Quantization effects in the complex LMS adaptive algorithm: Linearization using dither-theory

Abstract

This paper describes the use of dither to linearize the gradient quantizer in a digitally implemented LMS adaptive algorithm. When the LMS algorithm is implemented in a fixed-point digital processor, a choice must be made between rounding the gradient estimate before addition to the contents of the weight accumulator, or rounding the weight at the accumulator output and operating a double-precision accumulator. Because of hardware constraints, the former approach is often elected. However, when the weight accumulator input is quantized, care must be exercised to prevent the algorithm from stalling. To overcome this difficulty, a sequence of random vectors, called "dither," is used to "linearize" the gradient quantizer. A difference equation for the weight covariance matrix is derived, and a solution for transient mean-square error is obtained that includes both the effects of dither and quantization noise.