Complexity Reduction for Consumer Device Compressed Sensing Channel Estimation

High mobility has become a mandatory consideration in the design and development of wireless communication systems today. It results in a doubly selective or a time-varying multipath channel that is arduous to estimate. Compressed Sensing (CS) schemes like the Rake Matching Pursuit (RMP) algorithm exploit the inherent sparsity in these channels and are often able to resolve the multipath environments into their respective sparse representations, even under the presence of large Doppler shifts. However, the complexity involved is substantial and might imperil practical implementation on resource limited consumer device hardware. We propose a novel low-complexity CS scheme, called as Gradient Rake MP (GRMP) that optimizes the search related to the multipath delays resulting in a complexity that is significantly lower than all CS based channel estimation schemes. Additionally, the results confirm that the Bit Error Rate (BER) performance of GRMP is comparable to that of the more complex RMP algorithm. The dictionary is an imperative requirement of CS schemes and plays a decisive role in the quality of the channel estimate. Often in literature, details regarding the generation of the dictionary and its complexity is ignored and instead a suitable dictionary is assumed to be available at the receiver. This paper investigates the complexity and memory demands associated with the dictionary and presents a novel scheme to build it using the concept of wavelets. The ideas proposed in this paper are targeted towards reducing the complexity associated with the estimation of a doubly selective channel with a goal to enable implementation on consumer hardware. Although implemented for the IEEE 802.11p standard, the proposed ideas are applicable to any Orthogonal Frequency-Division Multiplexing (OFDM) based wireless system that is expected to work in highly mobile environments.