Partial Channel Knowledge Research Articles

Max-Min Fairness Precoding for Physical Layer Security With Partial Channel Knowledge

We propose secure max-min fairness (MMF) precoding for a downlink multi-antenna system with multiple users and eavesdroppers. Since the problem is non-convex and non-smooth and partial channel knowledge is assumed, it is highly challenging to solve. To resolve the difficulties, we first reformulate the problem with conditional average rates, allowing to exploit the partial channel knowledge. Then, we derive the original problem as an approximate smoothing problem using a LogSumExp approach. We identify the first-order optimality condition and cast it to a generalized eigenvalue problem. Solving the problem via a power iteration offers the best local optimal solution. Simulations validate the proposed secure-MMF precoding method.

Joint Precoding and Artificial Noise Design for MU-MIMO Wiretap Channels

Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.

On the Synergistic Benefits of Reconfigurable Antennas and Partial Channel Knowledge for the MIMO Interference Channel

Author(s): Yuan, Bofeng; Ismailoglu, Nilab; Jafar, Syed A | Abstract: Blind Interference Alignment (BIA) schemes create and exploit channel coherence patterns without the knowledge of channel realizations at transmitters, while beamforming schemes rely primarily on channel knowledge available to the transmit- ters without regard to channel coherence patterns. In order to explore the compatibility of these disparate ideas and the possibility of synergistic gains, this work studies the Degrees of Freedom (DoF) of the 2-user (?1 × ?1)(?2 × ?2) Multiple- Input Multiple-Output (MIMO) Interference Channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge, while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. Taking a fundamental dimensional analysis perspective, the main question is to identify which antenna configurations allow synergistic DoF gains. The main results of this work are two-fold. The first result identifies antenna configurations where both reconfigurable antennas and partial channel knowledge are individually beneficial, as those where ?1 l ?1 l min(?2,?2). The second result shows that synergistic gains exist in each of these settings, over the best known solutions that rely on either reconfigurable antennas or partial channel knowledge alone. Coding schemes that jointly exploit partial channel knowledge and reconfigurable antennas emerge as a byproduct of the analysis.

Communication Under Channel Uncertainty: An Algorithmic Perspective and Effective Construction

The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes have been well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is less understood and closed-form characterizations of optimal schemes remain unknown in many cases. This paper approaches this question from a fundamental, algorithmic point of view by studying whether or not such optimal schemes can be constructed algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the concepts of compound channels and averaged channels are considered as models for channel uncertainty and block fading and it is shown that, although the compound channel and averaged channel themselves are computable channels, the corresponding capacities are not computable in general, i.e., there exists no algorithm (or Turing machine) that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal (i.e., capacity-achieving) signal processing and coding schemes possible. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed. Thus, there is a crucial difference between the existence of optimal schemes and their algorithmic constructability. In addition, it is shown that there is no search algorithm that can find the maximal number of messages that can be reliably transmitted for a fixed blocklength. Finally, the case of partial channel knowledge is studied in which either the transmitter or the receiver have perfect channel knowledge while the other part remains uncertain. It is shown that also in the cases of an informed encoder and informed decoder, the capacity remains non-computable in general and, accordingly, optimal signal processing and coding schemes are not effectively constructible.

Generalized Degrees of Freedom of the Symmetric Cache-Aided MISO Broadcast Channel With Partial CSIT

We consider the cache-aided MISO broadcast channel (BC) in which a multi-antenna transmitter serves $K$ single-antenna receivers, each equipped with a cache memory. The transmitter has access to partial knowledge of the channel state information. For a symmetric setting, in terms of channel strength levels, partial channel knowledge levels and cache sizes, we characterize the generalized degrees of freedom (GDoF) up to a constant multiplicative factor. The achievability scheme exploits the interplay between spatial multiplexing gains and coded-multicasting gain. On the other hand, a cut-set-based argument in conjunction with a GDoF outer bound for a parallel MISO BC under channel uncertainty is used for the converse. We further show that the characterized order-optimal GDoF is also attained in a decentralized setting, where no coordination is required for content placement in the caches.

