Semidefinite Relaxation Detector Research Articles

Block-Based Spatial Modulation: Constellation Design and Low-Complexity Detection

Spatial modulation (SM) uses antenna indices to transmit information, along with modulation symbols. The conventional SM scheme fixes the number of active antennas, and consequently the number of transmit symbols, in a transmit vector to avoid detection ambiguity. This work proposes a generalized block-based spatial modulation (GBSM) scheme which varies the number of active antennas in each transmit vector, but fixes their number over a transmission block. The proposed GBSM scheme, which transmits information using the spatial dimensions created over a block of transmit vector, resolves detection ambiguity as the number of transmit symbols over a block remains fixed. It crucially also has a large constellation cardinality, which we exploit by proposing novel low bit error rate (BER) constellation design algorithms. We also propose a novel low-complexity semi-definite relaxation detector, which has similar BER as that of the optimal maximum likelihood detector but with ≈ 85% lower complexity.

A Semidefinite Relaxation Approach to OFDM-IM Detection in Rapidly Time-Varying Channels

In this paper, the signal detection of orthogonal frequency division multiplexing with index modulation (OFDM-IM) in the rapidly time-varying channel is studied. Due to the inter-carrier interference, the conventional block detectors based on the successive interference cancellation (SIC) strategy, e.g., the signal power (SP) detector, suffer from severe error propagation especially in the case with large normalized Doppler frequency. To address this problem, a semidefinite relaxation (SDR) approach is first proposed. In the proposed SDR detector, the signal feature of OFDM-IM is presented properly as the convex constraints in the SDR programming problem and utilized in the randomization procedure. The SDR detector can avoid the error propagation effectively with a cost of higher polynomial complexity. To reduce the complexity, the group-based SIC-SDR detector is then proposed, where the subcarriers in one OFDM symbol is partitioned into multiple groups, and the SDR detection is performed over each group successively in conjunction with the ordered SIC strategy. However, similar with the SP detector, the SIC-SDR detector also suffers from the error propagation. To boost the performance, we propose to take the solution of the SIC-SDR detector as the initial estimation of a further local search algorithm (LSA). Concretely, after a proper definition of the nearest neighbors of an OFDM-IM signal vector, the proposed combined detector employing the likelihood ascent-search as the LSA is presented. Finally, the validity of the proposed detectors is justified by simulation results, and the combined detector achieves an excellent performance-complexity trade off.

Multiuser MIMO Transmission Aided by Massive One-Bit Magnitude Measurements

This paper proposes a multiuser MIMO system with both full measurements and one-bit magnitude observations, which are acquired by several linear inphase-and-quadrature (IQ) structured radio frequency (RF) chains and massive one-bit envelope chains, respectively. The total circuit power and cost are not increased significantly, since the added one-bit envelope chains have low power and low cost. Channel side information on the one-bit envelope chains is acquired by sharing the IQ-structured RF chains and executing a channel calibration operation. Two multiuser detectors are constructed based on the semidefinite relaxation (SDR) and approximate message passing (AMP). The one-bit magnitudes are interpreted as inequality constraints in the SDR detector, and exploited in a Bayesian manner by the AMP detector. Simulation results show that the one-bit magnitude measurements bring about high MIMO multiplexing and diversity gains, and decrease the transmission power. With the increase of the channel coherence time, more one-bit envelope chains are prone to be equipped, and one-bit magnitude-aided MIMO becomes more and more spectral-and-energy-efficient than the conventional MIMO.

A Low Complex Sparse Formulation of Semidefinite Relaxation Detector for Large-MIMO Systems Employing BPSK Constellations

Semidefinite relaxation detector is a promising approach to large-MIMO detection but for its computational complexity. The major computational cost is incurred in solving the semidefinite program (SDP). In this paper, we propose a sparse semidefinite relaxation (S-SDR) detector by reformulating the SDP problem thereby reducing the computational complexity. We formulate the system model using a sparse approach and further introduce a regularization term inducing sparsity into the semidefinite programming model. We provide a sparse formulation requiring approximately 50 % of the computations compared to the conventional semidefinite programming approach. We apply the proposed semidefinite relaxation detector in large-MIMO channels upto $$100 \times 100$$100×100 systems and compare its BER performance and complexity. We observe that the BER performance is similar to the conventional semidefinite relaxation with the proposed S-SDR detector requiring relatively fewer computations.

