Low Complexity Asynchronous DS-CDMA Detectors

dk (m)
sk (t)
n(t) rreceived(t)
k
user k user K
bk (t ? mTs )
pP ej k k
Figure 1: The channel model. a complex alphabet, D k . For example, when BPSK is used D k = f?1; +1g. The kth user's data stream dk (m) is multiplied with the corresponding code sequence to form the signal sk (t), i.e.,
sk (t) =
1 X
m=?1
dk (m)bk (t ? mTs) :
The transmitted signal is formed by multiplying the signal sk (t) with Pk ej k , where Pk is the power and k is the random carrier phase uniformly distributed on the interval 0; 2 ). Since the transmission is assumed to be on an AWGN channel with an unknown propagation delay k , the received signal can b Vector Model
The DS-CDMA system under consideration is a K -user system using symbols from a complex alphabet. The system operates over an additive white Gaussian noise (AWGN) channel with an unknown propagation delay k . The symbol duration is denoted Ts and each symbol consists of N chips with duration Tc = Ts =N each, where N is an integer. The code sequences, bk (t), are all assumed to have unit amplitude and to be periodic with period Ts (i.e., short codes are used), i.e., bk (t) = bk (t ? Ts ); t 2 0; Ts). Generally, a subscript k implies that = the subscripted quantity is due to the kth user. The channel model assumed throughout this paper is illustrated in Fig. 1. The symbols dk (m) are taken from user 1
1
1 Introduction
A major issue is DS-CDMA (Direct Sequence-Code Division Multiple Access) systems is the near-far problem. In general, when solutions are proposed to this problem, the algorithms work on the samples from code-matched lters. The aim of this work is to present multiuser-detectors for an asynchronous DSCDMA system which are near-far resistant and do not need the code-matched lter outputs from all users. The motivation for using this in some sense nonstandard model is that the time-delays of the users are not known a priori which renders code-matched ltering impossible. The time-delays are typically estimated from asynchronous samples of the chip-matched lter. Thus it is of interest to formulate detectors that work on the same statistics as the synchronization algorithm. Furthermore, when samples from the chip-matched lter are used, it is possible to circumvent the problems which arises due to the asynchronous channel. Detectors for bit-detection on the output of code-matched lters is studied in many references, e.g., 7] and 2]. The system is assumed to work on an AWGN-channel. It is of course not a realistic channel for a multiuser-system, it gives however a possibility for theoretical analysis and the extension of the models and algorithms, presented in this paper, to a multi-path environment is rather straightforward.
Low Complexity Asynchronous DS-CDMA Detectors
Thomas Ostman
IR-S3-SB-9523
Signal Processing Department of Signals, Sensors and Systems Royal Institute of Technology
p
rreceived(t) =
K X k=1
sk (t ? k ) Pk ej k + n(t) :
p
The noise waveform, n(t), is modeled as a complex white Gaussian signal with two-sided power spectral density N0 . Thus, the channel simply delays each user with a xed delay and multiplies each user with a complex number. Noise and the di erent users' signals are then super-positioned together by the channel. The receiver front-end consists an integrate-and-dump lter as shown in Fig. 2. The integration time is de ned as Ti = Tc=Q where Q is an integer and is referred to as the oversampling factor. A carrier-modulated system consist of an IQ-mixer on the input. Out of the IQ-mixer there are double frequency terms, which can be neglected as long as !c 1=Ti, holds. Thus, as long as this holds, the system can be interpreted as a base-band equivalent to a carrier-modulated 5
Abstract
In this paper near-far resistant multiuser-detectors for an asynchronous directsequence code-division multiple access (DS-CDMA) system, which do not need the code-matched lter outputs from all users are presented. The DS-CDMA system under consideration is a multiuser system using BPSK modulation. The system operates over an additive white Gaussian noise channel with unknown propagation delays. Two complex-valued, discrete-time vector models for the system are formulated. The di erence between the models is mainly in the dimensions of the matrices and vectors involved. Detectors for both models, that work on blocks of data of M symbols are considered. The problem of estimation of the bits is posed in a least squares sense and as a minimum mean squared error problem. If the dimensions of the matrices used are kept low this implies that soft-decisions of each bit appears twice and weighting of these is necessary. Expressions of the optimum weighting matrices are derived, however due to complexity reasons, they are di cult to implement. Approximations of the optimum weighting matrices, which are easy to calculate, are therefore proposed. In order to compare the di erent suggested detectors, expressions of the SNIR (Signal to Noise and Interference Ratio) are derived and it is shown that the proposed detectors are near-far resistant. Furthermore, the impact of making decisions on samples which are not chip-synchronous and the need for oversampling is studied. The performance of the detection algorithm is investigated by computing the BER (Bit Error Rate) on simulated data. Comparisons with traditional detectors is also carried out. It is shown that detectors based on the compact vector model performs slightly worse than detectors based on the more complex vector model. However, the complexity is much lower for a detector based on the compact vector model.