Metropolis-Hastings Random Walk along the Gradient Descent Direction for MIMO Detection

Abstract

In this paper, we present a gradient descent and Metropolis-Hastings (MH) principle based low-complexity, highly parallelizable, near-optimal MIMO demodulation framework. The optimal maximum-likelihood (ML) demodulation is a discrete optimization problem and is computationally infeasible for large MIMO dimensions. Many continuous-relaxed versions of ML, such as least-squares (LS) demodulation, have closed-form solutions but are highly suboptimal to ML. However, the continuous surface of, for example, LS cost function can serve as a proxy for the discontinuous staircase-like surface of the ML cost function. The key idea in this work is to search for the ML solution by performing an MH random walk around the gradient-descent direction of the LS surface (scheme referred hereafter as MHGD). In MH algorithm, a Markov Chain Monte Carlo (MCMC) technique, first a random perturbation over the previous state is proposed. Then, the proposal is accepted/rejected with non-zero probability. In MHGD, gradient-descent and MH work synergistically-gradient-descent shows the likely directions to MH making it very efficient and MH navigates the discrete space, which the gradient-descent alone cannot. To achieve near-ML performance, MHGD uses a preconditioner on the gradient and channel-matrix based covariance for the MH random step. The complexity of MHGD algorithm is comparable or lower than the well-known low-complexity, near-ML algorithms. But more importantly, MHGD is highly parallelizable, has simple vectorizable operations, scalable to very large MIMO due to the use of gradients, and can also be extended to distributed computing paradigm. Simulations demonstrate the aforementioned strengths and salient features of near-ML MHGD algorithm.