Introduction

In recent years, multiple-input multiple-output (MIMO) wireless communication technology has gained considerable attention due to its potential to significantly increase spectral efficiency compared to traditional single-input single-output (SISO) technology. A number of computationally efficient algorithms for reliable symbol detection in time-invariant flat-fading MIMO systems have been developed, such as the V-BLAST architecture [1].

A direct application of these algorithms to time-varying channels is difficult, however, due to the need of perfect channel state information at the receiver side. A number of adaptive algorithms have been proposed to resolve this issue, such as an adaptive receiver based on the V-BLAST algorithm with a generalized decision feedback equalizer (GDFE) [2], a numerically more robust version of this algorithm [3], and a channel tracking algorithm based on decision-directed recursive least squares[4]. All of these are supervised equalization algorithms, requiring an initialization phase in which a number of pilot symbol slots are sent.

An approach for blind equalization in communication problems can be based on clustering techniques, which have mainly been applied in time-invariant SISO systems, using for instance radial basis function networks [5] or a cluster-based MLSE equalizer [6]. Some of these algorithms maintain their performance under slowly time-varying channels. Extensions to MIMO systems have also been proposed [7,8].

Most algorithms for equalization of fast time-varying channels are supervised adaptive algorithms. However, thanks to the recently proposed advances in the field of machine learning, some efficient clustering techniques can also be extended to tackle this problem. In particular, it appears that the non-convex clustering capabilities of the recently proposed spectral clustering technique [9] can be applied to this end.

The main contributions of this work are twofold. First, it is shown that by incorporating the temporal variable in the clustering process, it is possible to untangle the different clusters representing different input symbol slots. The major limitation of the method is that the number of clusters increases exponentially as a function of the number of transmitting antennas, $N_t$ . To relax this limitation, the second contribution of this paper is to exploit the geometry of the transmitted constellation within the spectral clustering algorithm in order to reduce the number of clusters. Once these different clusters have been identified, a simple decoding process is applied to relate each cluster with a symbol slot. It is shown that this can be done by sending as few as $N_t$ pilot symbol slots.

This paper organized as follows: In Section 2 a detailed formulation of the problem is given. In Section 3 spectral clustering is introduced, followed by a description of how it can be applied directly to this equalization problem. Its performance can then be enhanced by exploiting the constellation's geometry, as presented in Section 4, and in Section 5 a decoding stage concludes the algorithm. Test results and comparisons with the GDFE algorithm are given in Section 6, followed by the conclusions of this work in Section 7.