Multiple-input Multiple-output Cognitive Radio Research Articles

Secure communication over RIS-aided underlay CR MIMO wiretap channel without Eve’s CSI

This paper investigates a reconfigurable intelligent surface (RIS)-aided underlay cognitive radio (CR) multiple-input multiple-output (MIMO) wiretap channel where the secondary transmitter (ST) communicates with primary user (PU) and secondary user (SU) in the absence of the eavesdropper’s (Eve’s) channel state information (CSI). To enhance the secrecy performance in CR MIMO wiretap channel, the power of useful signal is minimized at ST, and then the residual power is further utilized to design artificial noise (AN) based on statistical CSI at ST. Specifically, we first optimize the transmit covariance matrix at ST and the diagonal phase-shifting matrix at RIS jointly leveraging large-system approximation results. Then the power allocation for SU is optimized to obtain the minimum transmit power of useful information at ST. Besides, we further design AN with the residual power by aligning it into the null space of the SU channel and thus avert the harmful effects of AN to improve the secure communication quality of SU. Finally, through numerical simulations, we illustrate the effectiveness of the proposed algorithm and validate the existence of a trade-off between the quality-of-service (QoS) at SU and secrecy rate.

Improved Multifunctional MIMO Cognitive Radio System for Integrated Interweave-Underlay Operations

This article presents the design of an integrated system involving multiple-input–multiple-output (MIMO) and cognitive radio (CR) technologies for sub-6 GHz applications. Two types of CR techniques, i.e., interweave and underlay CR, have been discussed in this article. The design model has a four-port multifunctional MIMO antenna system involving lumped elements for three selectable operation choices. Based on the switching conditions, the MIMO antenna system can operate as a wideband antenna (for sensing purpose), or narrowband frequency tunable antenna (for communicating purpose in interweave CR), or a wideband antenna with frequency tunable band notch (for communicating purpose in underlay CR). The sensing frequency range is 2.45–5.3 GHz. The interweave CR communicating antenna frequency tuning range is 3.6–4.2 GHz. To cover the entire desired spectrum range, i.e., from 2.5 to 4.2 GHz, another four-port narrowband MIMO antenna system with resonance frequency tuning from 2.5–3.6 is designed on the other/backside of the substrate. In the underlay CR communicating antenna, the stopband frequency tuning range is 3.1–3.85 GHz. The complete structure is having dimensions of 110 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 70 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 1.52 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The measurements are performed, and good matching is found between simulated and measured results.

Enhanced precoder for secondary user of MIMO cognitive radio in the presence of CSIT uncertainties in the desired and interference links

This paper advances the design of transmit precoder for a secondary user (SU) coexisting with a primary user (PU) in multiple-input multiple-output (MIMO) cognitive radio, where the channel state information at transmitter (CSIT) of SU is inaccurate in both the desired link (DL) to its receiver and the interference link (IL) to the PU. The design seeks to maximize performance in the worst scenario, by optimizing the capacity of SU while maintaining a given quality of service (QoS) of PU at the most unfavorable uncertainty errors of the two links. The proposed technique improves the previous design by solving for the precoder in a more accurate and efficient manner, and by using the variable metric projected subgradient method. The most unfavorable realization in the DL is obtained by the alternate-iterate optimization method and the worst uncertainty realization in the IL is derived from the projected subgradient method. The convergence properties and computational complexity of the proposed algorithm are analyzed. Numerical results confirm the proposed precoder has better performance than the previous solution while having lower practical time complexity, especially when the PU has higher tolerance level of SU interference.

Intelligent Reflecting Surface Aided MIMO Cognitive Radio Systems

In cognitive radio (CR) systems, the spectrum efficiency (SE) of the secondary users (SUs) is always limited by the interference temperature constraint imposed on the primary users (PUs). Intelligent reflecting surface (IRS) has been recently proposed as a revolutionary technique which can help to enhance the SE of wireless communications. In this paper, we propose to employ an IRS to assist the SUs’ data transmission in the multiple-input multiple-output (MIMO) CR system. By jointly optimizing the transmit precoding (TPC) of the SU transmitter (ST) and the phase shifts of the IRS, we aim to maximize the achievable weighted sum rate (WSR) of SUs subject to the ST's total power, the PU's interference temperature and unit modulus constraints. To solve this complicated optimization problem in which the variables are coupled, the block coordinate descent (BCD) algorithm is introduced to alternately solve the subproblems. For each subproblem, the Lagrange dual or inner approximation method is adopted with a low complexity. Simulation results confirm the benefits of employing IRS in a MIMO CR system. The performance comparisons of the proposed algorithm with several other benchmarks are carried out by evaluating the impacts of various parameters on the WSR.

