Space–time channel estimation and soft detection in time-varying multiaccess channels
Introduction
Wireless fading channels are hostile media where communication signals suffer from severe distortion due to time-varying multipath propagation [6], [20], [25]. Hence, sophisticated signal processing and channel coding techniques are necessary to achieve high spectral efficiencies. Towards this aim, it has been demonstrated that deploying multiple transmitting and receiving antennas in a wireless link can yield a significant capacity increase if multipath propagation is correctly exploited [4], [23], [31], [29], [5], [9]. Indeed, it was first shown by G.J. Foschini that the system capacity grows linearly with the number of transmitting antennas as long as this is less than, or equal to, the number of receiving antennas [4], [5]. Further combination of vector coding techniques, suitable for multi-antenna transmitters, with signal processing methods at the receiver, for efficient channel equalization and data detection, has led to the development of the so-called space–time coding (STC) concept [28], [29], [30], [31], [5], [9], [16].
From the signal processing point of view, a number of techniques previously developed for static (or quasi-static) channel estimation and data detection1 in several kinds of multiple input multiple output (MIMO) systems are also relevant for STC. When a sufficiently large number of transmitted data are known a priori by the receiver (i.e., training sequences are employed), conventional criteria, such as minimum mean square error (MMSE) and least squares (LS) [10], [32], can be applied for supervised estimation of both the channel and the data. Alternatively, when the transmission of training sequences is not possible or desirable, blind techniques that rely on the statistical and structural knowledge of the communication signal are preferred [1], [33]. Algorithms for blind source separation (BSS) [2], [1], [18], [35], [21], blind channel identification [34], [33], [8], [36], [37] and joint channel/data estimation [27], [41], [24] fall within this category. Blind techniques, however, pose a number of practical problems, which may include misconvergence due to inadequate initialization [24], [27], [41], the need of very large data records [2], [1], [35] and poor performance in the low signal-to-noise-ratio (SNR) region [40]. Semiblind methods try to alleviate these drawbacks by combining statistical criteria and the transmission of short training sequences [14], [13]. Most decision directed algorithms for joint channel/data estimation can be classified as semiblind when a training sequence is used for computing initial estimates [24], [27], [41].
Both channel estimation and data detection become more involved when the quasi-static channel assumption does not hold. The conventional approach to address the environment variability is to use adaptive algorithms that track the channel evolution [10]. If the environment is a quickly changing one (e.g., a transmitter placed on top of a rapidly moving vehicle, such as a car or a train coach), it is very difficult to guarantee the convergence of LMS-like or RLS-like algorithms2 [17]. It has already been shown [17], [15], [12] that taking explicitly into account the time-varying nature of the channel leads to an improved performance. Some authors have addressed this problem in the context of code division multiple access (CDMA) systems, including the higher order statistics (HOS) approach in [19], the time-varying parallel interfence cancellation (PIC) scheme, based on Wiener filtering, in [12] or the probabilistic criterion in [38]. Nevertheless, the most common approach to deal with rapidly varying channels is to use a block-adaptive procedure [17], [15]. This approach basically consists of computing a set of snapshot estimates of the channel in different (e.g., equally spaced) observation windows using training data and, then, interpolating the channel coefficients between successive snapshots.
In this paper, we propose a block-iterative space–time scheme that alternates channel estimation and data detection. The time-varying multipath channel is modelled as a correlated multi-dimensional Gaussian random process. Within this framework, we derive a linear channel estimator that takes into account the autocovariance of the Gaussian process according to the MMSE criterion. We show that, under a homogeneous scattering assumption, the autocovariance function of a stationary channel can be characterized by means of a single scalar function, and we derive a globally convergent block-adaptive algorithm to estimate it. Furthermore, although the homogeneity and stationarity assumptions are necessary for the formal derivation of the method, computer simulations show that the resulting estimation algorithm is very robust in environments where these properties do not hold, since only a slight performance loss is experienced. In exchange, a significant reduction in information requirements (i.e., knowledge of the full channel autocovariance matrices) is achieved.
