A Simple FPGA-Based Lossless Wireless Transmitter/Receiver Using the Residue Number System
Michael Ekonde Sone, N. Ntomambang Ningo · The African review of physics · 2009
Wireless system design often feature FPGAs alongside DSPs and FPGAs, which offer superior speed compared to other processors and operate close to the antenna and are the core of a larger processor in the transmitter and receiver blocks. In the transmitter, a methodology to analyze factored orthogonal 1-D DWT based on the wavelet lifting scheme and the RNS is used. The wavelet lifting scheme is used because it allows an in-place implementation and reduces the forward transform to a sequence of simple steps involving elementary algebraic operations that make it trivial to find the inverse transform [1, 2]. However, scaling is inherent in all lifting transforms and does not yield integer results. Many methods exist to overcome this scaling [3]. However, these approaches introduce further processing that can increase algorithmic complexity. To simplify system design, the scaling factor is assumed to be unity in this approach. As a result, minimization of the circuit design is enhanced while retaining system high-fidelity. The residue digits from the RNS and wavelet lifting scheme are transformed into orthogonal signals through the mapping to a set of Walsh functions. The orthogonal signals are then multiplexed unto a carrier wave and transmitted to the receiver. In the receiver, the low-pass equivalent composite signal made-up of the set of orthogonal signals is passed through a bank of correlators. The scalar products of the transmitted signal and stored copies of the Walsh functions are used to find the optimum estimate of the residue digits. The Chinese remainder theorem is later used to recover the message. In the proposed communication system, the message is considered to be subjected only to quantization noise. The channel requirements and the FPGA inherent speed render effects due to additive white Gaussian noise negligible. It is shown that [4], for a quantization error, Pe ≤ 10 the decoding errors have negligible effect. Using this error threshold, the RMS error for different moduli set is calculated for a given test signal.