2009/01/30 by Lan Zhang, Zhang, Lan, Rui Zhang +8
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0901.4830
26 pages, 6 figures
arxiv created 2009/01/30 · openalex publication_date 2009/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty, we explore a relationship between the MIMO secrecy channel and the recently developed MIMO cognitive radio (CR) channel, in which the multi-antenna secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called ``interference temperature (IT)'' constraints. By constructing an auxiliary CR MIMO channel that has the same channel responses as the MIMO secrecy channel, we prove that the optimal transmit covariance matrix to achieve the secrecy capacity is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Based on this relationship, several algorithms are proposed to solve the non-convex secrecy capacity computation problem by transforming it into a sequence of CR spectrum sharing capacity computation problems that are convex. For the case with single-antenna eavesdroppers, the proposed algorithms obtain the exact capacity of the MIMO secrecy channel, while for the case with multi-antenna eavesdroppers, the proposed algorithms obtain both upper and lower bounds on the MIMO secrecy capacity.