Journal of Electrical and Computer Engineering

Volume 2018, Article ID 4034625, 7 pages

https://doi.org/10.1155/2018/4034625

## Low-Complexity Detection Algorithms for Spatial Modulation MIMO Systems

^{1}School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China^{2}National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu 611731, China^{3}State Grid Liaoning Information and Communication Company, Shenyang 110006, China

Correspondence should be addressed to Xinhe Zhang; moc.anis@hxzsadc

Received 9 August 2018; Revised 11 October 2018; Accepted 25 October 2018; Published 15 November 2018

Academic Editor: Jit S. Mandeep

Copyright © 2018 Xinhe Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, the authors propose three low-complexity detection schemes for spatial modulation (SM) systems based on the modified beam search (MBS) detection. The MBS detector, which splits the search tree into some subtrees, can reduce the computational complexity by decreasing the nodes retained in each layer. However, the MBS detector does not take into account the effect of subtree search order on computational complexity, and it does not consider the effect of layers search order on the bit-error-rate (BER) performance. The ost-MBS detector starts the search from the subtree where the optimal solution is most likely to be located, which can reduce total searches of nodes in the subsequent subtrees. Thus, it can decrease the computational complexity. When the number of the retained nodes is fixed, which nodes are retained is very important. That is, the different search orders of layers have a direct influence on BER. Based on this, we propose the oy-MBS detector. The ost-oy-MBS detector combines the detection order of ost-MBS and oy-MBS together. The algorithm analysis and experimental results show that the proposed detectors outstrip MBS with respect to the BER performance and the computational complexity.

#### 1. Introduction

To meet the demand of wireless communication systems for higher data transmission rate, multiple-input multiple-output (MIMO) technology has been adopted in mobile terminals. MIMO technology improves data throughput without increasing additional bandwidth and transmit power. Spatial modulation (SM) [1–3] is an emerging transmission scheme for MIMO systems. The main characteristic of SM is that only one transmit antenna is activated at one time slot, but simultaneously, the SM systems can use the original signal domain (signal constellation) and the transmit antenna (TA) indices (spatial constellation) to convey information. Compared to MIMO systems, SM systems can only equip one radio frequency (RF) chain, avoid interchannel interference (ICI) and interantenna synchronization (IAS), and also reduce the complexity of demodulation.

For the detection of SM signals, maximum ratio combining (MRC) algorithm was proposed in [4], in which the active-antenna index and the transmit symbol are separately estimated. The MRC detector has a low computational complexity and only performs well on the constrained channels. This detector was improved in [5], and it further can be applied in conventional channel conditions. The optimum maximum likelihood (ML) detector which involves joint detection of the TA index and of the transmit symbol was proposed in [6]. However, the computational complexity linearly grows as the number of TA (), the number of receive antennas (), and the size of the modulation scheme (). In order to obtain the near-optimal solution with a lower computational complexity, several low-complexity detectors have been put forward [7–17]. In [7, 8], two low-complexity hard-limiter-based ML (HL-ML) detectors which have the same BER performance as the ML detector were proposed for *M*-PSK and square- or rectangular-QAM modulation. The computational complexity has nothing to do with the constellation size. In [9–11], sphere-decoding (SD) algorithms were put forward for SM systems, which are capable of achieving near-optimal performance with a lower computational complexity on average. At worst, the computational complexity is equivalent to that of the ML detector. However, its detection performance depends mainly on the initial search radius and the transmit parameters. Compared with SD detectors, SD aided by the ordering strategy proposed in [12] can greatly reduce the computational complexity. Two matched filter- (MF-) based detectors were proposed in [13]. In [14], Wang et al. proposed a novel signal vector-based detection (SVD) scheme. Tang et al. [15] presented a distanced-based ordered detection (DBD) algorithm to reduce the receiver complexity and achieve a near-maximum likelihood performance. To reduce the detection complexity of ML detection, Xu [16] presented simplified ML-based optimal detection (OD) and simplified multistage detection (MD). In the simplified ML-based detection and multistage detection schemes, the signal set is firstly partitioned into four “level-one subsets”. Each level-one subset is further partitioned into four “level-two subsets” if each subset contains more than four signals. The simple low-complexity detection (SLCD) and adaptive simple low-complexity detection (ASLCD) were proposed in [17].

