Efficient channel estimation using expander graph based compressive sensing

Compressive sensing (CS) has recently attracted lots of attention and has been extended to more structured architectures, for example the linear time-invariant system identification. However, prevalent CS methods used for channel estimation, such as Basis Pursuit Denoising (BPDN) and Dantzig selector (DS), require computational complexity as high as O(N³), where N is the length of the channel. When N is very large, the complexity will aggravate the hardware burden. In this paper, we propose a new channel estimation scheme that uses the expander graph based compressive sensing. The computation complexity is demonstrated to be as low as O((P - N)N), where P is the length of the training vector.