NOMA-Aided Multicell Downlink Massive MIMO

Novel user clustering and pilot assignment schemes are proposed for non-orthogonal multiple access (NOMA) aided multicell massive multiple-input multiple-output systems. Our proposed designs leverage the spatial covariance matrices of users, and they are applicable to both overloaded and underloaded cases. Users having linearly dependent covariance matrices are grouped into the same cluster, and they are assigned with orthogonal pilots to mitigate intra-cluster pilot contamination. These pilots are shared among the users in different clusters to reduce the training overhead. Then, the inter-cluster pilot contamination can be mitigated by exploiting asymptotically linearly independent covariance matrices of pilot-sharing users located in different clusters. The achievable downlink rates are derived by capturing the detrimental effects of practical transmission impairments and partial channel knowledge. Our analysis reveals that the user rates are not fundamentally limited by the intra/inter-cluster pilot contamination arising from pilot reuse for the underloaded case. We show that the achievable rate of each user increases without bound under zero-forcing precoding as the number of base-station antennas grows large. However, for the overloaded case, the users, which share the same spatial direction and located within a NOMA cluster, will have to share pilots. Thus, the achievable rate gains must be traded-off to enable massive connectivity. Three transmit power control policies are designed to maximize the sum rate, while achieving max-min user-fairness by mitigating the adverse near-far effect.

Security-Enhanced SC-FDMA Transmissions Using Temporal Artificial-Noise and Secret Key Aided Schemes

We investigate the physical-layer security of uplink single-carrier frequency-division multiple-access (SC-FDMA) systems. Multiple users, Alices, send confidential messages to a common legitimate base-station, Bob, in the presence of an eavesdropper, Eve. To secure the legitimate transmissions, each user superimposes an artificial noise (AN) signal on the time-domain SC-FDMA data symbol. We reduce the computational and storage requirements at Bob's receiver by assuming simple per-sub-channel detectors. We assume that Eve has global channel knowledge of all links in addition to high computational capabilities, where she adopts high-complexity detectors such as single-user maximum likelihood (ML), multi-user minimum-mean-square-error, and multi-user ML. We analyze the correlation properties of the time-domain AN signal and illustrate how Eve can exploit them to reduce the AN effects. We prove that the number of useful AN streams that can degrade Eve's signal-to-noise ratio is dependent on the channel memories of Alices-Bob and Alices-Eve links. Furthermore, we enhance the system security for the case of partial Alices-Bob channel knowledge at Eve, where Eve only knows the precoding matrices of the data and AN signals instead of knowing the entire Alices-Bob channel matrices, and propose a hybrid security scheme that integrates temporal AN with channel-based secret key extraction.

Secure Hybrid Digital and Analog Precoder for mmWave Systems With Low-Resolution DACs and Finite-Quantized Phase Shifters

Millimeter wave (mmWave) communication has been regarded as one of the most promising technologies for the future generation wireless networks because of its advantages of providing a ultra-wide new spectrum and ultra-high data transmission rate. To reduce the power consumption and circuit cost for mmWave systems, hybrid digital and analog (HDA) architecture is preferred in such a scenario. In this paper, an artificial-noise (AN) aided secure HDA beamforming scheme is proposed for mmWave MISO system with low resolution digital-to-analog converters (DACs) and finite-quantized phase shifters on RF. The additive quantization noise model for AN aided HDA system is established to make an analysis of the secrecy performance of such systems. With the partial channel knowledge of eavesdropper available, an approximate expression of secrecy rate (SR) is derived. Then using this approximation formula, we propose a two-layer alternately iterative structure (TLAIS) for optimizing digital precoder (DP) of confidential message (CM), digital AN projection matrix (DANPM) and analog precoder (AP). The inner-layer iteration loop is to design the DP of CMs and DANPM alternatively given a fixed matrix of AP. The outer-layer iteration loop is in between digital baseband part and analog part, where the former refers to DP and DANPM, and the latter is AP. Then for a given digital part, we propose a gradient ascent algorithm to find the vector of AP vector. Given a matrix of AP, we make use of general power iteration (GPI) method to compute DP and DANPM. This process is repeated until the terminal condition is reached. Simulation results show that the proposed TLAIS can achieve a better SR performance compared to existing methods, especially in the high signal-to-noise ratio region.

