Dividing the grids of compressed sensing for channel estimation and investigating Markov codes

Abstract

Bajwa et al. proposed a channel estimation method based on compressed sensing. This method is markedly superior to the conventional methods. However, there is a problem in the method that multi-path delays may not be resolved if they span between the grids. We study to overcome the drawback of the method. Firstly, we investigate upsampled codes so that we could more accurately estimate the channel. Secondly, we investigate Markov codes. It was shown that Spread Spectrum (SS) codes with negative autocorrelation reduces the Multiple Access Interference (MAI) as well as Bit Error Rate (BER) in chip-asynchronous Spread Spectrum Multiple Access (SSMA) systems. Such SS codes are generated from a Markov chain whose transition probability matrix has a negative eigenvalue λ = -2 + √3. The mean square error (MSE) of channel estimation using upsampled Markov code is shown to be better than the MSE of channel estimation using upsampled independent and identically distributed code at certain conditions.