Detection for multiple-input multiple-output systems: probabilistic data association and semidefinite programming relaxation

Abstract

As a highly effective physical-layer interference management technique, the joint detection of a vector of non-orthogonal information-bearing symbols simultaneously transmitted over multiple-input multiple-output (MIMO) channels is of fundamental importance for high throughput digital communications. This is because the generic mathematical model of MIMO detection underpins a wide range of relevant applications including (but not limited to) the equalization of dispersive band-limited channels imposing intersymbol interference (ISI), the multiuser detection (MUD) in code-division multiple-access (CDMA) systems and the multi-stream detection for multiple-antenna based spatial-division multiplexing (SDM) systems. With the evolution of wireless networks, the “virtual MIMO” concept was conceived, which is also described by the generic mathematical MIMO model. MIMO detection becomes even more important, because the achievable performance of spectrum-efficient wireless networks is typically interference-limited, rather than noise-limited.

In this thesis, a pair of detection methods that are well-suited for large-scale MIMO systems are investigated. The first one is the probabilistic data association (PDA) algorithm, which is essentially an interference-modelling approach based on iterative Gaussian approximation. The second one is the semidefinite programming (SDP) relaxation based approach, which approximates the optimal maximum likelihood (ML) detection problem to a convex optimization problem. The main advantage of both methods is that they impose a moderate computational complexity that increases as a polynomial function of the problem size, while providing competitive performance.

The contributions of this thesis can be broadly categorized into two groups. The first group is related to the design of virtually antipodal (VA) detection of rectangular M-ary quadrature amplitude modulation (M-QAM) symbols transmitted in SDM-MIMO systems. As a foundation, in the first parts of Chapter 2 and Chapter 3 the rigorous mathematical relationship between the vector space of transmitted bits and that of transmitted rectangular M-QAM symbols is investigated. Both linear and nonlinear bit-to-symbol mappings are considered. It is revealed that the two vector spaces are linked by linear/quasi-linear transformations, which are explicitly characterized by certain transformation matrices. This formulation may potentially be applicable to many signal processing problems of wireless communications. For example, when used for detection of rectangular M-QAM symbol vector, it enables us to transform the conventional three-step “signal-to-symbol-to-bits” decision process to a direct “signal-to-bits” decision process. More specifically, based on the linear VA transformation, in Chapter 2 we propose a unified bit-based PDA (B-PDA) detection method for linear natural mapping aided rectangular M-QAM symbols transmitted in SDM-MIMO systems. We show that the proposed linear natural mapping based B-PDA approach attains an improved detection performance, despite dramatically reducing the computational complexity in contrast to the conventional symbol-based PDA detector. Furthermore, in Chapter 3 a quasi-linear VA transformation based generalized low-complexity semidefinite programming relaxation (SDPR) detection approach is proposed for Gray-coded rectangular M-QAM signalling over MIMO channels. Compared to the linear natural mapping based B-PDA of Chapter 2, the quasi-linear VA transformation based SDPR method is capable of directly deciding on the information bits of the ubiquitous Gray-mapping aided rectangular M-QAM by decoupling the M-QAM constellation into several 4-QAM constellations. Moreover, it may be readily combined with the low-complexity bit-flipping based “hill climbing” technique for exploiting the unequal error protection (UEP) property of rectangular M-QAM, and the resultant VA-SDPR detector achieves the best bit-error rate (BER) performance among the known SDPR-based MIMO detectors conceived for high-order QAM constellations, while still maintaining the same order of polynomial-time worst-case computational complexity. Additionally, we reveal that the linear natural mapping based VA detectors attain the same performance provided by the binary reflected Gray mapping based VA detectors, but the former are simpler for implementation. Therefore, only if there are other constraints requiring using the nonlinear Gray mapping, it is preferable to use the linear natural mapping rather than the Gray mapping, when the VA detectors are used in uncoded MIMO systems.

The second group explores the application of the PDA-aided detectors in some more sophisticated systems that are of great interest to the wireless research community. In particular, the design of iterative detection and decoding (IDD) schemes relying on the proposed low complexity PDA methods is investigated for the turbo-coded MIMO systems in Chapter 4 and 5. It has conventionally been regarded that the existing PDA algorithms output the estimated symbol-wise a posteriori probabilities (APPs) as soft information. In Chapter 4 and 5, however, we demonstrate that these probabilities are not the true APPs in the rigorous mathematical sense, but a type of nominal APPs, which are unsuitable for the classic architecture of IDD receivers. Moreover, our study shows that the known methods of calculating the bit-wise extrinsic logarithmic likelihood ratios (LLRs) are no longer applicable to the conventional PDA based methods when detecting M-ary modulation symbols. Additionally, the existing PDA based MIMO detectors typically operate purely in the probabilistic domain. Therefore, the existing PDA methods are not readily applicable to IDD receivers. To overcome this predicament, in Chapter 4 and Chapter 5 we propose the approximate Bayes’ theorem based logarithmic domain PDA (AB-Log-PDA) and the exact Bayes’ theorem based logarithmic domain PDA (EB-Log-PDA) detectors, respectively. We present the approaches of calculating the bit-wise extrinsic LLRs for both the AB-Log-PDA and the EB-Log-PDA, which makes them well-suited for IDD receivers. Furthermore, we demonstrate that invoking inner iterations within the PDA algorithms – which is common practice in PDA-aided uncoded MIMO systems – would actually degrade the IDD receiver’s performance, despite significantly increasing its overall computational complexity. Additionally, we investigate the relationship between the extrinsic LLRs of the proposed EB-Log-PDA and of the AB-Log-PDA. It is also shown that both the proposed AB-Log-PDA- and the EB-Log-PDA-based IDD schemes dispensing with any inner PDA iterations are capable of achieving a performance comparable to that of the optimal maximum a posteriori (MAP) detector based IDD receiver in the scenarios considered, despite their significantly lower computational complexity. Finally, in Chapter 6, a base station (BS) cooperation aided distributed soft reception scheme using the symbol-based PDA algorithm and soft combining (SC) is proposed for the uplink of multiuser multicell MIMO systems. The realistic 19-cell hexagonal cellular model relying on radical unity frequency reuse (FR) is considered, and local cooperation based message passing is used instead of a global message passing chain for the sake of reducing the backhaul traffic. We show that despite its moderate complexity and backhaul traffic, the proposed distributed PDA (DPDA) aided SC (DPDA-SC) reception scheme significantly outperforms the conventional non-cooperative benchmarkers. Furthermore, since only the index of the quantized converged soft information has to be exchanged between collaborative BSs for SC, the proposed DPDA-SC scheme is relatively robust to the quantization errors of the soft information exchanged. As an appealing benefit, the backhaul traffic is dramatically reduced at a negligible performance degradation.

More information

Identifiers

ORCID for L. Hanzo: orcid.org/0000-0002-2636-5214

Catalogue record

Export record