In [1] the authors consider linearly independent channel covariance matrices, however, they do not mention if it is symmetric or not.
Therefore, I'd like to know if the covariance matrix for that case is symmetric.
[1] Emil Björnson, Jakob Hoydis, and Luca Sanguinetti,"Pilot contamination is not a fundamental asymptotic limitation in massive MIMO", IEEE International Conference on Communications (ICC), May 2017.
Thanks and Kind Regards,
Felipe
Dear Felipe,
A covariance matrix is always symmetric (and also positive semi-definite).
Regards,
Michael
Yes, Michael Ulrich is right, but please note that we consider complex-valued channels. Hence, covariance matrices are Hermitian matrices, which is the complex-valued version of a real-valued symmetric matrix.
https://en.wikipedia.org/wiki/Hermitian_matrix
By the way, I recommend you to read our journal article instead of the ICC paper:
Article Massive MIMO has Unlimited Capacity
Linear independent covariance matrix is symmetric : https://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm
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