In this paper, we study the power allocation problem in a relay assisted multi-band underlay cognitive radio network. Such a network allows unlicensed users (secondary users) to access the spectrum bands under a transmission power constraint. Due to the concave increasing property of logarithm function, it is not always wise for secondary users to expend all the transmission power in one band if their aim is to maximize achievable data rate. In particular, we study a scenario where two secondary users and a half-duplexing relay exist with two available bands. The two users choose different bands for direct data transmission and use the other band for relay transmission. By properly allocating the power on two bands, each user may be able to increase its total achievable data rate while satisfying the power constraint. We formulate the power allocation problem as a non-cooperative game and investigate its Nash equilibria. We prove the power allocation game is a supermodular game and that Nash equilibria exist. We further find the best response function of users and propose a best response update algorithm to solve the corresponding dynamic game. Numerical results show the overall performance in terms of achievable rates is improved through our proposed transmission scheme and power allocation algorithm. Our proposed algorithm also shows satisfactory performance in terms of convergence speed.

In this paper, we investigate the degrees of freedom (DoF) of a MIMO cellular interfering network (CIN) with L (L≥3) cells and K users per cell. Previous works established the DoF upper bound of LK(M+N)/(LK+1) for the MIMO CIN by analyzing the interference alignment (IA) feasibility, where M and N denote the number of antennas at each base station (BS) and each user, respectively. However, there is still a gap between the DoF upper bound and the achievable DoF in existing designs. To address this problem, we propose two linear IA schemes without symbol extensions to jointly design transmit and receive beamforming matrices to align and eliminate interference. In the two schemes, the transmit beamforming vectors are allocated to different cluster structures so that the inter-cell interference (ICI) data streams from different ICI channels are aligned. The first scheme, named fixed cluster structure (FCS-IA) scheme, allocates ICI beamforming vectors to the cluster structures of fixed dimension and can achieve the DoF upper bound under some system configurations. The second scheme, named dynamic cluster structure IA (DCS-IA) scheme, allocates ICI beamforming vectors to the cluster structures of dynamic dimension and can get a tradeoff between the number of antennas at BSs and users so that ICI alignment can be applied under various system configurations. Through theoretical analysis and numerical simulations, we verify that the DoF upper bound can be achieved by using the FCS-IA scheme. Furthermore, we show that the proposed schemes can provide significant performance gain over the time division multiple access (TDMA) scheme in terms of DoF. From the perspective of DoF, it is shown that the proposed schemes are more effective than the conventional IA schemes for the MIMO CIN.

In this paper, we study the degrees of freedom (DoF) of a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with two relays, two clusters and K (K≥3) users per cluster. We consider a clustered full data exchange model, i.e., each user in a cluster sends a multicast (common) message to all other users in the same cluster and desires to acquire all messages from them. The DoF results of the mRC with the single relay have been reported. However, the DoF achievability of the mRC with multiple relays is still an open problem. Furthermore, we consider a more practical scenario where no channel state information at the transmitter (CSIT) is available to each user. We first give a DoF cut-set upper bound of the considered mRC. Then, we propose a distributed interference neutralization and retransmission scheme (DINR) to approach the DoF cut-set upper bound. In the absence of user cooperation, this method focuses on the beamforming matrix design at each relay. By investigating channel state information (CSI) acquisition, we show that the DINR scheme can be performed by distributed processing. Theoretical analyses and numerical simulations show that the DoF cut-set upper bound can be attained by the DINR scheme. It is shown that the DINR scheme can provide significant DoF gain over the conventional time division multiple access (TDMA) scheme. In addition, we show that the DINR scheme is superior to the existing single relay schemes for the considered mRC.

Spectrum sharing effectively improves the spectrum usage by allowing secondary users (SUs) to dynamically and opportunistically share the licensed bands with primary users (PUs). The concept of cooperative spectrum sharing allows SUs to use portions of the PUs' radio resource for their own data transmission, under the condition that SUs help the PUs' transmission. The key issue with designing such a scheme is how to deal with the resource splitting of the network. In this paper we propose a relay-based cooperative spectrum sharing scheme in which the network consists of one PU and multiple SUs. The PU asks the SUs to relay its data in order to improve its energy efficiency, in return it rewards the SUs with a portion of its authorized spectrum. However each SU is only allowed to transmit its data via the rewarded channel at a power level proportional to the contribution it makes to the PU. Since energy cost is considered, the SUs must carefully determine their power level. This scheme forms a non-cooperative Stackelberg resource allocation game where the strategy of PU is the bandwidth it rewards and the strategy of each SU is power level of relay transmission. We first investigate the second stage of the sub-game which is addressed as power allocation game. We prove there exists an equilibrium in the power allocation game and provide a sufficient condition for the uniqueness of the equilibrium. We further prove a unique Stackelberg equilibrium exists in the resource allocation game. Distributed algorithms are proposed to help the users with incomplete information achieve the equilibrium point. Simulation results validate our analysis and show that our proposed scheme introduces significant utility improvement for both PU and SUs.