Coverage Optimization for UAV-Aided Internet of Things with Partial Channel Knowledge

Due to the high maneuverability of unmanned aerial vehicles (UAVs), they have been widely deployed to boost the performance of Internet of Things (IoT). In this paper, to promote the coverage performance of UAV-aided IoT communications, we maximize the minimum average rate of the IoT devices by jointly optimizing the resource allocation strategy and the UAV altitude. Particularly, to depict the practical propagation environment, we take the composite channel model including both the small-scale and the large-scale channel fading into account. Due to the difficulty in acquiring the random small-scale channel fading, we assume that only the large-scale channel sate information is available. On this basis, we formulate an optimization problem, which is not convex and challenging to solve. Then, an efficient iterative algorithm is proposed using block coordinate descent and successive convex optimization tools. Finally, simulation results are presented to demonstrate the significant performance gain of the proposed scheme over existing ones.

On Capacity of the Writing Onto Fast Fading Dirt Channel

The "Writing onto Fast Fading Dirt" (WFFD) channel is investigated to study the effects of partial channel knowledge on the capacity of the "writing on dirty paper" channel. The WFFD channel is the Gel'fand-Pinsker channel in which the output is obtained as the sum of the input, white Gaussian noise and a fading-times-state term. The fading-times-state term is equal to the element-wise product of the channel state sequence, known only at the transmitter, and a fast fading process, known only at the receiver. We consider the case of Gaussian distributed channel states and derive an approximate characterization of capacity for different classes of fading distributions, both continuous and discrete. In particular, we prove that if the fading distribution concentrates in a sufficiently small interval, then capacity is approximately equal to the AWGN capacity times the probability of this interval. We also show that there exists a class of fading distributions for which having the transmitter treat the fading-times-state term as additional noise closely approaches capacity. Although a closed-form expression of the capacity of the general WFFD channel remains unknown, our results show that the presence of fading can severely reduce the usefulness of channel state knowledge at the transmitter.

On Capacity of the Writing Onto Fast Fading Dirt Channel

The Writing onto Fast Fading Dirt (WFFD) channel is investigated to study the effect of partial channel knowledge on the performance of interference pre-cancellation. The WFFD channel is the Gel’fand-Pinsker channel in which the channel output is the sum of the channel input, white Gaussian noise, and a fading-times-state term. The fading-times-state term is obtained as the product of the channel state sequence, known only at the transmitter, and a fast fading process, known only at the receiver. We consider the case of Gaussian-distributed channel states and derive an approximate characterization of capacity for different classes of fading distributions, both continuous and discrete. In particular, we prove that if the fading distribution concentrates in a sufficiently small interval, then capacity is approximately equal to the AWGN capacity times the probability of such interval. We also show that there exists a class of fading distributions for which having the transmitter treat the fading-times-state term as additional noise closely approaches capacity.

Rate Adaptation, Scheduling, and Mode Selection in D2D Systems With Partial Channel Knowledge

Device-to-device (D2D) communication enables simultaneous data transmissions by cellular users (CU) and D2D user pairs, but at the expense of additional interference between them. The literature on resource allocation in D2D systems often assumes that the base station (BS) has complete channel state information (CSI) about all the links between all the users in a cell. However, acquiring the CSI of cross links between the CUs and the D2D receivers is a critical bottleneck because the number of cross links is the product of the number of CUs and D2D pairs. We study a novel partial CSI model in which the overhead of feeding back the CSI of the cross links is much lower. For a cell with one D2D pair and multiple CUs, we propose a novel throughput-optimal joint mode selection, user scheduling, and rate adaptation policy that exploits information about the statistics of the cross links and incorporates inter-cell interference. We derive closed-form expressions for the feedback-conditioned goodput for the underlay mode, which drives this optimal policy. We also present extensions that incorporate user fairness, quantized CSI, and multiple D2D pairs and multiple subchannels.

