A Class of 1-Bit Multi-Step Look-Ahead
$\Sigma $ - $\Delta $ Modulators
Digital Multi-Step Look-Ahead (MSLA) 1-bit $\Sigma $ - $\Delta $ modulators are introduced. They improve upon the stability and noise shaping characteristics of conventional 1-bit $\Sigma $ - $\Delta $ modulators by minimizing quantization error metrics of the current and future output samples. The mathematical model of the proposed MSLA modulators is analyzed. It is shown that the MSLA modulators are equivalent to a system of conventional $\Sigma $ - $\Delta $ modulators in parallel, but with a common multi-input 1-bit quantizer instead of a typical one. The properties of this multi-input quantizer are studied and the transfer functions of the MSLA modulators are derived. Simulation results are presented demonstrating the advantages of the MSLA modulators over conventional 1-bit $\Sigma $ - $\Delta $ ones in a number of applications. A parametric hardware architecture of the MSLA modulators is presented offering an adjustable trade-off between performance and hardware complexity based on the number of look-ahead steps. Finally, a FPGA implementation of a MSLA modulator is presented along with simulation results.