A New Sparse Signal-Matched Measurement Matrix for Compressive Sensing in UWB Communication

Ultra wideband (UWB) technology is suitable for high data rate short range wireless communication, localization, and imaging techniques. However, UWB systems require high sampling rate and precise synchronization. In order to reduce the sampling rate, have precise synchronization, and for low power requirement, UWB systems are implemented using compressive or sub-Nyquist rate measured samples by exploiting the sparsity of the UWB signal. Compressive sensing (CS)-based UWB systems are being designed in two ways: 1) signal demodulation or detection is performed in the CS domain without full signal recovery at the front-end. Thus, demodulation or detection works on compressive measurements. However, system performance deteriorates in the CS domain as compared with full Nyquist rate sampling and 2) after, Nyquist rate signal is recovered using efficient algorithms at the front-end, the signal demodulation or detection is performed using the conventional receiver. Thus, one requires an efficient CS/sampling of signal measurement at the front-end for better system performance for both the cases stated earlier. In this paper, we propose a deterministic (partial) UWB waveform-matched measurement matrix. The proposed measurement matrix has a circulant structure and is sparse in nature. The proposed matrix is easy to implement in hardware and is operationally time efficient as needed in a practical system. The bit error rate performance of the corresponding UWB system and the operational time complexity with the proposed measurement matrix are better as compared with the existing measurement matrices in the CS domain for both the above receiver designs. The efficacy of the proposed measurement matrix is verified through extensive simulations in both the additive white Gaussian noise and multipath communication environments. In addition, we have also compared other desirable properties of the proposed measurement matrix with the existing measurement matrices.