A lower bound on the MSE of the single loop sigma delta modulator
W e derive a lower bound far the Mean Square Error (MSE) of singie loop Sigma Delta modulators. This is done by exploiting the inherent structure of the codewords the modulator is capable of producing as a S O U ~ E ~ coder. Spedfically, we find a unique ordering of the codewords in order to derive an upper bound on the size of the collection of the codewords. This upper bound is then used to find a lower bound for MSE which is shown to be independent of the decoder configuration, and inversely proportionalto M', where M is the oversampling ratio. Numerical simulations are used to show that the actual number of codewords the modulator is capable of producing is proportional to M2. It is also shown that the sigma delta modulator can be thought of as a nonuniform quantizer in which the ratio between largest and smallest quantization intervals is approximately equal to the oversampling ratio. Numerical values of the quantization intervals are used to show that the MSE of a nonlinear decoder based on "lwk up" table approach is inversely proportional to M3.