We determine the optimum training strategy for a multiple-antenna wireless link in a Rician fading channel using a training based lower bound on capacity. We consider the standard Rician block fading channel where the channel coefficients are modeled as independent circular Gaussian random variables with non-zero means (the specular component). The specular component is known to both the transmitter and receiver. The channel coefficients of this model are constant over a block of T symbol periods but, independent over different blocks. For such a model, it is shown that the training based capacity, the optimum training signals, the training period, transmit and training energy are dependent on the Rician factor tau along with SNR rho, the number of transmit antennas M, the number of receive antennas N and the coherence interval T. Also, unlike in the case of Rayleigh fading channels, it can be shown using the lower bound for Rician fading channels that for low SNR Rician fading channels behave like a purely AWGN channel and the optimum strategy is to spend no effort in learning the channel. When SNR is not low and training is required then the optimum training period is as many symbol intervals as there are transmit antennas

Calculation of the differential entropy of the limiting density of a sequence of probability density functions (pdf) is an interesting mathematical problem and is important in asymptotic analysis of communication systems. In such cases, it would be of interest to know if the limit of the differential entropies H/sub n/, corresponding to the sequence of pdf f/sub n/, is equal to the differential entropy H, of the limiting pdf f. In this correspondence, we establish sufficient conditions under which H/sub n/ /spl rarr/ H.

We analyze the capacity of a multiple-antenna wireless link with M antennas at the transmitter and N antennas at the receiver in a Rician fading channel when the channel is unknown at both the transmitter and the receiver. The Rician model is a nonstandard model with a Rayleigh component and an isotropically random rank-one specular component. The Rayleigh and specular components remain constant for T symbol periods, after which they change to completely independent realizations, and so on. To maximize mutual information over the joint density of T/spl middot/M complex transmitted signals it is sufficient to maximize over a joint density of min{T,M} real transmitted signal magnitudes. The capacity-achieving signal matrix is equal to the product of two independent matrices, a T/spl times/T isotropically random unitary matrix and a T/spl times/M real nonnegative diagonal matrix. If M>T, optimum signaling uses only T out of the M transmit antennas. We derive a novel lower bound on capacity which enables us to compute achievable rate regions for many cases. This lower bound is also valid for the case of purely Rayleigh-fading channels, where it has not been feasible, in general, to compute capacity, or mutual information. Our numerical results also indicate that the Rayleigh model is surprisingly robust: under our Rician model, up to half of the received energy can arrive via the specular component without significant reduction in capacity compared with the purely Rayleigh case.

We introduce rigorous definitions for two quantities of interest, diversity and degrees of freedom, that are used to quantify the advantages of a multiple antenna multiple-input multiple-output (MIMO) system when compared to a single-input single-output (SISO) system. These definitions are in a general setting which will allow the computation of these quantities for systems other than multiple antenna MIMO systems. We verify the effectiveness of the definitions by computing the quantities of interest for various existing examples.

Partial updating of LMS filter coefficients is an effective method for reducing the computational load and the power consumption in adaptive filter implementations. The sequential partial update LMS algorithm is one popular algorithm in this category. A first-order stability analysis of this algorithm was performed (Douglas, 1997) on wide sense stationary signals under the restrictive assumption of small step size parameter /spl mu/. The necessary and sufficient condition derived on /spl mu/ for convergence in the mean was identical to the one for guaranteeing stability in the mean of LMS. First-order sufficient conditions were derived (Godavarti et al., 1999) for stability without the aforementioned small /spl mu/ assumption. The sufficient region of convergence derived was smaller than that of regular LMS. In this paper, we establish that for stationary signals the sequential algorithm converges in mean for the same values of the step size parameter /spl mu/ for which the regular LMS does. In other words, we show that the conclusion drawn Douglas holds without the restrictive assumption of small /spl mu/. We also derive sufficient conditions for stability on /spl mu/ for cycle-stationary signals.

Partial updating of LMS filter coefficients is an effective method for reducing the computational load and the power consumption in adaptive filter implementations. Only in the recent past has any work been done on deriving conditions for filter stability, convergence rate, and steady state error for the partial update LMS algorithm. Douglas (see IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing, vol.44, p.209-16, 1997) derived approximate bounds on the step-size parameter /spl mu/ which ensure stability in-the-mean of the alternating even/odd index coefficient updating strategy. Unfortunately, due to the restrictiveness of the assumptions, these bounds are unreliable when fast convergence (large /spl mu/) is desired. In this paper, tighter bounds on /spl mu/ are derived which guarantee convergence in the mean of the coefficient sequence for the case of wide sense stationary signals.