Incremental Gaussian Elimination Approach to Implement OMP for Sparse Signal Measurement

Abstract

An efficient architecture of the orthogonal matching pursuit (OMP) algorithm is proposed to recover signals compressively measured at the sub-Nyquist rate. The proposed architecture is implemented on the field-programmable gate array (FPGA) for performance validation. In the place of matrix factorization-based pseudoinverse computation, Gaussian elimination (GE) is used to compute the signal estimate. A novel incremental Gaussian elimination (IGE) algorithm is proposed and used in the OMP algorithm. The proposed design is targeted to the Virtex6 FPGA device to compare with other reported works for $K=256$ , $N=1024$ , and $m=36$ , where $N$ is the number of samples, $K$ is the measurement vector length, and $m$ is the signal sparsity level. The recovery signal-to-noise ratio (RSNR) of 23.98 dB is achieved. The proposed work is validated by implementing it on the Artix7 FPGA device by taking compressed measurements from an analog to information converter (AIC). The input signal is synthesized as a random combination of sine waves with different frequencies. The proposed architecture is hardware-efficient and faster, and consumes low dynamic power than other existing designs. The proposed design is hardware-efficient even for the higher value of $m/K$ .