Showing papers on "Channel state information published in 2011"

Tool release: gathering 802.11n traces with channel state information

Abstract: We are pleased to announce the release of a tool that records detailed measurements of the wireless channel along with received 802.11 packet traces. It runs on a commodity 802.11n NIC, and records Channel State Information (CSI) based on the 802.11 standard. Unlike Receive Signal Strength Indicator (RSSI) values, which merely capture the total power received at the listener, the CSI contains information about the channel between sender and receiver at the level of individual data subcarriers, for each pair of transmit and receive antennas.Our toolkit uses the Intel WiFi Link 5300 wireless NIC with 3 antennas. It works on up-to-date Linux operating systems: in our testbed we use Ubuntu 10.04 LTS with the 2.6.36 kernel. The measurement setup comprises our customized versions of Intel's close-source firmware and open-source iwlwifi wireless driver, userspace tools to enable these measurements, access point functionality for controlling both ends of the link, and Matlab (or Octave) scripts for data analysis. We are releasing the binary of the modified firmware, and the source code to all the other components.

Pilot Contamination and Precoding in Multi-Cell TDD Systems

Abstract: This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

Compute-and-Forward: Harnessing Interference Through Structured Codes

Abstract: Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.

Robust Beamforming for Security in MIMO Wiretap Channels With Imperfect CSI

Abstract: In this paper, we investigate methods for reducing the likelihood that a message transmitted between two multi-antenna nodes is intercepted by an undetected eavesdropper. In particular, we focus on the judicious transmission of artificial interference to mask the desired signal at the time it is broadcast. Unlike previous work that assumes some prior knowledge of the eavesdropper's channel and focuses on maximizing secrecy capacity, we consider the case where no information regarding the eavesdropper is available, and we use signal-to-interference-plus-noise-ratio (SINR) as our performance metric. Specifically, we focus on the problem of maximizing the amount of power available to broadcast a jamming signal intended to hide the desired signal from a potential eavesdropper, while maintaining a prespecified SINR at the desired receiver. The jamming signal is designed to be orthogonal to the information signal when it reaches the desired receiver, assuming both the receiver and the eavesdropper employ optimal beamformers and possess exact channel state information (CSI). In practice, the assumption of perfect CSI at the transmitter is often difficult to justify. Therefore, we also study the resulting performance degradation due to the presence of imperfect CSI, and we present robust beamforming schemes that recover a large fraction of the performance in the perfect CSI case. Numerical simulations verify our analytical performance predictions, and illustrate the benefit of the robust beamforming schemes.

QoS-Based Transmit Beamforming in the Presence of Eavesdroppers: An Optimized Artificial-Noise-Aided Approach

Abstract: Secure transmission techniques have been receiving growing attention in recent years, as a viable, powerful alternative to blocking eavesdropping attempts in an open wireless medium. This paper proposes a secret transmit beamforming approach using a quality-of-service (QoS)-based perspective. Specifically, we establish design formulations that: i) constrain the maximum allowable signal-to-interference-and-noise ratios (SINRs) of the eavesdroppers, and that ii) provide the intended receiver with a satisfactory SINR through either a guaranteed SINR constraint or SINR maximization. The proposed designs incorporate a relatively new idea called artificial noise (AN), where a suitable amount of AN is added in the transmitted signal to confuse the eavesdroppers. Our designs advocate joint optimization of the transmit weights and AN spatial distribution in accordance with the channel state information (CSI) of the intended receiver and eavesdroppers. Our formulated design problems are shown to be NP-hard in general. We deal with this difficulty by using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Interestingly, we prove that SDR can exactly solve the design problems for a practically representative class of problem instances; e.g., when the intended receiver's instantaneous CSI is known. Extensions to the colluding-eavesdropper scenario and the multi-intended-receiver scenario are also examined. Extensive simulation results illustrate that the proposed AN-aided designs can yield significant power savings or SINR enhancement compared to some other methods.

Cooperative Jamming for Secure Communications in MIMO Relay Networks

Abstract: Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for two-hop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decode-and-forward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closed-form jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)-based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVD-based cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming.

Rethinking the Secrecy Outage Formulation: A Secure Transmission Design Perspective

Abstract: This letter studies information-theoretic security without knowing the eavesdropper's channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.

Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming

Abstract: In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.

