Some Proof Derivations and Further Simulation Results for "Semidefinite Relaxation and Approximation Analysis of a Beamformed Alamouti Scheme for Relay Beamforming Networks"

This is a companion technical report of the main manuscript “Semidefinite Relaxation and Approximation Analysis of a Beamformed Alamouti Scheme for Relay Beamforming Networks”. The report serves to give detailed derivations of Lemma 1-2 in the main manuscript, which are too long to be included in the latter. In addition, more simulation results are presented to verify the viability of the BF Alamouti AF schemes developed in the main manuscript. 1 ar X iv :1 60 2. 06 50 0v 1 [ cs .I T ] 2 1 Fe b 20 16 In the main paper [1], we propose the BF Alamouti AF scheme for the one-hop one-way relay networks. Specifically, the new AF scheme aims at exploring 2-DoF in the relay AF structure for improving users’ SINRs. To analyze the system performance, Theorem 1 is provided in the main paper to prove the SDR approximation bound for the two-variable QCQP problem. Due to the page limit, two important lemmas for proving Theorem 1 is relegated to this companion technical report in Sections 2.1 and 2.2. We also provide some explanations for the system model and supplementary simulation results in Sections 1 and 3. 1 Exact Expressions of the Received Signals at User-(k, i) To help the readers to well understand the Alamouti BF AF structure, we write the receive signals at user-(k, i) as follows yk,i(m) = [ yk,i(2m), yk,i(2m+ 1) ] (1) = L ∑ `=1 (g k,i) [w1,`, w2,`]C(r`(m)) + [vk,i(2m), vk,i(2m+ 1)],