The Misspecified Cramér-Rao Bound for DOA Estimation with One-Bit Quantized Data

One-bit quantization has gained significant attention in communications and signal processing due to its potential for reducing energy consumption and system costs. However, parameter estimation methods that account for the quantization model tend to be complex and computationally intensive. Consequently, many applications opt to ignore the quantization effects during estimation, leading to model misspecification. This results in estimation errors that are influenced not only by the inherent information loss from quantization but also by the inaccuracies due to model misspecification. In this paper, we derive the misspecified Cramér-Rao bound (MCRB) for the problem of direction-of-arrival (DOA) estimation using one-bit quantized data from a sensor array. The MCRB serves as a valuable analytical tool for assessing the expected performance degradation caused by both model misspecification and quantization. Simulations demonstrate that the MCRB accurately predicts the expected performance of the maximum-likelihood estimator, and the unique effects arising from quantization are thoroughly investigated.