A Mixture Gamma Distribution to Model the SNR of Wireless Channels

Abstract: Composite fading (i.e., multipath fading and shadowing together) has increasingly been analyzed by means of the K channel and related models. Nevertheless, these models do have computational and analytical difficulties. Motivated by this context, we propose a mixture gamma (MG) distribution for the signal-to-noise ratio (SNR) of wireless channels. Not only is it a more accurate model for composite fading, but is also a versatile approximation for any fading SNR. As this distribution consists of N (≥ 1) component gamma distributions, we show how its parameters can be determined by using probability density function (PDF) or moment generating function (MGF) matching. We demonstrate the accuracy of the MG model by computing the mean square error (MSE) or the Kullback-Leibler (KL) divergence or by comparing the moments. With this model, performance metrics such as the average channel capacity, the outage probability, the symbol error rate (SER), and the detection capability of an energy detector are readily derived.

Mode-dependent loss and gain: statistics and effect on mode-division multiplexing.

Abstract: In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information.

Optimal Power Allocation Strategies for Fading Cognitive Radio Channels with Primary User Outage Constraint

Abstract: In this paper, we consider a cognitive radio (CR) network where a secondary (cognitive) user shares the spectrum for transmission with a primary (non-cognitive) user over block-fading (BF) channels. It is assumed that the primary user has a constant-rate, constant-power transmission, while the secondary user is able to adapt transmit power and rate allocation over different fading states based on the channel state information (CSI) of the CR network. We study a new type of constraint imposed over the secondary transmission to protect the primary user by limiting the maximum transmission outage probability of the primary user to be below a desired target. We derive the optimal power allocation strategies for the secondary user to maximize its ergodic/outage capacity, under the average/peak transmit power constraint along with the proposed primary user outage probability constraint. It is shown by simulations that the derived new power allocation strategies can achieve substantial capacity gains for the secondary user over the conventional methods based on the interference temperature (IT) constraint to protect the primary transmission, with the same resultant primary user outage probability.

Interference Alignment for Secrecy

Abstract: This paper studies the frequency/time selective K-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [(K-2)/(2K-2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [(K-2)/(2K)] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.

MIMO Interference Alignment Over Correlated Channels With Imperfect CSI

Abstract: Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the postprocessing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.

Training and Feedback Optimization for Multiuser MIMO Downlink

Abstract: We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over time-frequency blocks that span a coherent time x a coherence bandwidth. In closed-loop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In open-loop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use closed-form lower bounds and tight approximations of the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three time-frequency block models inspired by actual systems, we provide useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.

Adaptive Limited Feedback for Sum-Rate Maximizing Beamforming in Cooperative Multicell Systems

Abstract: Base station cooperation improves the sum-rates that can be achieved in cellular systems. Conventional cooperation techniques require sharing large amounts of information over finite-capacity backhaul links and assume that base stations have full channel state information (CSI) of all the active users in the system. In this paper, a new limited feedback strategy is proposed for multicell beamforming where cooperation is restricted to sharing only the CSI of active users among base stations. The system setup considered is a linear array of cells based on the “soft hand-off model,” where each cell contains single-antenna users and multi-antenna base stations. Beamforming vectors are designed using a generalized eigenvector approach to maximize the sum-rate in a single-interferer scenario, at high signal to noise ratio. Users are assumed to feedback quantized CSI of the desired and interfering channels using a finite-bandwidth feedback link. An upper bound on the mean loss in sum rate due to random vector quantization is derived. A new feedback-bit allocation strategy, to partition the available bits between the desired and interfering channels, is developed to reduce the mean loss in sum-rate due to quantization for the soft hand-off model. The proposed feedback-bit partitioning algorithm is shown, using simulations, to yield sum-rates close to the those obtained using full CSI at base station.

Strong Secrecy from Channel Resolvability

Abstract: We analyze physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability. Instead of considering capacity-based constructions, which associate to each message a sub-code that operates just below the capacity of the eavesdropper's channel, we consider channel-resolvability-based constructions, which associate to each message a sub-code that operates just above the resolvability of the eavesdropper's channel. Building upon the work of Csiszar and Hayashi, we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that at least for symmetric wiretap channels, random capacity-based constructions fail to achieve the strong secrecy capacity while channel-resolvability-based constructions achieve it. We then leverage channel resolvability to establish the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information, mixed channels and compound channels with receiver Channel State Information (CSI), as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to channel resolvability, we obtain achievable rates for strong secrecy metrics with simple proofs.

