A matrix-algebraic approach to successive interference cancellation in CDMA

Abstract

In this paper we describe the linear SIC scheme based on matrix-algebra. We show that the linear SIC schemes (single-and multi-stage) correspond to linear matrix ltering that can be performed directly on the received chip-matched ltered signal vector without explicitly performing the interference cancellation. This leads to an analytical expression for calculating the resulting bit error rate which is of particular use for short-code systems. Convergence issues are discussed and it is shown that the simple implementation of the linear SIC provides similar or better performance than the decorrelator at only a few stages. The concept ofconvergence is introduced to determine the number of stages required for practical convergence for both short and long codes. It has previously been observed that the linear SIC has an optimum number of stages for which the bit error rate is minimised. This behaviour is here related to the mean squared error which can be used to estimate the number of stages required to minimise the bit error rate.

Regularization property of linear interference cancellation detectors

“…Therefore, the performance of the LPIC detector is expected to improve at early stages but after a certain number of stages the noise starts dominating the solution and deteriorating the performance of the LPIC detector. This explains the phenomenon pointed out in [11][12][13][14][15][16], which we call here the semi-convergence property of the LPIC detector.…”

“…An important phenomenon that was noticed in the literature of linear IC detectors is their semi-convergence behavior, i.e., the best Bit Error Rate (BER) is obtained prior to convergence. This phenomenon was noticed first in [11][12][13][14][15], and recently in [16], and it seems to be a common feature in most linear IC's if some conditions are met. However, no study has been yet carried out to explain the roots of this phenomenon and to devise necessary conditions for its occurrence.…”

Asymptotic normality of linear multiuser receiver outputs

“…As far as the performance is concerned, we can assume that user 1 always transmits . 4 User 1's decision statistic is a scalar (10) where , like , denotes the element of on the th row and the th column. Clearly, this decision statistic consists of the transmitted symbol scaled by , the multiaccess interference aggregated from all the other users, and a Gaussian noise term.…”

“…A set of sufficient decision statistics is obtained by matched filtering using all user's unnormalized spreading sequences 3 (5) where the correlation matrix is determined by (4), and is a zero-mean Gaussian noise vector with covariance matrix , where is the noise sample variance.…”

“…The conventional matched filter, the decorrelator, and the minimum mean square error (MMSE) receiver are among the earliest and most well known linear receivers. More recently, linear interference cancelers have also been analyzed [4]- [9].…”