiver is derived for binary, uniformly orthogonal signaling. Because of the high corn plexity of this optimum receiver, two suboptimal structures are considered a Linear equal gain combiner (LEGC) receiver and a quadratic coherent combiner, which is also a generalized likelihood ratio test (GLRT) receiver for this case. We examine the combiner output signal‐to‐noise ratio (SNR) for the two suboptimal receivers and show that this measure cannot be a performance comparison criterion for receivers of different orders. The exact performance of the GLRT receiver is evaluated in terms of the conditional, average and asymptotic bit error rates (BER), and graphical results are presented. An interesting result is that these BER expressions are obtained, for even and odd diversity orders, via different routes and that quadratic noncoherent detection represents a degenerate case of quadratic coherent detection with even diversity. The average BER of LEGC is exactly evaluated for dual diversity. LEGC and quadratic coherent combining are compared with respect to the asymptotic BEA and the exact BER for dual diversity. It is shown that LEGC is better in terms of the average BER in fading, while quadratic coherent combining is conditionally better whenever the signals received over different links have significantly different strengths.

Performance of the noncoherent biquadratic and GLRT receivers over two-path channels with known amplitudes and Rayleigh fading

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the receiver, optimum at low signal-to-noise ratios (SNR's), and the bilinear receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest. >

A GLRT-based spread-spectrum receiver for joint channel estimation and interference suppression

The author considers the problem of demodulating a direct-sequence (DS) spread-spectrum signal in the presence of narrowband interference and multipath. A receiver is considered that is based on the generalized likelihood-ratio test (GLRT), in which the interferer is modeled as an Nth-order circular Gaussian autoregressive (AR) process and the multipath channel is represented by a tapped-delay line. The maximum-likelihood joint estimator for the channel coefficients and interferer AR parameters is then derived. Analytical expressions for bit-error rate are presented for GLRT receiver, under the assumption of perfect estimates of the channel and interferer parameters. The performance of the GLRT receiver is compared to that of a DS receiver using a transversal equalizer. It is shown that the GLRT receiver consistently outperforms the equalizer-based receiver by 2-3 dB. The performance of an adaptive GLRT receiver is evaluated where the recursive least-squares algorithm is used to jointly estimate the interferer and channel parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>