Toward Overcoming a Hidden Terminal Problem Arising in MIMO Cognitive Radio Networks: A Tensor-Based Spectrum Sensing Algorithm

As the main enablers of cognitive radio (CR), numerous spectrum sensing techniques have been proposed to date. Despite the numerous techniques, the existing spectrum sensing techniques tend to fail in rendering an efficient spectrum sensing whenever a hidden terminal problem arises. Meanwhile, this problem can happen at any time in any severely fading primary-to-secondary channels resulting in very low primary signal-to-noise ratios (SNRs) and hence ineffective detection of the primary user. Toward overcoming this problem, by introducing a tensor-based hypothesis testing framework, this paper proposes an efficient tensor-based detector (TBD) for a multiple-input multiple-output (MIMO) CR networks over multi-path fading channels. For the proposed spectrum sensing technique, insightful asymptotic performance analyses are provided and Monte-Carlo simulations that assess its performance have been conducted. These simulations corroborate that TBD outperforms the generalized likelihood ratio test (GLRT) detector and the maximum-minimum eigenvalue (MME) detector, especially in the very low SNR regime which is a manifestation of the hidden terminal problem. Moreover, the simulations validate the derived asymptotic performance characterizations.

Nonconvex utility-based power allocation for cognitive radio MIMO system over fading channels

In this paper, we present a power control algorithm in cognitive radio multiple-input–multiple-output (MIMO) system over time-varying fading channels based on the utility-based framework. In particular, a more general objective function framework is proposed under a long- or short-term transmitting and interference power constraints for secondary users, which results the optimization problem is nonconvex. A stochastic optimization algorithm is proposed based on an improved quantum-behaved particle swarm optimization (IQPSO), which can solve the nonconvex optimization problem efficiently. The acceleration coefficients are adjusted with time-varying equations which can help the particles jump out the local optimum. Due to the characteristics of wave function of quantum Delta potential well model, IQPSO can get better optimal solutions in search space for the stochastic optimization problem. To show the efficiency of the proposed algorithm, the utilities of the MIMO CR system got by IQPSO are compared with other approaches in the literature in different case studies, which show that the proposed algorithm can solve the nonconvex problem efficiently and achieve significant throughput.

Symbol Error Rate Analysis of Scheduled STBC With Power Allocation in CR-MIMO Systems

This paper studies symbol error rate (SER) analysis of a user scheduling and space-time block coding (i.e., scheduled STBC) with power allocation using statistical channel state information (CSI) in cognitive radio multiple-input multiple-output (CR-MIMO) systems. The exact SER of the proposed scheme with the statistical CSI is derived for CR-MIMO systems including asymptotic analysis under nonfeedback delay. From analytical results, we observe that the proposed scheduled STBC scheme with the statistical CSI provides the transmit and receive spatial diversity, as well as the multiuser diversity, while the conventional transmit antenna selection (TAS)-based scheme with the statistical CSI only provides the receive spatial diversity. Furthermore, the exact SER of the scheduled STBC with the statistical CSI in CR-MIMO systems is derived under feedback delay between the transmitter and the receiver of the CR system. From the analysis, we find that though the multiuser diversity is diminished by feedback delay, the proposed scheme with feedback delay still provides the transmit and receive spatial diversity, which results in diversity order gain over the conventional TAS-based scheme with nonfeedback delay. Also, the signal-to-noise ratio gain is getting better as the power correlation coefficient and the number of user terminals increase under feedback delay.

