We consider the design of sufficiently informative inputs for estimating the parameters of a time-varying linear system. Specifically, we assume the output of the system may be modeled as linear combinations of known time-varying elements whose parameters are points in an appropriately chosen grid for the parameter space, such that these parameters are sparse in comparison with the grid size. The sufficiently informative inputs we study are signals that guarantee a unique sparsest solution thereby satisfying minimum requirements for numerically solving the estimation problem. Since in practice the parameters of interest may not lie on the grid constructed for the parameter space, we discuss how our input designs can be modified to provide robustness in the presence of modeling error and noise.

Recently, we proposed a decentralized cooperative communication scheme [1]. In this paper we show that randomized decentralized schemes perform well even when the cooperating nodes are asynchronous. In particular we study the attainable diversity for frequency selective channels, and the coding gain in comparison to a centralized scheme.

We examine the application of current research in sparse signal recovery to the problem of channel estimation. Specifically, using an orthogonal frequency division multiplexed (OFDM) transmission scheme with pilot symbol assisted modulation (PSAM), we consider the problem of identifying a frequency selective channel from a limited number Q out of a possible M tones of an OFDM symbol. The main observation is that if M is chosen as prime, one can identify the channel uniquely if Q ges 2T, where T is the number of nonzero taps in the frequency-selective channel. The identifiability result requires the minimization of the lo norm, leading to an intractable combinatorial search problem. Several methods have been proposed to deal with these issues, and the one we examine involves l1norm regularization known as basis pursuit, We apply these methods specifically to the problem of estimating a frequency selective channel with PSAM. As a result, the bandwidth efficiency of the system is increased due to the sparsity of the channel.