ABSTRACT
As wireless services spread and become integrated into people’s daily life, the expectation of the performance and reliability of wireless devices naturally increases. As a result, system designers now face more challenges such as limited bandwidth, dynamic resource allocation, and particularly, channel fading effects introduced by the variability in the time, frequency, and space domains. Diversity techniques have been widely adopted to combat deleterious channel fading effects. To exploit the diversity embedded in the channel, both transmitter and receiver must be designed appropriately. To collect the full diversity enabled by the transmitter, maximum-likelihood equalizers (MLEs) or near-MLEs are usually adopted at the receiver. However, the high decoding complexity makes MLE or near-MLE infeasible in practical systems. To reduce the decoding complexity, low-complexity equalizers, such as linear equalizers (LEs) and decision feedback equalizers (DFEs), are often adopted. These methods, however, may not utilize the diversity enabled by the transmitter and as a result have degraded performance relative to the system with the MLE. Recently, lattice reduction (LR) techniques have been introduced to improve the performance of low-complexity equalizers without increasing the complexity significantly. In this chapter, we first present the development of the LR techniques by introducing the various LR algorithms. Then, the detailed procedures of the LR-aided LEs and the LR-aided DFEs are given for general linear systems. The performance and the complexity of LR-aided equalizers with different LR algorithms are compared. Finally, we demonstrate the effectiveness of LR-aided equalizer by two applications on multiantenna multi-input multi-output (MIMO) systems and precoded orthogonal frequency division multiplexing (OFDM) systems.
