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While 1-bit analog-to-digital conversion (ADC) allows to significantly reducethe analog complexity of wireless receive systems, using the exact likelihoodfunction of the hard-limiting system model in order to obtain efficientalgorithms in the digital domain can make 1-bit signal processing challenging.If the signal model before the quantizer consists of correlated Gaussian randomvariables, the tail probability for a multivariate Gaussian distribution with Ndimensions (general orthant probability) is required in order to formulate thelikelihood function of the quantizer output. As a closed-form expression forthe general orthant probability is an open mathematical problem, formulation ofefficient processing methods for correlated and quantized data and ananalytical performance assessment have, despite their high practical relevance,only found limited attention in the literature on quantized estimation theory.Here we review the approach of replacing the original system model by anequivalent distribution within the exponential family. For 1-bit signalprocessing, this allows to circumvent calculation of the general orthantprobability and gives access to a conservative approximation of the receivelikelihood. For the application of blind direction-of-arrival (DOA) parameterestimation with an array of K sensors, each performing 1-bit quantization, wedemonstrate how the exponential replacement enables to formulate a pessimisticversion of the Cram\'er-Rao lower bound (CRLB) and to derive an asymptoticallyachieving conservative maximum-likelihood estimator (CMLE). The 1-bit DOAperformance analysis based on the pessimistic CRLB points out that alow-complexity radio front-end design with 1-bit ADC is in particular suitablefor blind wireless DOA estimation with a large number of array elementsoperating in the medium SNR regime.

DOA Parameter Estimation with 1-bit Quantization - Bounds, Methods and the Exponential Replacement