Exploiting Scalar Effect in Wireless Access Networks: A Case Study and Research Directions

Introduction

The fundamental scenario for exploiting the scale effect (as shown in the Figure 1) is that some algorithm is instantiated for many times and all the instances are executed together under a sum complexity constraint. This algorithm shall have variable complexity, which has many parameters affecting the statistics of its complexity. It is assumed that the algorithm has instances, and the complexity of different instances (each of which is denoted by ξ_j) are random variables. Then, the sum complexity of instances is

Figure 1.

Illustration of the scenario for exploiting the scale effect

Due to the run-time limit, the sum complexity S_n cannot exceed a constraint C_n, otherwise, it leads to an outage event.

Considering the multiple-user scenario, it is proposed in this chapter to realize the full diversity multiple-input multiple-output (MIMO) detection under a polynomial constraint of unit complexity (i.e., complexity per user) by exploiting the scale effect. It is worth noting that the multiple-user scenario is a typical case of applying the scale effect, in which every algorithm is always instantiated for all the users. To be specific, the ET-FSD algorithm is developed in the multiple-user scenario, and the corresponding mathematic model primarily based on the large deviation principle is established for analyzing the scale effect. The existence of scale effect in ET-FSD can be clearly revealed by this study. Hence, one can expect that, due to the scale effect, the goal to make the MIMO detection work under a polynomial constraint of unit complexity while maintaining the full diversity performance can be accomplished.

After presenting ET-FSD as a case study, this chapter also focuses on discussing the future research directions of the scale effect study with respect to the algorithmic complexity issues in wireless access networks. Besides the MIMO detection, channel decoding algorithms (including these of Turbo codes and LDPC codes) of baseband processing in wireless access networks shall also have the scale effect. Thus this chapter will explain on the details of investigating the scale effect of channel decoding algorithms.

Background

For the multiple-antenna system with n_T transmit and n_R receive antennas, one can use the matrix to represent this MIMO channel. The channel matrix considered in this study has the entries which are independent and identically distributed (i.i.d.) zero-mean complex Gaussian random variables with unit variance. If letting be the transmit signal vector in which each entry belongs to a constellation set with size m, the signal model of the MIMO channel would be written as y=Hs+v, where denotes the receive signal vector and is the zero-mean circularly symmetric complex Gaussian noise vector with covariance matrix .

By assuming that is perfectly known at the receiver, the maximum-likelihood (ML) detector that could minimize the average error probability, is the optimal MIMO detection scheme and can be given by

The optimality of ML detector also implies that this detector is able to achieve the diversity order n_R (i.e., full diversity order) (Paulraj, Nabar, &Gore, 2003). Despite the optimal performance of average error probability, the ML detector is not a feasible scheme of MIMO detection for practical deployment because of its extremely high complexity. It can be found from (1) that the ML detector has to perform exhaustive search among all the possible candidates and thus has the exponential complexity .