A Performance Study of Semidefinite Relaxation Detector in Spatially Correlated and Rank Deficient Large MIMO Systems

Large MIMO detection has gained significant attention in the recent past with computational complexity as the research focus. However, they assume the channel to be i.i.d and uncorrelated, which is not a valid assumption in practice due to the fixed physical space constraints in large MIMO. Nevertheless, there is a little work carried out in these lines. In this paper, we consider the problem of detection in large spatial multiplexing MIMO systems and we investigate the semidefinite relaxation (SDR) approach to solve this problem. We investigate the applicability of SDR approach in large MIMO setting and study its performance in spatially correlated and rank deficient channel conditions. Through the simulation results, we demonstrate the superior performance of semidefinite relaxation detector over other existing methods in uncorrelated and correlated large MIMO systems especially in low SNR regime. The performance of SDR detector is noteworthy with large number of antennas despite the system being rank deficient and the average running time also scales up well for large systems.

Comparison of Semidefinite Relaxation Detectors for High-Order Modulation MIMO Systems

Multiple-input multiple-output (MIMO) system is considered to be one of the key technologies of LTE since it achieves requirements of high throughput and spectral efficiency. The semidefinite relaxation (SDR) detection for MIMO systems is an attractive alternative to the optimum maximum likelihood (ML) decoding because it is very computationally efficient. We propose a new SDR detector for 256-QAM MIMO system and compare its performance with two other SDR detectors, namely, BC-SDR detector and VA-SDR detector. The tightness and complexity of these three SDR detectors are analyzed. Both theoretical analysis and simulation results demonstrate that the proposed SDR can provide the best BLER performance among the three detectors, while the BC-SDR detector and the VA-SDR detector provide identical BLER performance. Moreover, the BC-SDR has the lowest computational complexity and the VA-SDR has the highest computational complexity, while the proposed SDR is in between.

SDR Lattice-Reduction-Aided Detector

Communication techniques based on multiple-input multiple-output (MIMO) have been heavily exploited in the past decade, in order to obtain high capacity communication systems, aim to dealing with increasing spectrum scarcity scenarios. In this context, the semidefinite relaxation (SDR) signal detection strategy is promising due to its very near-optimal maximum-likelihood (ML) performance combined with polynomial complexity. However, the SDR detector has proved insufficient for systems with high order modulation, exactly where the recent pre-detection technique by lattice reduction (LR) has demonstrated excellent results in terms of performance-complexity. This paper investigates the performance-complexity tradeoff of the SDR detector under high order modulation in uncorrelated MIMO channels aided by lattice reduction technique applied in the pre-detection stage.

PIC-based iterative SDR detector for OFDM systems in doubly-selective fading channels

OFDM data detection in doubly-selective fading channels requires high complexity due to intercarrier interferences (ICI). We present a low-complexity receiver consisting of a semidefinite relaxation (SDR) based detector and parallel interference cancellation (PIC). The entire band is divided into clusters of adjacent subcarriers. SDR is applied on each cluster while PIC tackles ICI from other clusters. An upper bound of ICI power is derived and used to omit far-away clusters in performing PIC. Finally, an adaptive detector based on PIC, PIC-based SDR and the snap-shot SNR in channel is proposed to achieve a better tradeoff between complexity and performance.

Efficient Implementation of Quasi- Maximum-Likelihood Detection Based on Semidefinite Relaxation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper we develop two quasi-maximum likelihood (ML) channel detectors for multiuser detection: semidefinite relaxation (SDR) detector and phase-shift-keying (PSK) detector. These detectors can deliver near-ML bit error rate (BER) performance with a polynomial worst-case complexity. The SDR detector for binary-phase-shift-keying (BPSK) constellation is based on a convex SDR, whereas the PSK detector for <formula formulatype="inline"><tex Notation="TeX">$M$</tex></formula>-PSK constellations is based on a nonconvex low-rank SDR. The SDR detector is implemented using a dual-scaling interior-point method, while the PSK detector is based on a coordinate descent strategy on a feasible region homotopy. We use dynamic dimension reduction and warm start techniques to achieve signal-to-noise ratio (SNR)-sensitive improvements for both detectors. Numerical simulations of BER performance and running time indicate the effectiveness of the two quasi-ML detectors when compared to the conventional sphere decoder and its variants. </para>

The Diversity Order of the Semidefinite Relaxation Detector

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we consider the detection of binary (antipodal) signals transmitted in a spatially multiplexed fashion over a fading multiple-input–multiple-output (MIMO) channel and where the detection is done by means of semidefinite relaxation (SDR). The SDR detector is an attractive alternative to maximum-likelihood (ML) detection since the complexity is polynomial rather than exponential. Assuming that the channel matrix is drawn with independent identically distributed (i.i.d.) real-valued Gaussian entries, we study the receiver diversity and prove that the SDR detector achieves the maximum possible diversity. Thus, the error probability of the receiver tends to zero at the same rate as the optimal ML receiver in the high signal-to-noise ratio (SNR) limit. This significantly strengthens previous performance guarantees available for the semidefinite relaxation detector. Additionally, it proves that full diversity detection is also possible in certain scenarios when using a noncombinatorial receiver structure. </para>

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).