Our channel estimation method resembles the one in [12], where linear channel estimation is also studied, but remarkable differences exist. First, we address the estimation of a full MIMO time-varying channel in a multi-antenna system, whereas in [12] a CDMA system with known spreading codes is considered and channel estimation is carried out per-user (i.e., several single-input single-output channels are separately estimated). Moreover, we investigate, in detail, the problem of estimating and tracking the channel statistics, which is left open in [12].
The linear filters for channel estimation depend on the transmitted symbols, which are unknown at the receiver except for the training data. Therefore, we propose to iteratively alternate channel estimation and data detection until convergence. From the point of view of performance alone, it is convenient to feed back the high-quality decisions obtained after channel decoding into the channel estimator. Iterating these two steps, however, may be computationally prohibitive depending on the decoding strategy (e.g., the complexity of Viterbi-based decoders grows exponentially with the channel memory and the number of independent data streams to be jointly decoded [39]). Hence, we study a suboptimum scheme where channel estimation and soft data detection are iterated until convergence before decoding. Note that both the channel state information and the soft symbol estimates can be useful for an efficient decoding. Although many other possibilities exist, we consider a decision feedback (DF) structure with two linear filters and an intercalated threshold detector for soft detection, where the coefficients of both filters are selected according to the MMSE criterion. We evaluate through computer simulations the performance (before decoding) of the space–time iterative soft detector in terms of the mean squared-error (MSE) of the channel and symbol estimates.
The remaining of this paper is organized as follows. Section 2 contains a description of the system structure and its associated signal model. In Section 3, we introduce and analyze the linear MMSE channel estimator. The task of joint channel estimation and DF MMSE soft data detection is considered in Section 4. The results of computer simulations that illustrate the performance of the proposed space–time schemes are shown in Section 5. Finally, Section 6 is devoted to the conclusions.
Section snippets
System and signal model
The aim of this paper is to derive an iterative space–time soft estimator (ISSE) that jointly performs channel estimation and soft data detection in a wireless communication system with N antennas at the transmitter and L antennas at the receiver. The block diagram of such a system is depicted in Fig. 1. The information bits to be transmitted, {b(l)}l=0,1,2…, are fed into a channel encoder and interleaver to yield a coded bit sequence. A serial to parallel (S/P) converter followed by a bank of N
Linear MMSE channel estimation
A linear estimator of the channel coefficients at time n can be obtained by processing a window of M+1 observation vectors (being M an even number) according to the MMSE criterion, i.e.,where E[·] denotes statistical expectation, is the L×(M+1) observation matrix used to estimate H(n), MSE(·,i,n) is the associated mean squared-error cost function, is the (M+1)×Nm
Joint soft data detection and channel estimation
The LMMSE filters for channel estimation (4) clearly depend on the transmitted symbols, which are unknown in a practical receiver. Therefore, data detection and channel estimation should be carried out jointly. In this paper, we study the performance of an ISSE scheme that alternates LMMSE channel estimation, as described in the previous section, and DF MMSE soft data detection. DF structures [22], [26] are very appealing, from a practical point of view, because they can attain a remarkable
Setup
In order to illustrate the performance of the proposed ISSE, we consider a system with N=3 transmitting antennas, L=3 receiving antennas, BPSK modulation and rectangular pulses. The burst length, per antenna, is K=800 and the symbol period is , hence an overall bit rate of . We assume a land mobile communication environment with the classical Jake's model of the power Doppler spectrum [20], [25], which yields the autocovariance function,where is
Conclusions
We have introduced an iterative space–time soft estimator (ISSE) that performs joint channel estimation and soft data detection in time-varying multiple-input multiple-output (MIMO) channels. The ISSE alternates channel estimation, taking explicitly into account the channel variability, and soft data detection. Due to its appealing balance between computational complexity and performance, we have proposed a decision feedback (DF) structure to implement the latter stage that consists of two
Acknowledgements
This work has been supported by Ministerio de Ciencia y Tecnologı́a of Spain and FEDER funds from the European Union (grant no. TIC2001-0751-C04-01).
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