Performance analysis of scheduled STBC using statistical CSI under multiple interferers with different power in CR-MIMO systems

This paper studies the impact of the multiple interferers with different power on performance of a scheduled space–time block coding (STBC) using the statistical channel state information (CSI) in cognitive radio-multiple input multiple output (CR-MIMO) systems. This paper derives the exact closed-form cumulative density function (CDF) expression of the instantaneous post-processing signal to noise plus interference ratio (SINR) random variable at the user terminal of the proposed system. Using the derived CDF, the exact closed-form symbol error rate (SER) expression of the proposed system is derived for M-ary quadrature amplitude modulations (QAM). Further, this paper derives the exact closed-form expressions of outage probability and capacity for the proposed system. From the results, we know that the performance of the proposed system is saturated at different peak power constraint depending on the peak interference constraint. Also, the performance floor gets better by multi-user diversity and receive spatial diversity below the peak interference constraint in the presence of multiple interferers.

Proactive Spectrum Sharing for SWIPT in MIMO Cognitive Radio Systems Using Antenna Switching Technique

In this paper, we consider simultaneous wireless information and power transfer for spectrum sharing (SS) in a multiple-input multiple-output cognitive radio (CR) network. The secondary transmitter (ST) selects only one antenna, which maximizes the received signal-to-noise ratio at the secondary receiver (SR) and minimizes the interference induced at the primary receiver (PR). Moreover, PR is an energy harvesting node using the antenna switching, which assigns a subset of its antennas to harvest the energy and assigns the rest to decode its information data. The objective of this paper is to show that the SS is advantageous for both SR and PR sides and leads to a win–win situation. To illustrate the incentive of the SS in CR network, we evaluate the energy and data performance metrics in terms of the average harvested energy, the power outage, and the mutual outage probability, which declares a data outage event if the PR or SR is in an outage. We present some special cases and asymptotic results of the derived analytic results. Through the simulation results, we show the impact of various simulation parameters and the benefits due to the presence of ST.

Bit error rate analysis of the scheduled TAS with MRC for CR-MIMO systems

In this paper, we investigate the bit error rate (BER) analysis of the scheduled transmit antenna selection (TAS) with maximal ratio combining (MRC) for the cognitive radio multiple-input multiple-output (CR-MIMO) systems. As a first step, this paper derives approximate probability density functions (PDFs) of the effective signal to noise ratio (SNR) of the proposed scheduled TAS with MRC in CR-MIMO systems. Next, the tight closed-form expressions of the BER for the M-ary QAM and M-ary PSK modulations are presented, respectively. Using asymptotic analysis, we approximate the BER for the scheduled system, and quantify the diversity order and SNR gain, respectively. Analytical results show that the diversity order of the scheduled system is the product of spatial diversity (SD) and multiuser diversity (MUD). Thus, BER performance of the proposed system is improved as the number of users increases by MUD regardless of modulation types. Also, the SNR gain is getting worse as the number of received antennas at the primary system increases regardless of modulation types.

MIMO Cognitive Radio Spectrum Sharing Using Spatial Coding and User Scheduling for Fading Channels

Spectrum scarcity is one of the issue in wireless communication. Dynamic spectrum sharing is the solution for this problem in which the underutilized spectrums are utilized efficiently. Multiple Input Multiple Output (MIMO) based cognitive radio using spatial coding is used to dynamically share the spectrum which allows simultaneous usage of spectrum by more than one user. The drawback of spatial coding is the achievable capacity get reduced with the increased number of cognitive users which limits the number of users to share the spectrum. In order to maximize the number of secondary users sharing the spectrum of the primary user, this paper presents a cluster based multiple primary and secondary user’s MIMO spatial coding which provides higher capacity. The entire network is divided into number of cluster based on the location such that each cluster will be interference free from other. Each cluster is designed with one primary user and many secondary users and a User Scheduling algorithm called Cluster Based Max Signal Power User Scheduling (CBMSPUS) is proposed to select two best secondary users in each cluster. Since the performance of spatial coder depends on the channel matrix, this paper analyze the spatial pre-coder under Rayleigh, Rican and Nakagami fading channels with multiple users and evaluate the capacity of users under CBMSPUS scheduling algorithm. The results show that the Nakagami fading channel achieves high capacity than others. Primary user calculated capacity is 10.8bits/HZ /channel at low SNR region and 14.2 bits/HZ/channel at high SNR region. The secondary user archives maximum capacity of 9.8bits/HZ /channel at low SNR and 13 bits/HZ/channel at high SNR. The Proposed Scheduling method offers maximum of 15dB gain comparing FIFO scheduling algorithm.

