Robustness to quantization errors in LMS adaptation via degree of excitation

The quantized regressor (QReg) algorithm, a variant of the least mean square (LMS) algorithm, is attractive due to its computational simplicity, and it serves as a model of LMS under quantization errors due to digital implementation. A description is given of excitation conditions which guarantee convergence of QReg assuming that the quantization in the algorithm is fine enough. In addition, given a fixed fineness of quantization, excitation conditions can be developed such that QReg with that quantization fineness converges. The excitation conditions take the form of a degree of excitation, and one may interpret this as a measure of robustness of LMS to quantization errors. Examples are given which demonstrate the theory