Estimation of sparse multipath channels

In many communication systems the channel impulse response can be characterized with a parametric form, though the channel estimation is often performed using an equivalent discrete-time linear time-invariant system (usually modeled as a Moving Average (MA) system). When the number of parameters which describe the channel is less than the number of unknowns in the MA model, the ML estimate of the parameters describing the channel may lead to a better estimate of the channel response. However, this ML estimation procedure is highly complex. The objectives of this paper are 1) to cast the parameter estimation problem as a sparse estimation problem, 2) to compare the performance of this estimate with the CRB of the parameter estimation problem and the least squares estimate, and 3) to present novel guidelines on the amount of resources which one must devote to training for identification of the channel.