Secure Degrees of Freedom of User Rank-Deficient Multiple Access Wiretap Channel

In this study, we investigate a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel, in which the channel matrices of users exhibit rank deficiency. In this model, the legitimate transmitters and receiver are equipped with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> antennas, respectively, while the eavesdropper has <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> antennas. The channel matrices of legitimate users are rank-deficient, whereas those between transmitters and the eavesdropper are full-rank, representing a worst-case scenario. We derive the optimal secure degrees of freedom (SDoF) for this model by combining two separate outer bounds. Considering the variations in the number of antennas at each node and the rank of user channels, we categorize our analysis into several regimes. We then present achievable schemes for each regime, grounded in spatial interference alignment, symbol extension and zero-forcing techniques.