Markov Chain Monte Carlo Detector Research Articles

A Capacity Achieving MIMO Detector Based on Stochastic Sampling

Spatial-multiplexing multiple-input multiple-output (MIMO) systems have been developed and enhanced over the past two decades. In particular, a great amount of effort has gone towards development of capacity achieving detectors with affordable computational complexity. The developed detectors may be broadly divided into two classes: (i) deterministic sampling, such as list sphere decoding detector; and (ii) stocastic sampling, such as those based on Markov chain Monte Carlo (MCMC) search schemes. This paper proposes a novel detection scheme that is based on stochastic sampling, but is fundamentally different from the MCMC detectors. While MCMC follows a set of sequential sampling steps, hence, the sample sets obtained are highly correlated, the method proposed in this paper takes stochastic samples that are completely independent. This new approach of stochastic sampling leads to a detector with significantly reduced complexity. It also allows reduction in the detector latency.

MCMC-Based Detection for Random Access With Preambles in MTC

Random access has been considered for machine-type communication (MTC). In particular, a random access scheme with a pool of preambles is widely studied, which is similar to multichannel ALOHA, to support a number of MTC devices. In this paper, we study optimal approaches for user activity detection in random access with preambles over fading channels. Since the computational complexity grows exponentially with the number of preambles, a low-complexity detector is derived using Markov chain Monte Carlo (MCMC) approaches that can approximately solve an optimal maximum a posteriori detection problem. The resulting MCMC detector can enjoy a trade-off between performance and complexity, while its complexity to obtain a sample is linearly proportional to the number of preambles. A performance analysis for optimal detection is also studied to see the optimal performance. Simulation results confirm that the MCMC detector performs better than compressive sensing-based approaches and can provide a near optimal performance under certain conditions with a reasonable computational complexity.

Achieving Near MAP Performance With an Excited Markov Chain Monte Carlo MIMO Detector

We introduce a revised derivation of the bitwise Markov Chain Monte Carlo (MCMC) multiple-input multiple-output (MIMO) detector. The new approach resolves the previously reported high SNR stalling problem of MCMC without the need for hybridization with another detector method or adding heuristic temperature scaling factors. Another common problem with MCMC algorithms is the unknown convergence time making predictable fixed-length implementations problematic. When an insufficient number of iterations are used on a slowly converging example, the output log likelihood ratios can be unstable and overconfident. Therefore, we develop a method to identify rare slowly converging runs and mitigate their degrading effects on the soft-output information. This improves forward-error-correcting code performance and removes a symptomatic error floor in bit error rate plots. Next, pseudo-convergence is identified with a novel way to visualize the internal behavior of the Gibbs sampler. An effective and efficient pseudo-convergence detection and escape strategy is suggested. Finally, the new excited MCMC (X-MCMC) detector is shown to have near maximum-a-posteriori performance even with challenging, realistic, and highly-correlated channels at the maximum MIMO sizes and modulation rates supported by the 802.11ac WiFi specification, $8\times 8$ MIMO 256 quadrature amplitude modulation.

Large-Scale MIMO Detection Using MCMC Approach With Blockwise Sampling

In this paper, a low-complexity approach for the large-scale (underdetermined) multiple-input multiple-output (MIMO) detection is proposed using the Markov chain Monte Carlo (MCMC) algorithm in conjunction with blockwise sampling. Klein’s algorithm is employed in each sub-system to draw multidimensional samples for an MCMC detector in iterative detection and decoding (IDD). From analysis, we find that the lattice reduction (LR) technique cannot improve the performance of the proposed MCMC-based approach under low-correlated channel environment. In addition, due to blockwise sampling, the proposed method exhibits a faster convergence speed when running a Markov chain and provides a near-optimal performance for the detection of underdetermined MIMO systems. Complexity analysis and simulation results show that the proposed approach outperforms the conventional LR-based Klein randomized successive interference cancellation (SIC) detection with a relatively low complexity.

An MCMC–MIMO Detector as a Stochastic Linear System Solver Using Successive Overrelexation

In this paper, we consider a Markov chain Monte Carlo (MCMC) algorithm using Gibbs sampling for signal detection in multiple input multiple output (MIMO) or code division multiple access (CDMA) systems. It is shown that the MCMC detector can be seen as a stochastic linear system solver. Based on this point of view, we generalize the MCMC detector using a relaxation factor that can improve the convergence rate. For the MCMC detector, since a faster convergence rate implies a lower computational complexity, it is important to have a faster convergence rate especially for large MIMO systems, which can also be achieved by optimizing the temperature parameter. While the optimal temperature parameter heavily depends on the signal-to-noise ratio (SNR), it is shown that a good relaxation factor can be found for wide range of the SNR and other parameters.

