Grid Mismatch in MmWave Sparse Channel Estimation: Analysis & Implications

• Published in: IEEE International Conference on Communications (2003) pp. 5033 - 5038
• Main Authors: Daryanavardan, Negar, Nosratinia, Aria
• Format: Conference Proceeding
• Language: English
• Published: IEEE 09.06.2024
• Subjects: Accuracy; Channel estimation; Dictionaries; Matching pursuit algorithms; Millimeter wave communication; Millimeter wave technology; Superresolution
• ISSN: 1938-1883
• DOI: 10.1109/ICC51166.2024.10622810

The millimeter wave (mmWave) channel is inherently sparse, allowing sparse estimation methods such as compressive sensing to be used. This has been welcomed due to the mmWave antenna arrays leading to larger channel dimensions. These channels are sparse in the angular domain, requiring the continuous angle variables to be quantized in order to employ finite-dimensional compressive sensing. This creates a version of the well-known grid mismatch problem in compressive sensing. The impact of this grid mismatch on the accuracy of channel estimates, and the associated requirements, constraints, and guidelines for mmWave system design, have not been analyzed to date. In this work, we present a thorough analysis of grid mismatch in the context of mmWave channel estimation. We calculate the mean squared error of the popular orthogonal matching pursuit algorithm subject to grid mismatch. We clarify the needed dictionary size for a prescribed mean squared error performance, thus assisting system designers and highlighting the implied performance-complexity tradeoff. Numerical results support our analysis. We show that by proper design of compressive sensing subject to our analysis, results comparable to super-resolution methods can be obtained at much lower complexity.