Analyzing the Impact of Sigma-Delta Modulation on Performance Parameters of Adaptive Filters

Abstract

Sigma-delta modulation (SDM), initially introduced for ADCs and DACs is now well known in an alternative domain of short word-length (SWL) algorithm based digital system design. Its applications start from simple arithmetic operations to very complex circuits, like the adaptive filters. The conventional multi-bit processing systems consume more resources in their implementation on ASICs and FPGAs, whereas, SDM based systems being processing the data in a single-bit result a compact design. This paper is an effort towards SDM based single-bit, design of adaptive filter using Wiener–Hopf equation on FPGA, along with analyzing the impact of SDM on performance parameters, like, Signal to Noise Ratio (SNR), Probability of Error (PE), and Mean Square Error (MSE). Besides, the error graph, showing the difference between the filtered signal in multi-bit and SDM based is also shown and analyzed using Matlab. As, the mobile phone operates in a continuous varying environment (for example, during the travel), and hence the statistical parameters (SNR, MSE, and PE) due to varying channel also vary accordingly in its conventional operations and architectures, but results show that instead if SDM is used, those statistical parameters remain constant, and in comparison to the multi-bit approach the SDM based system outdoes in all means of functionality as well as performance. Hence, it may be concluded that for continuous varying environments of wireless communication, especially the mobile communication systems, the SDM based approach may be adopted for reasons of good performance as well as compact system design.