Iterative dual downlink beamforming for cognitive radio networks

Abstract

We address the problem of multi-user downlink beamforming and power allocation in a cognitive radio (CR) secondary network (SN) with constraints on the total interference in the primary network (PN). We derive the Lagrange dual of the problem and show that both problems are equivalent. Two algorithms are proposed to solve the problem. The first is based on convex optimization and the second algorithm exploits the uplink-downlink duality that is enforced by the introduction of appropriate slack variables in the constrained optimization problem. This leads to a simple iterative technique that enjoys easy implementation and low computational costs. Simulation results illustrate that the proposed iterative technique converges to the global optimum in all cases.

Robust joint transceiver beamforming for cognitive radio network

“…In [2], it demonstrates that there exists a dual virtual uplink problem which is equivalent to the downlink MISO problem. According to this result, the inner problem is equivalent to a dual problem that minimizing the total virtual uplink power with respect to virtual uplink QoS requirements.…”

“…The efficient approximate solution is to use SDP relaxation by introducing new variables U k = t k t H k and V k = r k r H k [5]. SDP relaxation does not involve any approximation as the resulting solution is always rank-one [2]. Hence, the rank-one solutions can be recovered from the optimal solution U k and V k straightforwardly by using the principal eigenvector corresponding to the only non-zero eigenvalue.…”

“…2 It is well known that the MMSE receiver can achieve many of the performance levels for multi-user downlink system without the need for side information like user sequences and clock offsets [9]. 3 Perfect knowledge of secondary links can be estimated by using the cognitive radio's pilot signal or in a decision-directed fashion.…”

“…where q k and q K+l are the power allocation for the kth secondary uplinks and the lth primary uplinks to SBS, respectively [2]. It can be considered that the problem is optimized over the remaining variables with fixed t k .…”

“…Distributed beamforming and rate allocation for the SUs was addressed that maximizes the minimum weighted secondary rate [1]. Moreover, an iterative dual downlink beamforming was designed to minimize total transmit power under SINR and interference constraints over multiple-input single-output (MISO) cognitive channel [2] and underlay MISO interference channel [3]. Moreover, robust cognitive beamforming was developed to provide robustness against channel uncertainty for MISO cognitive radio network, such as the minimization of the transmit power subject to the quality-of-service (QoS) [4], and further improvement by using Lagrange duality [5].…”