Beamforming and power allocation in the downlink of MIMO cognitive radio systems based on multiobjective optimization

Abstract

Summary In this paper, power allocation and beamforming are considered in a multiple input multiple output (MIMO) downlink cognitive radio (CR) communication system, which a base station (BS) serves one primary user (PU) and one secondary user (SU). In order to design the CR system, a constrained multiobjective optimization problem is presented. Two objectives are the signal to noise plus interference ratios (SINRs) of PU and SU. Since PU has a spectrum license for data communication, a constraint in the optimization problem is that the SINR of PU must be greater than a predefined threshold based on the PU demand requirement. Another constraint is a limitation on power in BS. By considering the mentioned model, three iterative algorithms are proposed. At each iteration of all algorithms, the receiver beamforming vectors are derived based on the maximization of PU and SU SINRs, by assuming that the allocated powers and BS beamforming vectors are known. Also, power is assigned to users such that the constraint of power limitation is satisfied. The difference between the algorithms is in the obtaining of transmitter beamforming parameters. We evaluate the performance of the proposed algorithms in terms of bit error rate (BER) in simulations. Also, the computational complexity of the proposed algorithms is obtained.

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

“…It is acceptable because when the required SINR for D2D link increases the interference from CUs should be reduced, so the desired signal power of CUs decrease and consequently non-outage probability for CUs decreases. As can be seen in Figure 10, our proposed robust scheme outperforms the robust proposed scheme in Asgari et al, 28 Wang et al, 53 hybrid MRT-ZF, ZF, and MRT whether with imperfect CSI or partial CSI. But with partial CSI, the minimum non-outage probability of CUs is improved in comparison with imperfect CSI.…”

“…Notice that again our approach outperforms Wang et al 53 because we solve the optimization problem for a special convex set, and thus, better results have been obtained, especially for small values of ϕ where the beamforming has become more complicated. Figure 11 shows the fairness function for Scenario 3, the robust proposed scheme in Asgari et al, 28 Wang et al, 53 hybrid MRT-ZF, ZF, and MRT schemes versus ϕ, again, the Jain's fairness index have been taken as the fairness factor. According to this figure, our proposed scheme can effectively guarantee the fairness of each CU's non-outage probability, and the fairness factor is almost equal to 1.…”

“…F I G U R E 1 2 Probability of feasibility for Scenario 3 and robust proposed scheme in Asgari et al 28 and Wang et al 53…”

“…As can be seen from Figures 6 and 12, the max-min fairness problem may not be feasible for every possible threshold. Here, the probability of feasibility for different values of the maximum consumed power of the BS, that is, P max and F I G U R E 1 0 Comparison of Scenario 3, the robust proposed scheme in Asgari et al, 28 Wang et al, 53 the minimum required SINR, that is, α th is evaluated to compare Scenario 1 and Scenario 3. To compare these two scenarios, we take σ θ ¼ 2 ∘ and p ¼ 0:6.…”

“…I G U R E 1 2 Probability of feasibility for Scenario 3 and robust proposed scheme in Asgari et al28 and Wang et al53 versus σ 2 e for different values of M when ϕ ¼ 10 ∘ , σ θ ¼ 2 ∘ , ϵ ¼ 0:05, and d ¼ 25 m F I G U R E 1 3 Probability of feasibility for Scenario 1 and Scenario 3 versus P max for different values of σ 2 e when ϕ ¼ 10 ∘ , σ θ ¼ 2 ∘ , d ¼ 25 m, α th ¼ 3 dB, and M ¼ 6…”