In [18, 19], the M-algorithm to maximum likelihood (MML) detector with prioritized tree-search structure was presented. The detection is considered as a breadth-first search tree with branches and layers, in which the *i*th layer corresponds to the *i*th receive antenna (RA). The MML detector only examines partial nodes in the tree, whereas the ML detector traverses all nodes. Compared with the ML detector, the MML detector can achieve a lower computational complexity. In [20], a low-complexity symbol detection based on modified beam search (MBS) was proposed. The detection process of the MBS algorithm can be represented by constructing a tree with subtrees and layers, where each subtree has complete paths from the root node to the leaf nodes, and each of the paths stands for a candidate solution. The solution is found by performing modified beam search. Compared with the MML algorithm, the MBS algorithm reduces the computational complexity by discarding unpromising candidate solutions.

In the MBS detector, the detection sequence of different subtrees is confined to the ascending order of the subtree indices, whereas it ignores the influence of different search orders on the computational complexity. Moreover, the detection of all layers is confined to the ascending order of the layer indices, whereas it ignores the influence of different search orders on its bit-error-rate (BER) performance. That is to say, the influence of different search orders on the BER performance and the computational complexity is not considered in the MBS detector. In recent years, the sorting strategy has attracted more and more attention. To some degree, the sorting strategy can improve the algorithm detection performance. In [12, 21], different ordering strategies were proposed to improve the detection performance. In this paper, we proposed three MBS-based detectors with novel ordering strategies: (1) the ost-MBS detector rearranges the search order of subtrees; (2) the oy-MBS detector performs SM signal detection in a descending order of the received signal amplitude; (3) the detection orders of the abovementioned two detectors were jointly considered in the ost-oy-MBS detector.

The rest of this paper is organized as follows. In Section 2, the system model of SM systems is introduced. Section 3 gives a brief overview of the MBS detector. The ordering strategy is introduced to the MBS detector. Section 4 demonstrates ost-MBS, oy-MBS, and ost-oy-MBS detectors. Section 5 illustrates the simulation results. Finally, we conclude the paper with a summary in Section 5.

*Notations*. Boldface upper/lower case symbols denote matrices and column vectors; is the Frobenius norm of a vector or a matrix; is the amplitude of a complex quantity or the cardinality of a set; and are the real and imaginary parts of a complex-valued quantity; is the conjugate transpose of a vector or a matrix; denotes a complex Gaussian random variable with mean and variance .

#### 2. System Model

Consider an SM system with constellation . In each time slot, the incoming data bits are rearranged into blocks of bits, in which bits are used to select the activated TA and bits are used to select the transmit symbol , . Hence, the system model for SM systems can be represented bywhere is the received signal vector; is the transmit symbol vector, whose element is at the *l*th position and zero at the other positions; and are the channel matrix and the noise vector, whose elements follow the circularly symmetric complex Gaussian distributions with and , respectively. The system model expressed in (1) can be reshaped aswhere , , and . Since only one TA is activated in each time slot, the system model expressed in (2) can be simplified aswhere is the *l*th column of .

It follows from (3) that the optimal ML-based demodulator can be formulated aswhere denotes the set containing all possible transmit antenna indices and complex constellation points, , , and is the entry of matrix .

#### 3. MBS Detector

According to Kim and Yi [20], the detection of the SM signal can be regarded as a tree with subtrees and layers, where each subtree has complete paths from the root node to the leaf nodes. For ease of understanding, we give an illustration (Figure 1) for the idea of the MBS detector. Suppose we have a SM system with 4QAM modulation; thus the search tree has 4 layers and 8 branches. 4 branches of each subtree (TA) correspond to 4 symbols from the 4QAM constellation. We define the branch metric of node at the *k*th layer as the squared Euclidean distance between the received and the transmit signals, which can be denoted as . The accumulated metric of node at the *k*th layer is the summation of the branch metric at the *k*th layer and the accumulated metric at layer, which can be expressed as .