Transceiver Design in Full-Duplex MIMO Cognitive Radios Under Channel Uncertainties

In this paper, the operation of a full-duplex (FD) multiple-input multiple-output (MIMO) underlay cognitive radio (CR) network is studied. Each pair of secondary users (SUs) operate in FD mode, and each SU communicates with its peer within the coverage area of multiple primary users (PUs). Each SU suffers from self-interference, along with interference created by all other SUs and, in its turn, generates interference towards the PU. We assume that the channel-state-information (CSI) of the interference links between the SUs and the PU is imperfectly known and the channel estimation errors are norm bounded. Under such channel uncertainties, we address the problem of robust minimization of the aggregate mean-squared-error (MSE) of all estimated symbols, subject to a set of transmit power constraints, as well as interference constraints, with the aim of protecting PU communication. It is shown that the problem can be cast as a semidefinite programming problem and the optimal precoding matrices can be obtained via an iterative algorithm. By means of simulation, the proposed FD precoding scheme is shown to outperform the standard half-duplex scheme.

MIMO Cognitive Radio User Selection With and Without Primary Channel State Information

In this paper, we study user selection (US) strategies for a multiple-input-multiple-output (MIMO) cognitive radio (CR) downlink network, where the r-antenna underlay CR secondary users (SUs) coexist with a primary user (PU), and all terminals are equipped with multiple antennas. Two main scenarios are considered: 1) The t-antenna cognitive base station (CBS) has perfect or partial channel state information at the transmitter (CSIT) from the CBS to the PU receiver (RX), and 2) the CBS has absolutely no PU CSIT. For these scenarios, we propose and evaluate multiple SU selection schemes that are applicable to both best-effort PU interference mitigation and hard interference temperature (IT) constraints. The computational complexity of the proposed schemes can be significantly smaller than that of an exhaustive search with negligible performance degradation. For the selection of C SUs out of K candidates, our proposed sliding window scheme, for example, is of complexity O(Krt <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), whereas an exhaustive search is on the order of O(( <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sup> )C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). When t and r are C of the same order, the computational complexity of the proposed scheme can be ( <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sup> )C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> /K times smaller. Mathematical complexity analysis and C numerical simulations are provided to show the advantage of our schemes.

Efficient transceiver beamforming in multiple‐input–multiple‐output cognitive radio network

Owing to the ability of improving spectrum utilisation and quality-of-service (QoS) in wireless communications, multiple-input–multiple-output (MIMO) cognitive radio (CR) network has been identified as an excellent choice for the next generation communication. To protect primary users (PUs) from excessive interference while ensuring a meaningful QoS of secondary users (SUs), one key challenge of such system is the joint design of transceiver beamforming for SUs. In this study, the authors investigate the beamforming in MIMO CR network, and two optimisation problems in terms of the minimisation of the total transmission power and the maximisation of the smallest received signal-to-interference-plus-noise ratio (SINR) are considered. The problems can be formulated as indefinite quadratic optimisation programs which are known to be non-convex NP-hard. Hence, a distributed algorithm based on semi-definite programming and minimum-mean-squared-error is proposed to achieve the optimal beamforming weight vector. The findings of this study demonstrated that the proposed algorithm outperforms the existing ones with respect to the total transmitted power and SUs SINR.

Joint single transmit and receive antenna selection for MIMO cognitive radios without channel state information

For multiple-input multiple-output cognitive radios, a single transmit and receive antenna selection scheme is proposed for when the channel state information from a cognitive transmitter to a cognitive receiver is unknown to the transmitter. In the proposed scheme, the transmit antenna at the cognitive transmitter that maximises the transmit power and the receive antenna at the cognitive receiver that maximises the signal-to-interference-and-noise ratio are selected. Also derived is the exact closed-form outage probability considering the peak interference power constraint, the peak transmit power constraint, and interference from the primary transmitter to the cognitive receiver.

