Low-complexity detection by exploiting suboptimal detection order and subcarrier grouping for Multi-Layer MIMO-OFDM

Abstract

By combining the transmit diversity and space multiplexing, the multi-layer multiple-input multiple-output orthogonal frequency division multiplexing (Multi-Layer MIMO-OFDM) system can exploit the potentials of both techniques. The transmit antennas are divided into several layers and each layer is encoded by a certain Multi-Antenna Coding. The antennas transmit OFDM signals in order to deal with frequency-selective fading. In addition to Exhaustive Detection which applies the same detection at each subcarrier independently, we exploit the subcarrier correlation to develop a subcarrier grouping based Low-Complexity Detection scheme. The subcarriers bound into the same group share the same Layer Detection Order which is obtained by the Post-Nulling Signal Power comparison at the center subcarrier of that group. The simulation results show that compared with Exhaustive Detection, the proposed Low-Complexity Detection scheme is capable of reducing 50.7% complexity with only 0.8 dB performance degradation for 6 × 6 system, and reducing 60.7% complexity with about 1.0 dB performance degradation for 8 × 8 system, respectively.

Introduction

One problem of the diversity MIMO techniques is that simply increasing the antenna number at both the transmitter and receiver above a certain number does not definitely lead to significant performance improvement [1], [2]. On the other hand, spatial multiplexing [3] can theoretically offer a nearly linear increase in system capacity. In [4], Tarokh et al. proposed a combinational scheme of diversity and multiplexing. Dai et al. [5] further improved this scheme by introducing the ordered array processing. The diversity loss encountered at the foregoing detection stages is compensated by always detecting the layer with the largest post-nulling SNR.

Both [4], [5] are focused on the single-carrier STTC (space–time trellis coding) over flat fading channels. We apply their concepts in the broadband channels by incorporating orthogonal frequency division multiplexing (OFDM), which results in Multi-Layer MIMO-OFDM system.

As shown in Fig. 1, we partition the total N transmit antennas into Q layers (groups) and each layer is composed of n_q (q = 1, …, Q) transmit antennas with ${\sum }_{q=1}^Q{n}_q=N$. Each transmit layer (as shown in Fig. 1) has its independent space–time (ST), space–frequency (SF) [8], [9] or space–time–frequency (STF) [10], [11] encoder. In the single-carrier Multi-Layer MIMO systems [4], [5], the space–time trellis coding (STTC) is used. However, the decoding of STTC is of exponential complexity with regard to the transmit antenna number and constellation size. For the layer encoder in the Multi-Layer MIMO-OFDM system discussed here, SF coding [8], [9] can be used to collect the frequency diversity and STF coding [10], [11] can be used as collect frequency-time diversity. However, the current commonly used decoding scheme of SF and STF is sphere decoding (SD) [12] which has very high complexity.

The embedded multi-antenna coding is not the focus of this work. Instead, we focus on developing low-complexity layer detection scheme for Multi-Layer MIMO-OFDM. Therefore, we just consider Alamouti’s twin-antenna STBC coding [6] as the embedded multi-antenna coding scheme. Alamouti coding is very appealing since it achieves very good tradeoff between complexity and performance. It can be decoded with very low (linear) complexity. Moreover, it can obtain the full space diversity order and full rate simultaneously. The transmission efficiency of such Multi-Layer MIMO-OFDM is Q symbols per subcarrier per channel use.

This Multi-Layer MIMO-OFDM scheme was used in a fourth-generation (4G) system [7]. We compared the Exhaustive Detection scheme which applies the same detection at each subcarrier independently, and the reduced-complexity detection scheme which exploit the subcarrier correlation [7].

In this paper, the mathematical model of the Low-Complexity Detection scheme is presented. This detection scheme is based on subcarrier grouping. The subcarriers of the same group share the same Layer Detection Order which is obtained by the Post-Nulling Signal Power comparison at the center subcarrier of that group. The simulation results show that compared with Exhaustive Detection, the Low-Complexity Detection scheme is capable of significantly reducing the complexity with very small performance degradation.

The remainder of this paper is organized as follows. In Section 2 we introduce the system model and Exhaustive Detection scheme for Multi-Layer MIMO-OFDM; then in Section 3 we present the mathematical model of the Low-Complexity Detection scheme which exploits suboptimal detection order and subcarrier grouping; the performance of the proposed scheme is investigated in Section 4 where the simulation results are presented; the complexity comparison is shown in Section 5; finally we conclude this paper by Section 6.

Notation

The vector and matrix variables are denoted by bold lower case and bold upper case letters, respectively. The superscripts, T, H and * stand for the transpose, Hermitian transpose and conjugate value, respectively. $\Vert ·{\Vert }_F$ is the Frobenius norm.