Transmitter Preprocessing Aided Spatial Modulation for Multiple-Input Multiple-Output Systems

Abstract: This paper proposes and studies a transmitter preprocessing aided spatial modulation (PSM) scheme, which conveys information jointly by a conventional amplitude-phase modulation (APM) and a preprocessing aided space shift keying (pre-SSK) modulation. In contrast to the existing SSK modulation, which carries information using the indexes of transmitter antennas and assumes channel state information at receiver (CSIR), the pre-SSK modulation extracts the transmitted information using the indexes of receive antennas and assumes channel state information at transmitter (CSIT). This paper addresses the issues of preprocessing optimization and detection of PSM signals. Furthermore, the bit-error-rate (BER) performance of the PSM is investigated, when assuming that the channel from any transmit antenna to any receive antenna experiences independent Rayleigh fading. Our studies show that, when appropriately designed, the pre-SSK and APM invoked can enhance each other, resulting in that the PSM is capable of attaining a better BER performance than the corresponding pure pre-SSK and pure APM.

Wireless Secrecy Regions With Friendly Jamming

Abstract: Inspired by recent results on information-theoretic security, we consider the transmission of confidential messages over wireless networks, in which the legitimate communication partners are aided by friendly jammers. We characterize the security level of a confined region in a quasi-static fading environment by computing the probability of secrecy outage in connection with two new measures of physical-layer security: the jamming coverage and the jamming efficiency. Our analysis for various jamming strategies based on different levels of channel state information provides insight into the design of optimal jamming configurations and shows that a single jammer is not sufficient to maximize both figures of merit simultaneously. Moreover, a single jammer requires full channel state information to provide security gains in the vicinity of the legitimate receiver.

Method for reporting channel state information in wireless communication system and device therefor

Abstract: The present specification relates to a method for reporting channel state information (CSI) in a wireless communication system, and the method performed by a terminal comprises the steps of: receiving, from a base station, a radio resource control (RRC) signaling including control information relating to a configuration of a 12-port CSI-reference signal (RS); receiving, from the base station, the 12-port CSI-RS through a 12-port CSI-RS resource on the basis of the received control information; and reporting CSI to the base station on the basis of the received CSI-RS. Therefore, full power transmission per port is enabled in the transmission of a 12-port CSI-RS.

Robust Linear Precoder Design for Multi-Cell Downlink Transmission

Abstract: Coordinated information processing by the base stations of multi-cell wireless networks enhances the overall quality of communication in the network. Such coordinations for optimizing any desired network-wide quality of service (QoS) necessitate the base stations to acquire and share some channel state information (CSI). With perfect knowledge of channel states, the base stations can adjust their transmissions for achieving a network-wise QoS optimality. In practice, however, the CSI can be obtained only imperfectly. As a result, due to the uncertainties involved, the network is not guaranteed to benefit from a globally optimal QoS. Nevertheless, if the channel estimation perturbations are confined within bounded regions, the QoS measure will also lie within a bounded region. Therefore, by exploiting the notion of robustness in the worst-case sense some worst-case QoS guarantees for the network can be asserted. We adopt a popular model for noisy channel estimates that assumes that estimation noise terms lie within known hyper-spheres. We aim to design linear transceivers that optimize a worst-case QoS measure in downlink transmissions. In particular, we focus on maximizing the worst-case weighted sum-rate of the network and the minimum worst-case rate of the network. For obtaining such transceiver designs, we offer several centralized (fully cooperative) and distributed (limited cooperation) algorithms which entail different levels of complexity and information exchange among the base stations.

Lattice Strategies for the Dirty Multiple Access Channel

Abstract: In Costa's dirty-paper channel, Gaussian random binning is able to eliminate the effect of interference which is known at the transmitter, and thus achieve capacity. We examine a generalization of the dirty-paper problem to a multiple access channel (MAC) setup, where structured (lattice-based) binning seems to be necessary to achieve capacity. In the dirty-MAC, two additive interference signals are present, one known to each transmitter but none to the receiver. The achievable rates using Costa's Gaussian binning vanish if both interference signals are strong. In contrast, it is shown that lattice-strategies (“lattice precoding”) can achieve positive rates, independent of the interference power. Furthermore, in some cases-which depend on the noise variance and power constraints-high-dimensional lattice strategies are in fact optimal. In particular, they are optimal in the limit of high SNR-where the capacity region of the dirty MAC with strong interference approaches that of a clean MAC whose power is governed by the minimum of the users' powers rather than their sum. The rate gap at high SNR between lattice-strategies and optimum (rather than Gaussian) random binning is conjectured to be 1/2 log2(πe/6) ≈ 0.254 bit. Thus, the doubly dirty MAC is another instance of a network setting, like the Korner-Marton problem, where (linear) structured coding is potentially better than random binning.

