Independent versus repeated measurements: A performance quantification via state evolution

Abstract

The paper quantifies and compares the exact asymptotic performance of multiple measurement vector (MMV) and distributed sensing (DS) models. Both models assume multiple measurement instances y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> + w <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> , k = 1, 2, ..., K. The difference is that MMV involves identical measurement matrices whereas DS allows different matrices for different measurement instances. It has been recognized that DS works better than MMV empirically. However, the quantification of the performance difference is not available in the literature. Our contribution is to quantify the asymptotic performance of MMV and DS in the asymptotic regime that the dimensions of the measurement matrices approach infinity proportionally but the number of measurement instances K remains a constant. The case study and numerical results justify the accuracy of the performance quantification. The analysis technique is based on the state evolution for approximate message passing.