Performance of UWB $N$-Orthogonal PPM in AWGN and Multipath Channels

Abstract

This paper studies pulse-based M-ary ultrawideband communications analyzing both the symbol error rate (SER) and the information theoretic capacity C for single-link communications over both additive white Gaussian noise and multipath channels (taking into account random variations in both energy and correlation values). In particular, we consider M-ary N-orthogonal pulse-position-modulated (PPM) signals with numerical pulse-position optimization to exploit the negative values in the pulse correlation function. On one hand, the N-orthogonal PPM (N-OPPM) signals can accommodate a larger value of M than the nonoverlapping orthogonal PPM (OPPM) signals for a constant frame size and pulse width, allowing increasing the symbol transmission rate and/or the use of error correcting codes. However, N-OPPM requires a receiver with N correlators, while the receiver for OPPM requires one correlator. On the other hand, the pulse positions of the N-OPPM signals can be manipulated to shape the power spectrum density and decrease the level of the discrete components. However, this PPM manipulation changes the N-OPPM correlation properties of the signal set. At the same time, N-OPPM signals have equal or better performance than OPPM signals. More specifically, simulations show that for low values of M, the N-OPPM has lower SER and higher C than OPPM for the same signal-to-noise ratio (SNR), and that for larger values of M, it achieves similar SER and C. Hence, N-OPPM signals allow a tradeoff between transmission rate, signal performance, and receiver complexity