Compressed detection for ultra-wideband impulse radio

The emerging theory of compressed sensing (CS) not only enables the reconstruction of sparse signals from a small set of random measurements [1, 2], but also provides an universal signal detection approach at sub-Nyquist sampling rates [3, 4]. Compressed signal detection is particularly suitable for impulse ultra-wideband (I-UWB) communications where Nyquist sampling of the signal is a formidable challenge [5]. In this paper, we propose a generalized likelihood ratio test (GLRT) detector for I-UWB receivers based on compressive measurements. Pilot symbol assisted modulation is proposed where received signals are randomly projected and subsequently correlated for data demodulation. The proposed receiver is simple to implement, which has the advantage that neither wideband delay lines nor ultra-fast analog to digital converters (ADC) are required. Given a channel realization, the exact bit error probability (BEP) of the proposed receiver is derived. Approximate BEP is also derived under the Gaussian assumption. Simulation results show that the proposed receiver with moderate compressive measurements has comparable performance to traditional analog autocorrelation (AcR) receivers [6, 7].