Joint Beamforming and Antenna Subarray Formation for MIMO Cognitive Radios

The antenna subarray formation (ASF) is a promising technique for multiple-input multiple-output (MIMO) receiver. For MIMO cognitive radio systems, we propose a joint beamforming and ASF scheme in this letter which maximizes the cognitive achievable capacity subject to the peak transmit power constraint at the secondary transmitter, peak interference power constraint at the primary receiver, and the limited number of nonzero elements in the ASF matrix. To solve the joint optimization problem, we propose a relax-and-recover scheme. Simulation results have shown that the proposed scheme outperforms the conventional antenna selection scheme.

Energy Efficiency Optimization for Cognitive Radio MIMO Broadcast Channels

Conventional designs of cognitive radio (CR) multiple-input multiple-output (MIMO) systems mainly focus on the system throughput. Since nowdays the energy efficiency (EE) of wireless systems has become more and more important, this paper intends to improve the system throughput for unit-energy consumption in CR MIMO broadcast channels (BC). The EE optimization problem of CR MIMO BC is studied under the total power constraint, the interference power constraint and the minimum system throughput constraint. Since the EE optimization problem is non-convex, in order to find the optimal solution, we transform it into an equivalent one-dimension problem with a quasi-concave objective function and use the golden section method to solve it. Through simulations, we show the efficiency of the proposed algorithm.

A New Outer Bound via Interference Localization and the Degrees of Freedom Regions of MIMO Interference Networks With No CSIT

The two-user multiple-input multiple-output (MIMO) interference and cognitive radio channels are considered, where the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> th transmitter and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> th receiver have <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> antennas, respectively. In particular, the degrees of freedom (DoF) regions of these channels are studied under the assumption of having no channel state information at the transmitters. Making certain assumptions about the distributions of channel matrices of increasing generality respectively, Huang, Zhu and Guo, and the authors of this paper characterized the DoF region of the MIMO interference channel for all values of the four-tuple ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ), except when min( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or min( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . More recently, for isotropic fading distributions, Zhu and Guo have solved this latter case by providing a tight outer bound to the DoF region. Here, a simpler and more widely applicable proof of that outer bound is given based on the idea of interference localization. Using the same idea, under Rayleigh fading, the DoF region is then also established for the MIMO cognitive radio channel (when the second transmitter is cognitive) with min( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> >; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -the only class for which the inner and outer bounds previously reported by the authors were not tight-thereby completing the DoF region characterization of this channel under Rayleigh fading for all values of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ).

The Degree-of-Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels With No CSIT

The degree-of-freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (ICs), including X and multihop ICs, and the cognitive radio channel (CRC), when there is no channel state information at the transmitter(s) (CSIT) and for fading distributions in which transmit directions are statistically indistinguishable. For the K-user MIMO BC, the exact DoF region is obtained, which shows that time division is DoF-region optimal. For the two-user MIMO IC and CRC, inner and outer bounds are obtained that coincide for a vast majority of the relative numbers of antennas at the four terminals. Finally, the DoF of the K-user MIMO IC, the CRC, and X networks are obtained for certain classes of these networks. The results herein are derived for fading distributions and additive noises that are more general than those considered in other simultaneous related works. The DoF with and without CSIT are compared and conditions under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby 1) providing robust no-CSIT schemes that have the same DoF as their previously found CSIT counterparts and 2) identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF could be improved.

Interference mitigation for cognitive radio MIMO systems based on practical precoding

In this paper, we propose two subspace-projection-based precoding schemes, namely, full-projection (FP)- and partial-projection (PP)-based precoding, for a cognitive radio multiple-input multiple-output (CR-MIMO) network to mitigate its interference to a primary time-division-duplexing (TDD) system. The proposed precoding schemes are capable of estimating interference channels between CR and primary networks, and incorporating the interference from the primary to the CR system into CR precoding via a novel sensing approach. Then, the CR performance and resulting interference of the proposed precoding schemes are analyzed and evaluated. By fully projecting the CR transmission onto a null space of the interference channels, the FP-based precoding scheme can effectively avoid interfering the primary system with boosted CR throughput. While, the PP-based scheme is able to further improve the CR throughput by partially projecting its transmission onto the null space.