Advanced ICA-based receivers for block fading DS-CDMA channels
Introduction
Code division multiple access (CDMA) technology is a strong candidate for the evolving wireless communications systems. Wideband CDMA (WCDMA) has already been selected for an air interface solution e.g. in UMTS, which will provide a multitude of services, especially multimedia, and high bit rate packet data. The existing commercial spread spectrum systems are based on long spreading codes, where the period of the code sequence is much longer than the duration of a symbol. However, along with the demand for higher data rates, also short code modes, e.g. time-division duplex (TDD) mode in WCDMA [7], are becoming a reality.
In CDMA systems the users share the same frequency band, and thus a good care must be taken to limit mutual interference. In principle, orthogonal codes would be the simplest solution. However, orthogonality between the users is destroyed e.g. by multipath propagation. This is why the traditional RAKE receiver [20] might be inadequate, even in the absence of background noise. Multiuser detection (MUD) is a technique which tries to exploit the structure of interference to be able to suppress it. Optimal MUD [25], however, is computationally exhausting, and requires several system parameters to be known. As a consequence, many suboptimal multiuser receivers and adaptive multiple access interference (MAI) suppression techniques have been studied extensively during the past 10 years [8], [15], [26], [27], [28], [29]. These techniques only utilize second order statistics. However, the assumption of independence is also realistic, which can be utilized e.g. in constant modulus (CM) algorithms [4], [17].
A more general approach than CM is a statistical technique called independent component analysis (ICA) [5], [10], [13]. Recently, ICA and the closely related blind source separation (BSS) problem have attracted a lot interest both in statistical signal processing and neural network communities. Several good algorithms utilizing higher-order statistics either directly or indirectly via suitable nonlinearities are now available for solving the basic linear ICA/BSS problem [1], [19]. ICA is mainly considered for real valued signals, whereas complex ICA is addressed less frequently [2], [3], [18]. In practice, however, the signal to be processed is often complex valued. This problem arises by nature in the reception of a CDMA system. This is because the spreading code might be complex valued, as well as the symbols depending on the data modulation. In addition, the received signal strengths, which characterize channel variations in time, are modelled as complex valued fading processes.
There exists many motivating reasons to use the means of ICA in the reception of a CDMA system. First of all, ICA provides a near-far resistant receiver, being able to resist strong interferences. Resistance is achieved by ICA quite naturally, since ICA only requires the source signals to be statistically independent, but their strengths are allowed to differ. In CDMA the sources are, roughly speaking, users’ symbol streams, and it is hence reasonable to assume that they are independent. Near-far resistance is one of the key requirements of a receiver, and it becomes even more important as there is a demand for higher data rates. This is because many solutions for higher data rates, e.g. smaller spreading factors, and higher symbol constellations, tend to worsen the near-far situation either directly or indirectly via e.g. power control imperfections. Secondly, the propagation delay and the state of the channel should be estimated prior to actual symbol estimation. For subspace-type receivers also the estimation for the model order should be available. The estimation of these parameters will always include some measurement errors, which degrade the accuracy of symbol estimation. ICA, on the other hand, does not need that precise knowledge of the system's parameters, since the estimation is based purely on the (higher order) statistical properties of the signal. Therefore, with ICA we should expect some robustness against erroneous parameter estimation. Thirdly, an ICA block can be used as an add-on feature, to be attached to any existing receiver structure. This makes it possible to consider hybrid receiver structures, in which the ICA block could be intelligently activated only when it is expected to improve performance.
In this paper, we consider ICA to assist the symbol estimation and interference suppression in DS-CDMA systems by attaching an ICA block to RAKE [20] and a subspace-type MMSE receiver [28]. The goal is hence to exploit the independence of the source signals, which is not possible by RAKE nor MMSE detector alone. In addition, it gives the possibility to compensate for any performance loss caused by erroneous propagation delay or channel estimation, which are prerequisite tasks for conventional receivers. FastICA [3], [9], which is one of the most promising ICA methods, is especially considered as the ICA block of the receivers. The contribution of the paper is two-fold. Firstly, a proof of global convergence is given for the complex FastICA algorithm [3], when a cubic nonlinearity is used. Then two types of receiver structures, namely RAKE-ICA, and MMSE-ICA, are proposed. They consist of a RAKE receiver [20] and a subspace MMSE detector [28], respectively, followed by receiver adjustment by FastICA. Numerical experiments are included, when the CDMA downlink channel is Rayleigh block fading. Compared to RAKE and the subspace MMSE detector, respectively, significant improvements in bit- and block-error-rates are achieved. Quite significantly, their performance is close to the theoretical bound of an equal length MMSE detector.
The rest of the paper is organized as follows. In the next section we discuss ICA and its application to CDMA. The data model is presented in Section 3. The ICA-based receiver structures are proposed in Section 4, followed by numerical experiments in Section 5. Section 6 summarizes the paper.
Section snippets
Independent component analysis and CDMA
Independent component analysis (ICA) is a statistical technique where the goal is to represent a set of random variables as a linear transformation of statistically independent component variables. The main application of ICA is blind source separation (BSS) problem, which has become an attractive field of research in the statistical signal processing and neural network communities. The growing interest in ICA is mainly due to emerging new practical application areas, where the assumption of
Data model
The channel model studied in this paper is a DS-CDMA downlink (e.g. base to mobile) multipath channel model, which is depicted in Fig. 1. In direct sequence (DS) CDMA each user spreads its narrowband information signal in frequency by direct sequence modulation before transmission via common channel. The spreading code is user-specific, and thus identifies each user in the system. The data in the observation interval have thus the formin which M
Complex FastICA
The observed data are first whitened, which is a common preprocessing task in blind source separation. It helps to reduce the number of unknowns in the mixing matrix, so that the remaining mixture can be modelled by a simpler orthonormal matrix. More precisely, whitening is a linear transform which de-correlates the observed mixtures, and normalizes the component variances to unity. This can be always performed e.g. by principal component analysis (PCA) as follows:Here
Numerical experiments
Since there does not exist an useful analytical performance measure for the iterative detectors, numerical simulations are given instead. We compare the methods in the downlink environment with Rayleigh block fading multipath channel. The methods for symbol estimation are: RAKE, RAKE-ICA, subspace MMSE detector, MMSE-ICA, and MMSEbit-ICA. In some experiments an exact MMSE detector of the same length as other detectors is also used as a reference. Exact MMSE assumes also the codes of interfering
Conclusions
In this paper we considered blind multiple access interference suppression in the DS-CDMA communication system by means of independent component analysis. Modifications of FastICA [3], [9] with complex valued data were proposed, and the proof of global convergence was given in the case of complex valued signals with circular distribution. Two types of receiver structures, RAKE-ICA and MMSE-ICA were proposed. The reasons for taking ICA as an additional tuning element, were the following:
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Acknowledgements
This work was supported by the Research Programme for Telecommunication Electronics (Telectronics) of the Academy of Finland.
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