Capacity scaling law by multiuser diversity in cognitive radio systems

This paper analyzes the multiuser diversity gain in a cognitive radio (CR) system where secondary transmitters opportunistically utilize the spectrum licensed to primary users only when it is not occupied by the primary users. To protect the primary users from the interference caused by the missed detection of primary transmissions in the secondary network, minimum average throughput of the primary network is guaranteed by transmit power control at the secondary transmitters. The traffic dynamics of a primary network are also considered in our analysis. We derive the average achievable capacity of the secondary network and analyze its asymptotic behaviors to characterize the multiuser diversity gains in the CR system.Comment: 5 pages, 2 figures, ISIT2010 conferenc

Multi-user Diversity Systems with Application to Cognitive Radio

abstract: This thesis aims to investigate the capacity and bit error rate (BER) performance of multi-user diversity systems with random number of users and considers its application to cognitive radio systems. Ergodic capacity, normalized capacity, outage capacity, and average bit error rate metrics are studied. It has been found that the randomization of the number of users will reduce the ergodic capacity. A stochastic ordering framework is adopted to order user distributions, for example, Laplace transform ordering. The ergodic capacity under different user distributions will follow their corresponding Laplace transform order. The scaling law of ergodic capacity with mean number of users under Poisson and negative binomial user distributions are studied for large mean number of users and these two random distributions are ordered in Laplace transform ordering sense. The ergodic capacity per user is defined and is shown to increase when the total number of users is randomized, which is the opposite to the case of unnormalized ergodic capacity metric. Outage probability under slow fading is also considered and shown to decrease when the total number of users is randomized. The bit error rate (BER) in a general multi-user diversity system has a completely monotonic derivative, which implies that, according to the Jensen's inequality, the randomization of the total number of users will decrease the average BER performance. The special case of Poisson number of users and Rayleigh fading is studied. Combining with the knowledge of regular variation, the average BER is shown to achieve tightness in the Jensen's inequality. This is followed by the extension to the negative binomial number of users, for which the BER is derived and shown to be decreasing in the number of users. A single primary user cognitive radio system with multi-user diversity at the secondary users is proposed. Comparing to the general multi-user diversity system, there exists an interference constraint between secondary and primary users, which is independent of the secondary users' transmission. The secondary user with high- est transmitted SNR which also satisfies the interference constraint is selected to communicate. The active number of secondary users is a binomial random variable. This is then followed by a derivation of the scaling law of the ergodic capacity with mean number of users and the closed form expression of average BER under this situation. The ergodic capacity under binomial user distribution is shown to outperform the Poisson case. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of different user distributions.Dissertation/ThesisM.S. Electrical Engineering 201

Opportunistic Scheduling for Full-Duplex Uplink-Downlink Networks

We study opportunistic scheduling and the sum capacity of cellular networks with a full-duplex multi-antenna base station and a large number of single-antenna half-duplex users. Simultaneous uplink and downlink over the same band results in uplink-to-downlink interference, degrading performance. We present a simple opportunistic joint uplink-downlink scheduling algorithm that exploits multiuser diversity and treats interference as noise. We show that in homogeneous networks, our algorithm achieves the same sum capacity as what would have been achieved if there was no uplink-to-downlink interference, asymptotically in the number of users. The algorithm does not require interference CSI at the base station or uplink users. It is also shown that for a simple class of heterogeneous networks without sufficient channel diversity, it is not possible to achieve the corresponding interference-free system capacity. We discuss the potential for using device-to-device side-channels to overcome this limitation in heterogeneous networks.Comment: 10 pages, 2 figures, to appear at IEEE International Symposium on Information Theory (ISIT) '1

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_j$ receive antennas, where $N_j$ is the number of jammer's transmit antenna each, and hence $KN_j$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.Comment: Accepted with minor revisions, IEEE Trans. on Signal Processin

Multi-Cell Random Beamforming: Achievable Rate and Degrees of Freedom Region

Random beamforming (RBF) is a practically favourable transmission scheme for multiuser multi-antenna downlink systems since it requires only partial channel state information (CSI) at the transmitter. Under the conventional single-cell setup, RBF is known to achieve the optimal sum-capacity scaling law as the number of users goes to infinity, thanks to the multiuser diversity enabled transmission scheduling that virtually eliminates the intra-cell interference. In this paper, we extend the study of RBF to a more practical multi-cell downlink system with single-antenna receivers subject to the additional inter-cell interference (ICI). First, we consider the case of finite signal-to-noise ratio (SNR) at each receiver. We derive a closed-form expression of the achievable sum-rate with the multi-cell RBF, based upon which we show an asymptotic sum-rate scaling law as the number of users goes to infinity. Next, we consider the high-SNR regime and for tractable analysis assume that the number of users in each cell scales in a certain order with the per-cell SNR. Under this setup, we characterize the achievable degrees of freedom (DoF) for the single-cell case with RBF. Then we extend the analysis to the multi-cell RBF case by characterizing the DoF region. It is shown that the DoF region characterization provides useful guideline on how to design a cooperative multi-cell RBF system to achieve optimal throughput tradeoffs among different cells. Furthermore, our results reveal that the multi-cell RBF scheme achieves the "interference-free DoF" region upper bound for the multi-cell system, provided that the per-cell number of users has a sufficiently large scaling order with the SNR. Our result thus confirms the optimality of multi-cell RBF in this regime even without the complete CSI at the transmitter, as compared to other full-CSI requiring transmission schemes such as interference alignment.Comment: 28 pages, 6 figures, to appear in IEEE Transactions of Signal Processing. This work was presented in part at IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto, Japan, March 25-30, 2012. The authors are with the Department of Electrical and Computer Engineering, National University of Singapore (emails: {hieudn, elezhang, elehht}@nus.edu.sg