MISO Capacity with Per-Antenna Power Constraint

Abstract: We establish in closed-form the capacity and the optimal signaling scheme for a MISO channel with per-antenna power constraint. Two cases of channel state information are considered: constant channel known at both the transmitter and receiver, and Rayleigh fading channel known only at the receiver. For the first case, the optimal signaling scheme is beamforming with the phases of the beam weights matched to the phases of the channel coefficients, but the amplitudes independent of the channel coefficients and dependent only on the constrained powers. For the second case, the optimal scheme is to send independent signals from the antennas with the constrained powers. In both cases, the capacity with per-antenna power constraint is usually less than that with sum power constraint.

Asymptotic Analysis of Cooperative Diversity Systems With Relay Selection in a Spectrum-Sharing Scenario

Abstract: Three low-complexity relay-selection strategies, namely, selective amplify and forward (S-AF), selective decode and forward (S-DF), and amplify and forward with partial relay selection (PRS-AF) in a spectrum-sharing scenario are studied. First, we consider a scenario where perfect channel state information (CSI) is available. For these scenarios, the respective asymptotic outage behaviors of the secondary systems are analyzed, from which the diversity and coding gains are derived and compared. Unlike the coding gain, which is shown to be very sensitive with the position of the primary receiver, the diversity gain of the secondary system is the same as the nonspectrum-sharing system. In addition, depending on the cooperative strategy employed, an increase in the number of relays may lead to severe loss of the coding gain. Afterwards, the impacts of imperfect CSI regarding the interference and transmit channels on the outage behavior of the secondary systems are analyzed. On one hand, the imperfect CSI concerning the interference channels only affects the outage performance of the primary system, whereas it has no effect on the diversity gain of the secondary system. On the other hand, the imperfect CSI concerning the transmit channels of the secondary systems may reduce the diversity gain of the three relay-selection strategies to unity, which is validated by both theoretical and numerical results.

Method for processing csi-rs in wireless communication system

Abstract: A method for processing a Channel State Information Reference Signal (CSI-RS) in a wireless communication system based on a multiple access scheme is provided. The CSI-RS transmission method defines a plurality of CSI-RS patterns, assigns the CSI-RS patterns to individual cells, uses the CSI-RSs alternately per Physical Resource Block (PRB) so as to utilize the transmission powers of all antenna ports for transmitting CSI-RSs, transmits Coordinated Multi Point (CoMP) CSI-RSs and non-CoMP CSI-RSs separately, and mutes specific resources in association with the CSI-RS pattern of adjacent cells.

The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed CSI

Abstract: The degrees of freedom (DoF) region of the 2-user multiple-antenna or MIMO (multiple-input, multiple-output) interference channel (IC) is studied under fast fading and the assumption of {\em delayed} channel state information (CSI) wherein all terminals know all (or certain) channel matrices perfectly, but with a delay, and each receiver in addition knows its own incoming channels instantaneously. The general MIMO IC is considered with an arbitrary number of antennas at each of the four terminals. Dividing it into several classes depending on the relation between the numbers of antennas at the four terminals, the fundamental DoF regions are characterized under the delayed CSI assumption for {\em all} possible values of number of antennas at the four terminals. In particular, an outer bound on the DoF region of the general MIMO IC is derived. This bound is then shown to be tight for all MIMO ICs by developing interference alignment based achievability schemes for each class. A comparison of these DoF regions under the delayed CSI assumption is made with those of the idealistic `perfect CSI' assumption where perfect and instantaneous CSI is available at all terminals on the one hand and with the DoF regions of the conservative `no CSI' assumption on the other, where CSI is available at the receivers but not at all at the transmitters.

Multi-Mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

Abstract: This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.