Stochastic Iterative MIMO Detection System: Algorithm and Hardware Design

In this paper, we propose a Stochastic iterative multiple-input multiple-output (SIM) detection system based on the Markov chain Monte Carlo (MCMC) method. To improve the detection performance, the Gibbs sampler of the MCMC detector in the SIM is updated by the decoded bits from a channel decoder directly. The channel decoder is part of the updating unit that generates the new samples in the MCMC updating process. We also implement the SIM in a fully parallel scheme, which achieves a high detection speed. As a case study, we have designed and synthesized a 128-parallel 4 $\times$ 4 16-QAM SIM system using a CMOS 130 nm technology with a core area of 1.98 mm $^{2}$ and 457K logic gates. The SIM detection system can achieve a throughput of 787.5Mbps with a frame error rate (FER) 10 $^{-3}$ at ${\rm E}_{b}/{\rm N}_{0}=7{\rm dB}$ , equaling the FER of a traditional iterative MIMO detection with four outer iterations.

Stochastic MIMO Detector Based on the Markov Chain Monte Carlo Algorithm

A stochastic computing framework for a Markov Chain Monte Carlo (MCMC) multiple-input-multiple-output (MIMO) detector is proposed, in which the arithmetic operations are implemented by simple logic structures. Specifically, we introduce two new techniques, namely a sliding window generator (SWG) and a log-likelihood ratio based updating method (LUM), to achieve an efficient design. The SWG utilizes the variance in stochastic computations to increase the transition probability of the MCMC detector, while the LUM reduces the hardware cost. As a case study, we design a fully-parallel stochastic MCMC detector for a 4 ×4 16-QAM MIMO system using 130 nm CMOS technology. The proposed detector achieves a throughput of 1.5 Gbps with only a 0.2 dB performance loss compared to a traditional floating-point detection method. Our design has a 30% better ratio of gate count to scaled throughput compared to other recent MIMO detectors.

Optimized Markov Chain Monte Carlo for Signal Detection in MIMO Systems: An Analysis of the Stationary Distribution and Mixing Time

In this paper we introduce an optimized Markov Chain Monte Carlo (MCMC) technique for solving the integer least-squares (ILS) problems, which include Maximum Likelihood (ML) detection in Multiple-Input Multiple-Output (MIMO) systems. Two factors contribute to the speed of finding the optimal solution by the MCMC detector: the probability of the optimal solution in the stationary distribution, and the mixing time of the MCMC detector. Firstly, we compute the optimal value of the "temperature" parameter, in the sense that the temperature has the desirable property that once the Markov chain has mixed to its stationary distribution, there is polynomially small probability ($1/\mbox{poly}(N)$, instead of exponentially small) of encountering the optimal solution. This temperature is shown to be at most $O(\sqrt{SNR}/\ln(N))$, where $SNR$ is the signal-to-noise ratio, and $N$ is the problem dimension. Secondly, we study the mixing time of the underlying Markov chain of the proposed MCMC detector. We find that, the mixing time of MCMC is closely related to whether there is a local minimum in the lattice structures of ILS problems. For some lattices without local minima, the mixing time of the Markov chain is independent of $SNR$, and grows polynomially in the problem dimension; for lattices with local minima, the mixing time grows unboundedly as $SNR$ grows, when the temperature is set, as in conventional wisdom, to be the standard deviation of noises. Our results suggest that, to ensure fast mixing for a fixed dimension $N$, the temperature for MCMC should instead be set as $\Omega(\sqrt{SNR})$ in general. Simulation results show that the optimized MCMC detector efficiently achieves approximately ML detection in MIMO systems having a huge number of transmit and receive dimensions.

Markov Chain Monte Carlo Detection for Frequency-Selective Channels Using List Channel Estimates

In this paper, we develop a statistical approach based on Markov chain Monte Carlo (MCMC) techniques for joint data detection and channel estimation over time-varying frequency-selective channels. The proposed detector, that we call MCMC with list channel estimates (MCMC-LCE), adopts the Gibbs sampler to find a list of mostly likely transmitted sequences and matching channel estimates/impulse responses (CIR), to compute the log-likelihood ratio (LLR) of transmitted bits. The MCMC-LCE provides a low-complexity means to approximate the optimal maximum a posterior (MAP) detection in a statistical fashion and is applicable to channels with long memory. Promising behavior of the MCMC-LCE is presented using both synthetic channels and real data collected from underwater acoustic (UWA) channels whose large delay spread and time variation have been the main motivation for the developed system. We also adopt an adaptive variable step-size least mean-square (VSLMS) algorithm for channel tracking. We find that this choice, which does not require prior knowledge on the CIR statistics, is a good fit for UWA channels. Superior performance of the MCMC-LCE over turbo minimum mean-square-error (MMSE) equalizers is demonstrated for a variety of channels examined in this work.

