Approximate Maximum Likelihood Detector Research Articles

SER Analysis for SWIPT-Enabled Differential Decode-and-Forward Relay Networks

In this article, we analyze the symbol error rate (SER) performance of the simultaneous wireless information and power transfer (SWIPT) enabled three-node differential decode-and-forward (DDF) relay networks, which adopt the power splitting (PS) protocol at the relay. The use of non-coherent differential modulation eliminates the need for sending training symbols to estimate the instantaneous channel state information (CSI) at all network nodes, and therefore improves the power efficiency, as compared with the coherent modulation. However, performance analysis results are not yet available for the state-of-the-art detectors such as the maximum-likelihood detector (MLD) and approximate MLD. Existing works rely on the Monte-Carlo simulation method to show the existence of an optimal PS ratio that minimizes the overall SER. In this work, we propose a near-optimal detector with linear complexity with respect to the modulation size. We derive an approximate SER expression and prove that the proposed detector achieves the full diversity order. Based on our expression, the optimal PS ratio can be accurately estimated without requiring any Monte-Carlo simulation. We also extend the proposed detector and its SER analysis for adopting the time switching (TS) protocol at the relay. Simulation results verify the effectiveness of our proposed detector and the accuracy of our SER results in various network scenarios for both PS and TS protocols.

MMSE One-Bit Precoding for MU-MIMO Systems With Enhanced Receive Processing

One-bit precoding is a recently proposed scheme that enables significant savings in hardware cost and power consumption for massive multiuser multiple-input–multiple-output systems. In this letter, a new minimum mean-square-error (MMSE) precoder is presented for both single- and multiple-antenna mobile stations with enhanced receive processing (ERP) capability. By exploiting the structure embedded in the formulated nonconvex optimization problem, a new algorithm is developed on the basis of a combination of the alternating minimization method and mathematical programming with equilibrium constraints. An approximate maximum likelihood detector is also proposed to collaborate with the MMSE-ERP precoder. Simulation results verify that our MMSE-ERP precoder can exploit the additional degrees of freedom in the general system model considered, resulting in significant performance gain compared with existing one-bit precoders.

An Approximate ML Detector for MIMO Channels Corrupted by Phase Noise

We consider the multiple-input multiple-output (MIMO) communication channel impaired by phase noises at both the transmitter and receiver. We focus on the maximum likelihood (ML) detection problem for uncoded single-carrier transmission. We derive an approximation of the likelihood function, based on which we propose an efficient detection algorithm. The proposed algorithm, named self-interference whitening (SIW), consists in: 1) estimating the self-interference caused by the phase noise perturbation; 2) whitening the said interference; and 3) detecting the transmitted vector. While the exact ML solution is computationally intractable, we construct a simulation-based lower bound on the error probability of ML detection. Leveraging this lower bound, we perform extensive numerical experiments demonstrating that SIW is, in most cases of interest, very close to optimal with moderate phase noise. More importantly and perhaps surprisingly, such near-ML performance can be achieved by applying only twice the nearest neighbor detection algorithm. In this sense, our results reveal a striking fact: near-ML detection of phase noise corrupted MIMO channels can be done as efficiently as for conventional MIMO channels without phase noise.

Maximum-Likelihood Detector for Differential Amplify-and-Forward Cooperative Networks

The exact maximum-likelihood (ML) detector for amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (DPSK) in Rayleigh fading is derived in a single-integral form, which serves as a benchmark for differential AF networks. Two algorithms are then developed to reduce the complexity of the ML detector. Specifically, the first algorithm can eliminate a number of candidates in the ML search, while causing no loss of optimality of ML detection. In high signal-to-noise ratios (SNRs), this algorithm almost surely identifies a single candidate that amounts to the ML estimate of the signal. For low to medium SNRs with multiple candidates determined, we then derive an accurate closed-form approximation for the integral involved in the likelihood function, which only requires a five-sample evaluation per symbol candidate. Finally, combining these algorithms, we propose a closed-form approximate ML detector, which achieves an almost identical bit-error-rate (BER) performance to the exact ML detector at practical complexity. In particular, it is shown that the proposed approximate ML detector is far less complex than the well-known diversity combiner in high SNRs, while achieving approximately 1.7-dB gain in the 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> BER when the relay is closer to the destination.

Exploiting temperature dependency in the detection of NQR signals

Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying land mines. Unfortunately, the practical use of NQR is restricted by the low signal-to-noise ratio (SNR), and the means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, an approximate maximum-likelihood detector (AML) is developed, exploiting the temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluation using both simulated and real NQR data indicate a significant gain in probability of accurate detection as compared with the current state-of-the-art approach.

EM-Based Multiuser Detection in Fast Fading Multipath Environments

We address the problem of multiuser detection in fast fading multipath environments for DS-CDMA systems. In fast fading scenarios, temporal variations of the channel cause significant performance degradation even with the Rake receiver. We use a previously introduced time-frequency (TF) Rake receiver based on a canonical formulation of the channel and signals to simultaneously combat fading and multipath effects. This receiver uses the Doppler spread caused by rapid time-varying channel as another means of diversity. In dealing with multiaccess interference and as an attempt to avoid the prohibitive computational complexity of the optimum maximum-likelihood (ML) detector, we use the expectation maximization (EM) algorithm to derive an approximate ML detector. The new detector turns out to have an iterative structure very similar to the well-known multistage detector with some extra parameters. At the two extreme values of these parameters, the EM detector reduces to either one-shot TF Rake or generalized multistage detector. For the intermediate values of the parameters, it combines the two estimates to obtain a better decision for the bits of the users. Because of using the EM algorithm, this detector has better convergence properties than the multistage detector; the bit estimates always converge, and if an appropriate initial vector is used, they converge to the global maximizer of the likelihood function. As a result, the new detector provides significantly improved performance while maintaining the low complexity of the multistage detector. Our simulation results confirm the expected performance improvements compared to the base case of the TF Rake as well as the multistage detector used with the TF Rake.

Recursive decision directed estimation of reflection coefficients for seismic data deconvolution

This paper concerns the problem of estimation of the location and intensity of reflections of a seismic wavelet. A recursive maximum a posteriori probability (MAP) algorithm is derived as an alternative to the maximum likelihood (ML) algorithm of Mendel and Kormylo. The MAP approach proposed here yields a suboptimal detector which is substantially different in details from the corresponding approximate ML detector of Mendel and Kormylo. Simulation studies are presented to show that the MAP detector performs as well as the ML detector and can yield comparable results with much less computational effort. A comparative study of both the MAP and ML detectors has been made via simulations which show some interesting differences in structure as well as performance.

Map Detection and Estimation of Seismic Reflection Coefficients

The paper is concerned with the problem of estimation of the location and intensity of reflections of a seismic wavelet. A recursive maximum a posteriori probability (MAP) algorithm is derived as an alternative to the maximum likelihood (ML) algorithm of Mendel and Kormylo. The MAP approach proposed here yields a suboptimal detector which is substantially different in details from the corresponding approximate ML detector of Mendel and Kormylo. Simulation studies are presented to show that the MAP detector performs equally well as the ML detector and can yield comparable results with much less computational effort.