Optimal Spectrum Sharing in MIMO Cognitive Radio Networks via Semidefinite Programming

Abstract: In cognitive radio (CR) networks with multiple-input multiple-output (MIMO) links, secondary users (SUs) can exploit "spectrum holes" in the space domain to access the spectrum allocated to a primary system. However, they need to suppress the interference caused to primary users (PUs), as the secondary system should be transparent to the primary system. In this paper, we study the optimal secondary-link beamforming pattern that balances between the SU's throughput and the interference it causes to PUs. In particular, we aim to maximize the throughput of the SU, while keeping the interference temperature at the primary receivers below a certain threshold. Unlike traditional MIMO systems, SUs may not have the luxury of knowing the channel state information (CSI) on the links to PUs. This presents a key challenge for a secondary transmitter to steer interference away from primary receivers. In this paper, we consider three scenarios, namely when the secondary transmitter has complete, partial, or no knowledge about the channels to the primary receivers. In particular, when complete CSI is not available, the interference-temperature constraints are to be satisfied with high probability, thus resulting in chance constraints that are typically hard to deal with. Our contribution is fourfold. First, by analyzing the distributional characteristics of MIMO channels, we propose a unified homogeneous quadratically constrained quadratic program (QCQP) formulation that can be applied to all three scenarios, in which different levels of CSI knowledge give rise to either deterministic or probabilistic interference-temperature constraints. The homogeneous QCQP formulation, though non-convex, is amenable to semidefinite programming (SDP) relaxation methods. Secondly, we show that the SDP relaxation admits no gap when the number of primary links is no larger than two. A polynomial-time algorithm is presented to compute the optimal solution to the QCQP problem efficiently. Thirdly, we propose a randomized polynomial-time algorithm for constructing a near-optimal solution to the QCQP problem when there are more than two primary links. Finally, we show that when the secondary transmitter has no CSI on the links to primary receivers, the optimal solution to the QCQP problem can be found by a simple matrix eigenvalue-eigenvector computation, which can be done much more efficiently than solving the QCQP directly.

Exploiting Channel Diversity in Secret Key Generation from Multipath Fading Randomness

Abstract: We design and analyze a method to extract secret keys from the randomness inherent to wireless channels. We study a channel model for multipath wireless channel and exploit the channel diversity in generating secret key bits. We compare the key extraction methods based both on entire channel state information (CSI) and on single channel parameter such as the received signal strength indicators (RSSI). Due to the reduction in the degree-of-freedom when going from CSI to RSSI, the rate of key extraction based on CSI is far higher than that based on RSSI. This suggests that exploiting channel diversity and making CSI information available to higher layers would greatly benefit the secret key generation. We propose a key generation system based on low-density parity-check (LDPC) codes and describe the design and performance of two systems: one based on binary LDPC codes and the other (useful at higher signal-to-noise ratios) based on four-ary LDPC codes.

An analysis of pilot contamination on multi-user MIMO cellular systems with many antennas

Abstract: This paper considers a two-cell cellular system with multiple antennas at the base station (BS) and single antenna user terminals. In such a scenario, the presence of channel state information (CSI) at the BS is essential for efficient system performance. In reciprocal TDD systems, CSI can be obtained via uplink training. Since only finite time-frequency resources are available, such uplink training generally must be performed using non-orthogonal resources (for different users), leading to pilot contamination between users who train simultaneously. In particular, we analyze the rate of convergence of SINR (in presence of pilot contamination) as the number of antennas (M) at the BS increases to an infinite limit. The effect of SNR and the fading coefficients of the user channels on this rate of convergence is also determined.

Robust MIMO Cognitive Radio Via Game Theory

Abstract: Cognitive radio (CR) systems improve the spectral efficiency by allowing the coexistence in harmony of primary users (PUs), the legacy users, with secondary users (SUs). This coexistence is built on the premises that no SU can generate interference higher than some prescribed limits against PUs. The system design based on perfect channel state information (CSI) can easily end up violating the interference limits in a realistic situation where CSI may be imperfect. In this paper, we propose a robust design of CR systems, composed of multiple PUs and multiple noncooperative SUs, in either single-input single-output (SISO) frequency-selective channels or more general multiple-input multiple-output (MIMO) channels. We formulate the design of the SU network as a noncooperative game, where the SUs compete with each other over the resources made available by the PUs, by maximizing their own information rates subject to the transmit power and robust interference constraints. Following the philosophy of the worst-case robustness, we take explicitly into account the imperfectness of SU-to-PU CSI by adopting proper interference constraints that are robust with respect to the worst channel errors. Relying on the variational inequality theory, we study the existence and uniqueness properties of the Nash equilibria of the resulting robust games, and devise totally asynchronous and distributed algorithms along with their convergency properties. We also propose efficient numerical methods, based on decomposition techniques, to compute the robust transmit strategy for each SU.