Global-Searching-Based Iterative Swapping Antenna Selection for Massive MIMO Systems with Imperfect Channel Estimation

With the growing of base station antenna number in massive multiple-input-multiple-output (MIMO), the complexity and the cost of the system rise rapidly. Fortunately, the antenna selection is an effective way to solve the problem, which can capture most of the advantages of massive MIMO. In this paper, a novel global-searching-based iterative swapping antenna selection method is proposed under the partial channel knowledge case for massive MIMO based on capacity maximization. The method is investigated with detailed mathematical derivations, as well as convergence discussion. Both global-searching-based “local” swapping (GSL-swapping) and global-searching-based “global” swapping algorithms are proposed for massive MIMO with imperfect channel state information (CSI). The former exchanges the selected antenna with the unselected one which is “better” than the selected one. Different from the GSL-swapping algorithm, the latter only swaps the “worst” selected antenna with the “best” unselected antenna which is “better” than the “worst” selected one. In addition, an improved global-searching-based “global” swapping algorithm with imperfect CSI is proposed to further decrease the complexity. Due to the “global searching” characteristic, the proposed algorithms can obtain a near optimal performance. Numerical simulations are provided to validate the proposed algorithms.

Hybrid Analog–Digital Precoding Design for Secrecy mmWave MISO-OFDM Systems

Millimeter-wave large-scale antenna systems typically apply hybrid analog-digital precoders to reduce hardware complexity and power consumption. In this paper, we design hybrid precoders for physical-layer security under two types of channel knowledge. With full channel knowledge at transmitter, we provide sufficient conditions on the minimum number of RF chains needed to realize the performance of the fully digital precoding. Then, we design the hybrid precoder to maximize the secrecy rate. By maximizing the average projection between the fully digital precoder and the hybrid precoder, we propose a low-complexity closed-form hybrid precoder. We extend the conventional projected maximum ratio transmission scheme to realize the hybrid precoder. Moreover, we propose an iterative hybrid precoder design to maximize the secrecy rate. With partial channel knowledge at transmitter, we derive a secrecy outage probability upper-bound. The secrecy throughput maximization is converted into a sequence of secrecy outage probability minimization problems. Then, the hybrid precoder is designed to minimize the secrecy outage probability by an iterative hybrid precoder design. Performance results show the proposed hybrid precoders achieve performance close to that of the fully digital precoding at low and moderate signal-to-noise ratios (SNRs), and sometimes at high SNRs depending on the system parameters.

Artificial Noise Aided Hybrid Precoding Design for Secure mmWave MISO Systems with Partial Channel Knowledge

In this letter, we propose a hybrid analog–digital precoder design to enhance the physical layer security of millimeter-wave (mmWave) multiple-input single-output (MISO) systems with partial channel knowledge. We derive a closed-form expression for the average signal-to-interference-and-noise ratio (SINR) of the eavesdropper (Eve) as a function of the hybrid precoder. Using the average SINRs of Eves, we derive a secrecy rate lower bound. Then, we propose a low-complexity artificial-noise-aided (AN-aided) hybrid precoder design to maximize the secrecy rate lower bound. Numerical results show that the proposed AN-aided hybrid precoder achieves comparable performance to that of the fully digital precoder, with much lower hardware complexity. Moreover, the proposed AN-aided hybrid precoder outperforms the existing hybrid precoder design. Effect of finite-resolution phase shifters on the proposed precoder is also investigated.

Optimal Relay Selection for Secure Cooperative Communications With an Adaptive Eavesdropper

Optimal relay selection is investigated for secure cooperative communications against an adaptive eavesdropper that can perform eavesdropping if the eavesdropping link has good channel quality or perform jamming otherwise. A number of decode-and-forward relays are available for legitimate communications, among which one relay can be selected to help. For legitimate communications, three cases for availability of the eavesdropping channel information are considered: full channel knowledge, partial channel knowledge, and statistical channel knowledge. An optimal relay selection scheme is proposed for each case. For the first and third cases, exact secrecy outage probability expressions in closed form are derived, and for the second case, an approximate secrecy outage probability is derived, which is tight in the high main-to-eavesdropper ratio regime. Moreover, secrecy diversity order for the proposed relay selection scheme in each case is also derived, which is shown to be a full secrecy diversity. Finally, numerical results are given to verify the theoretical analysis derived in this paper.

