Power Minimization in Multi-pair Two-Way Relaying

Clearly, setting the parameter λ to 1 reduces (2) to (1). Here, we allow λ to be an arbitrary positive number for ease of further discussions. We note that the power minimization in (2) can be efficiently solved with a single SDP [2]. We next establish a close relation between the max-min SINR problem (5) in [1] and the power minimization problem in (2). We first show that (2) can be solved via solving (5) in [1]. Let λ̃(P̌R) denote the optimal value of (8) in [1] for a given power budget P̌R. It can be shown that: Lemma 1: λ̃(P̌R) is a strictly increasing function of P̌R.