Approaching MIMO capacity using bitwise Markov Chain Monte Carlo detection

This paper examines near capacity performance of Markov Chain Monte Carlo (MCMC) detectors for multiple-input and multiple-output (MIMO) channels. The proposed MCMC detector (Log-MAP-tb b-MCMC) operates in a strictly bit-wise fashion and adopts Log-MAP algorithm with table look-up. When concatenated with an optimized low-density parity-check (LDPC) code, Log-MAP-tb b-MCMC can operate within 1.2-1.8 dB of the capacity of MIMO systems with 8 transmit/receive antennas at spectral efficiencies up to ¿ = 24 bits/channel use (b/ch). This result improves upon best performance achieved by turbo coded systems using list sphere decoding (LSD) detector by 2.3-3.8 dB, leading to nearly 50% reduction in the capacity gap. Detailed comparisons of the Log-MAP-tb b-MCMC with LSD based detectors demonstrate that MCMC detector is indeed the detector of choice for achieving channel capacity both in terms of performance and complexity.

Performance of channel coded noncoherent systems: modulation choice, information rate, and Markov chain Monte Carlo detection

This paper investigates performance of channel coded noncoherent systems over block fading channels. We consider an iterative system where an outer channel code is serially concatenated with an inner modulation code amenable to noncoherent detection. We emphasize that, in order to obtain near-capacity performance, the information rates of modulation codes should be close to the channel capacity. For certain modulation codes, a single-input single-output (SISO) system with only one transmit antenna may outperform a dual-input and single-output (DISO) system with two transmit antennas. This is due to the intrinsic information rate loss of these modulation codes compared to the DISO channel capacity. We also propose a novel noncoherent detector based on Markov Chain Monte Carlo (MCMC). Compared to existing detectors, the MCMC detector achieves comparable or superior performance at reduced complexity. The MCMC detector does not require explicit amplitude or phase estimation of the channel fading coefficient, which makes it an attractive candidate for high rate communication employing quadrature amplitude modulation (QAM) and for multiple antenna channels. At transmission rates of 1 ~ 1.667 bits/sec/Hz, the proposed SISO systems employing 16QAM and MCMC detection perform within 1.6-2.3 dB of the noncoherent channel capacity achieved by optimal input.

Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems

In this paper, we develop novel Bayesian detection methods that are applicable to both synchronous code-division multiple-access and multiple-input multiple-output communication systems. Markov chain Monte Carlo (MCMC) simulation techniques are used to obtain Bayesian estimates (soft information) of the transmitted symbols. Unlike previous reports that widely use statistical inference to estimate a posteriori probability (APP) values, we present alternative statistical methods that are developed by viewing the underlying problem as a multidimensional Monte Carlo integration. We show that this approach leads to results that are similar to those that would be obtained through a proper Rao-Blackwellization technique and thus conclude that our proposed methods are superior to those reported in the literature. We also note that when the channel signal-to-noise ratio is high, MCMC simulator experiences some very slow modes of convergence. Thus accurate estimation of APP values requires simulations of very long Markov chains, which may be infeasible in practice. We propose two solutions to this problem using the theory of importance sampling. Extensive computer simulations show that both solutions improve the system performance greatly. We also compare the proposed MCMC detection algorithms with the sphere decoding and minimum mean square error turbo detectors and show that the MCMC detectors have superior performance.

On performance of sphere decoding and Markov chain Monte Carlo detection methods

In a recent work, it has been found that the suboptimum detectors that are based on Markov chain Monte Carlo (MCMC) simulation techniques perform significantly better than their sphere decoding (SD) counterparts. In this letter, we explore the sources of this difference and show that a modification to existing sphere decoders can result in some improvement in their performance, even though they still fall short when compared with the MCMC detector. We also present a novel SD detector that is an exact realization of max-log-MAP detector. We call this exact max-log SD detector. Comparison of the results of this detector with those of the max-log version of the MCMC detector reveals that the latter is near optimal.