Artificial-Noise-Aided Secure Transmission Scheme With Limited Training and Feedback Overhead

We design a novel artificial-noise-aided secure ON–OFF transmission scheme in a wiretap channel. We consider a practical scenario, where the multi-antenna transmitter only obtains partial channel knowledge from the single-antenna receiver through limited training and feedback but has no channel knowledge about the single-antenna eavesdropper. In the design, we first propose a three-period block transmission protocol to capture the practical training and quantization features. We then characterize the statistics of the received signal-to-noise ratios at the receiver and the eavesdropper. Under the secrecy outage constraint, we exploit the ON–OFF scheme to perform secure transmission and derive a closed-form expression for the secrecy throughput. Moreover, we investigate the optimization problem of maximizing the secrecy throughput by proposing an iterative algorithm to determine the optimal power allocation between the information signal and artificial noise, as well as the optimal codeword transmission rate. Furthermore, we define the net secrecy throughput (NST), which takes the signaling overhead into account and address the problem of optimally allocating the block resource to the training and feedback overhead. Numerical results clearly demonstrate how the optimal signaling overhead changes with the number of transmit antennas, and there exists an optimal number of antennas that maximizes the NST.

Overlay Spectrum Sharing using Improper Gaussian Signaling

Improper Gaussian signaling (IGS) scheme has been recently shown to provide performance improvements in interference-limited networks as opposed to the conventional proper Gaussian signaling (PGS) scheme. In this paper, we implement the IGS scheme in an overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to match the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio to maximize the secondary link achievable rate while satisfying the primary network quality of service requirements. In particular, we consider full and partial channel knowledge scenarios and derive the feasibility conditions of operating the overlay cognitive radio systems. Moreover, we derive the superiority conditions of the IGS schemes over the PGS schemes supported with closed-form expressions for the corresponding power distribution and the circularity coefficient and parameters. Simulation results are provided to support our theoretical derivations.

Efficient Variational Bayesian Method for Joint Channel Estimation and Signal Detection in OFDM-Based AF Relay Networks

We propose improved joint channel estimation and data detection in orthogonal frequency division multiplexing (OFDM) amplify-and-forward (AF) relay network in the case of imperfect partial channel knowledge at the destination. To improve the detection accuracy, we adopt the variational Bayesian approximation (VBA) which is an iterative Bayesian method for channel estimation. We derive a modified iterative estimator that takes into account the channel estimation errors at the previous iteration, to reduce the impact of channel uncertainty at the next iteration, and hence, to improve the overall detection accuracy. By comparison with state of the art VBA-based estimators through numerical analysis, we highlight the superiority of our new VBA method and demonstrate a notable improvement in terms of bit error rate and mean square error between the true and the estimated channel.

Robust RF Beamforming for Millimeter Wave MIMO–OFDM Systems

In conventional multiple-input multiple-output systems, each antenna is connected to a radio-frequency (RF) chain. Due to the tiny wavelength of millimeter waves (mmWave), tens of antennas can be packed into a small area in mmWave transceivers. However, implementing an RF chain for each antenna is impractical due to the high cost and power of mixed-signal devices. In order to reduce the cost and get benefit from the antennas, an analog RF beamformer is implemented using variable gain amplifiers and analog phase shifters. In this paper, we propose a novel spatial diversity scheme for mmWave RF beamforming. The transmitter is assumed to have partial knowledge of the channel to the receiver. We formulate the spatial diversity problem as maximizing the geometric mean of the projections of the RF precoder on the transmit steering vectors and the geometric mean of the projections of the RF combiner on the receive steering vectors. To solve the optimization problem of the RF beamformers, we propose two solution algorithms. The first algorithm is based on semidefinite relaxation (SDR). Due to the high computational complexity of the SDR algorithm, we propose a simpler second algorithm, which is gradient ascent algorithm. Simulation results show that the proposed spatial diversity scheme outperforms the conventional spatial diversity schemes in case of no blockage and in case of blockage to any propagation path regardless of the number of propagation paths.