Code-Aided DOA Estimation From Turbo-Coded QAM Transmissions: Analytical CRLBs and Maximum Likelihood Estimator

In this paper, we address the problem of direction of arrival (DOA) estimation from turbo-coded square-QAM-modulated transmissions. We devise a new code-aware direction finding concept, derived from maximum likelihood (ML) theory, wherein the soft information provided by the soft-input soft-output decoder, in the form of log-likelihood ratios, is exploited to assist the estimation process. At each turbo iteration, the decoder output is used to refine the ML DOA estimate. The latter is in turn used to perform a more focused receiving beamforming thereby providing more reliable information-bearing sequences for the next turbo iteration. In order to benchmark the new estimator, we also derive the analytical expressions for the exact Cramer-Rao lower bounds (CRLBs) of code-aided (CA) DOA estimates. Simulation results will show that the new CA direction finding scheme lies between the two traditional schemes of completely non-data-aided and data-aided (DA) estimations. Huge performance improvements are achieved by embedding the direction finding and receive beamforming tasks into the turbo iteration loop. Moreover, the new CA DOA estimator reaches the new CA CRLBs over a wide range of practical SNRs thereby confirming its statistical efficiency. As expected intuitively, its performance further improves at higher coding rates and/or lower modulation orders.

I. Introduction

The rapid development of radio communications has resulted in a growing demand for location-aware services fueled in part by the soaring need to increasingly accommodate users’ mobility. Clearly, highly accurate DOA estimates are crucial for enhanced overall system performance. However, grasping this high level of estimation accuracy requires a sufficiently broad theoretical foundation for the underlying direction finding technique and more than ever the ability to be grounded in practical situations. Actually, The problem of DOA estimation has been a hot array signal processing research topic over the last few decades and a suitable DOA estimator can be selected from a plethora of state-of-the-art techniques (see [2], [3] and references therein). Recently, there has been a resurgence of interest in developing advanced DOA estimators that are specifically tailored to the emergent massive MIMO systems. Interested readers are referred to the very recent works in [4], [5] which introduce novel 2-D DOA estimation techniques that are geared toward massive MIMO systems in presence of multiple incoherently distributed sources. Depending on how the recorded data are processed to output the required DOA estimate, DOA estimation techniques can be broadly categorized into two major categories: i) subspace (SS)-based or ii) ML-based methods. To their credentials, SS-based approaches are known to be computationally less expensive. However, as they extract the DOA information from the covariance matrix of the received data instead of the data themselves, they are usually suboptimal [6]. They hence suffer from severe performance degradation at low SNR levels and/or small numbers of snapshots. ML approaches, however, apply the estimation process directly on the received samples and always enjoy higher accuracy and enhanced resolution capabilities, however, very often at the cost of substantial increase in complexity [7].