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In this chapter, we have defined a two phase cooperative system incorporating path-loss based and large scale shadowing based fading, with variable positioning of MIMO AF relays for a MIMO source and destination under a power constraint. In this system we have demonstrated cooperative ML detection that incorporates both phases of the received signal from the source and relays expressed as a single cooperative ML rule that can be processed by a SD detector, taking into account available information in the system and making appropriate substitutions so that the results can be numerically calculated. Also considered is the use of soft decision information and iterative processing for MAP detection, utilising the LSD as a soft decision detector that can be incorporated into a channel coded iterative processing detector. Several relay link selection strategies are also considered for the system, with limited channel information and full channel information scenarios considered. The proposed combinatorial link selection strategies have been shown to have BER performance gains over existing link selection schemes in both coded and uncoded cooperative MIMO systems. It has also been shown that adding relays to the system may not necessarily give BER gains, depending on the positioning and the number of relays present in the system model, and so the relay link selection strategies can be shown to give gains in BER performance over a full relay case, even when using less relays. It is also shown that some relay link strategies do not necessarily give BER gains, but it can be considered that the relay link selection can still maintain the BER performance, whilst releasing some relay resources that could be used by other potential users.

Chapter 4

Multi-Feedback Successive Interference

Cancellation with Dynamic Reliability

Ordering

Contents

3.1 Introduction . . . 42 3.2 System Model . . . 45 3.3 Cooperative ML Detection and Sphere Decoding . . . 48 3.4 Link Selection . . . 53 3.5 Iterative and Cooperative Detection and Decoding . . . 57 3.6 Simulations . . . 63 3.7 Summary . . . 69

4.1

Introduction

The SIC detector is a well-known technique for the detection of data symbols at the re- ceiving device in a multi-user or MIMO system, and typically to improve the performance of the SIC detector, the data streams with the greatest power are cancelled first, thus re-

moving the greatest source of interference first, which is known as the VBLAST tech- nique [100], and is implemented by considering the powers of the channels associated with each user or antenna. However, as shown in [103], although the VBLAST cancella- tion order within the SIC is the optimal for the vast majority of detected symbols, other cancellation orders can outperform the VBLAST ordering on a given occasion, which could result in performance gains.

In this chapter, dynamic reliability ordering (RO) based upon log-likelihood-ratios (LLR) [70] is considered in conjunction with a method of multiple-feedback (MF), [104], [105, 106] which is designed to provide alternative cancellation candidates for data sym- bols, to compensate for and correct potentially erroneous detected symbols. These meth- ods are integrated into the proposed MF-RO-SIC detector, which utilises both methods and makes considerations for reducing the computational complexity associated with these methods, whilst increasing the BER performance. A discussion on the complexity of the proposed detector with comparisons to existing methods, and a method for integrat- ing the proposed detector with iterative detection and decoding in a channel coded system is also considered.

This chapter is organised as follows, firstly the point-to-point MIMO system model on which this chapter’s work is based will be described, followed by an in-depth look at interference cancellation techniques, including SIC, RO and MF techniques, and an ex- planation of Voronoi diagrams. In the next section, the proposed MF-RO-SIC detector is detailed, and the integration of the methods involved is developed to produce an algorithm with reduced computational complexity. After this, an iterative detection and decoding system for the proposed MF-RO-SIC detector is detailed, which includes a method of hard decision feedback. Finally, the results of simulations in the point-to-point system model are presented, for both the proposed detector and the iterative detection and decoding methods, ending with a summary of this chapters main results.

4.2

System Model

The system under consideration is a point-to-point spatial multiplexing MIMO link, con- sisting of Nt transmit antennas and Nr receive antennas. At each time instant, the Nt

length column vector x consisting of Nt data symbols taken from the constellation set

V that is appropriate for the modulation scheme being used, is transmitted through the Nr× Ntchannel matrixH. At the Nrreceive antennas at the destination, the transmitted

signal vector is received, processed and organised as theNrlength column vectory. This

can be described as:

y = Hx + n, (4.1)

where n is the circular complex additive white Gaussian noise (AWGN) vector represent- ing noise at the receive antennas with a variance given by

σ2 = 1/(2γ), (4.2)

whereγ is the signal-to-noise ratio (SNR) per antenna. The channel H is modelled as a complex Rayleigh distributed channel, and can be expressed as the horizontal concatena- tion of the individual channel vector associated with each transmit antenna,

H = [h1, ..., hi, ..., hNt]. (4.3)

The linear MMSE detection technique described in Chapter 2 will be used in this chapter as the basis for the proposed interference cancellation method developed in this chapter. The MMSE filter detection can be described as below:

ˆ

x = WH

M M SEy, (4.4)

where ˆx is the Nt length vector of the estimated transmitted data, which can also be

described as per-antenna values[ˆx1, . . . , ˆxi, . . . , ˆxNt]. It is possible to estimate the distri-

bution of the bits (bi ∈ {−1, +1}) of the elements of ˆx as Gaussian random variables, as

shown in [60], with a probability density function (PDF) of:

f (ˆxi|bi) = 1 √ 2πσi exp  −(ˆxi− mi) 2 2σ2 i  , i = 1, ..., Nt, (4.5)

wheremiandσ2i are the mean and variance, respectively, mi = ¯ γi 1 + ¯γi bi, (4.6) σi2 = ¯ γi 2(1 + ¯γi)2 , (4.7)

withγ¯i representing the instantaneous SINR of receive antennai. The fact that the ele-

ments ofx can be accurately modelled as Gaussian random variables is important as thisˆ makes the analysis of the MMSE detection output convenient, thus making it easier to derive useful results for determining cancellation ordering in later sections.