Fast OMP algorithm and its FPGA implementation for compressed sensing‐based sparse signal acquisition systems

Abstract

Compressed sensing-based radio frequency signal acquisition systems call for higher reconstruction speed and low dynamic power. In this study, a novel low power fast orthogonal matching pursuit (LPF-OMP) algorithm is proposed for faster reconstruction of sparse signals from their compressively sensed samples and the reconstruction circuit consumes very low dynamic power. The searching time to find the best column is reduced by reducing the number of columns to be searched in successive iterations. A novel architecture of the proposed LPF-OMP algorithm is also presented here. The proposed architecture is implemented on field programmable gate array for demonstrating the performance enhancement. Computation of pseudoinverse in OMP is avoided to save time and storage requirement to store the pseudoinverse matrix. The proposed design incorporates a novel strategy to stop the algorithm without consuming any extra circuitry. A case study is carried out to reconstruct the RADAR test pulses. The design is implemented for K = 256, N = 1024 using XILINX Virtex6 device and supports maximum of K/4 iterations. The proposed design is faster, hardware efficient and consumes very less dynamic power than the previous implementations of OMP. In addition, the proposed implementation proves to be efficient in reconstructing low sparse signals. 1 | INTRODUCTION High-frequency radio frequency (RF) signals, such as RADAR pulses, are sparse in nature in the transform domain. Exploiting this sparsity property, modern signal measurement systems use compressed sensing (CS) [1,2] in place of other existing sampling techniques [3] to acquire RF signals. CSbased acquisition systems can work with low speed analog-todigital converters due to sampling at sub-Nyquist rate [4]. In CS-based sampling paradigm, random measurements are taken from the signal and then the original signal is recovered from the measurement samples using signal recovery algorithms. Orthogonal matching pursuit (OMP) [5,6] is a well known recovery algorithm. Unlike the other greedy pursuit algorithms, OMP provides better performance with moderate computational complexity. OMP estimates a sparse signal by executing two steps in every iteration, viz., perform the atom searching (AS) and solve a least squares (LS) problem. In AS step, OMP identifies an atom or a column of the sampling matrix which gives maximum correlation with the current residual. Subsequently the signal is estimated by solving an LS problem. The timing complexity of the AS step is very high as it is a linear function of the signal sparsity and the number of samples. Many techniques are reported in literature to reduce the timing complexity of AS step. In [7] authors applied clustering algorithms to group the similar columns and reported a tree-based pursuit algorithm. But such algorithm has no reports of implementation. Researchers reported parallel selection of multiple columns to address the timing complexity problem in [8,9]. Multiple selection of columns reduces the timing complexity but with greater cha...

Design and Verification of Deep Submergence Rescue Vehicle Motion Control System

“…For a more precise representation of the data, the samples with a size of 3 200 were selected. When the dictionary was trained, the orthogonal matching tracking method [ 62 ] was used to solve Equations (2) and (3) to realize sparse representation.…”

A review of optimisation and least-square problem methods on field programmable gate array-based orthogonal matching pursuit implementations

“…A new architecture of a low-power fast OMP (LPF-OMP) algorithm was presented in [20]. The LPF-OMP can avoid the computation of pseudoinverse to save time and storage requirement to store the pseudoinverse matrix.…”

“…HSL eases the process and increases design productivity but it may affect in terms of time and usage of area. [6], [15], [17], (c) Improved OMP in [13], [18], [19], [21], (d) Improved OMP in [14], (e) Improved OMP in [16], and (f) Improved OMP in [20]…”

“…Figure 1. Flow charts of methods for (a) Normal OMP, (b) Improved OMP in[6],[15],[17], (c) Improved OMP in[13],[18],[19],[21], (d) Improved OMP in[14], (e) Improved OMP in[16], and (f) Improved OMP in[20] …”