Blind adaptive equalization and diversity combining

Spatial-temporal equalizer can be used in the wireless communication systems with antenna arrays to improve the performance. In this article, we introduce two blind adaptive algorithms for spatial-temporal equalization, and present their convergence. Computer simulation demonstrates that the new algorithms converge faster than fractionally spaced constant-modulus algorithm (FSCMA). 1 PROBLEM FORMULATION To improve the quality of wireless communication systems, antenna arrays are used for diversity reception. To make full use of the information contained in each sensor, spatial-temporal equalizer is used to remove intersymbol interference and mitigate the additive channel noise. The wireless communication systems with antenna arrays can be modeled as single-input/multiple-output systems shown as in Figure 1. Since the channels are time-varying and training sequences are not always available, blind adaptive techniques have to be used in these systems. In Figure 1, the input sequence fs[n]g is sent The work was supported in part by the NSF grants MIP9309506 and MIP9457397. The work was done while he was at the University of Maryland. through M di erent linear channels with impulse response fhm[n]g for m = 1; 2; ;M . Hence, the channel outputs can be written in matrix form as xK [n] = HKsK [n]; or XK [n] = HKSK [n]; (1:1) where we have used the de nitions HK = 0 B@ h[L 1] h[0] 0 .. . . . . . . . . . .. 0 h[L 1] h[0] 1 CA ; (1:2) XK [n] = (xK[n]; ;xK[n+N 1]); (1:3) SK[n] = (sK[n]; ; sK[n+N 1]); (1:4) with sK [n] = (s[n L+ 1]; ; s[n+K 1]) ; h[n] = (h1[n]; ; hM [n]) T ; xK [n] = (x [n]; ;x [n+K 1]) ; and x T [n] = (x1[n]; ; xM [n]): The integer K in the above equations determines the dimensions of the matrices and the vectors. In this article, we will assume that the SIMO channels are of nite impulse response (FIR) with length L, and furthermore, they satisfy the lengthand-zero condition [2], which makes HK for any K L 1 to be of full column rank. Hence, from (1.1), there exists a KM (K + L 1) matrix F (not unique) such that sK [n] = F H xK [n]; F = (f1; f2; ; fK+L 1); (1:5)