Electrocardiogram (ECG) classification under the inter-patient paradigm remains a critical challenge due to significant intra- and inter-patient variability in cardiac signals. It causes domain shift and data imbalance issues that hinder model generalization across diverse patient cohorts, limiting the accuracy and robustness of existing classification approaches. We propose a novel distributionally adaptive learning framework that simultaneously performs ECG classification and label-supervised synthetic ECG generation using a generative adversarial network (GAN), addressing these challenges comprehensively. Our approach integrates a transformer-based generator with a convolutional discriminator to generate synthetic ECG signals, effectively alleviating data imbalance issues. To further mitigate domain discrepancy and improve generalization across unseen patient recordings, we introduce single-heartbeat test-time adaptation (TTA). We rigorously evaluate our model using the MIT-BIH Arrhythmia Database, MIT-BIH Supraventricular Database, and INCART Arrhythmia Database. Results outperform state-of-the-art models across intra- and inter-patient settings, highlighting the effectiveness of synthetic ECG augmentation and the robustness of our model in real-world clinical scenarios. It paves the way for personalized and adaptive ECG-based diagnostics, underscoring the potential of generative models for advancing digital health solutions in cardiovascular medicine.

We consider a status update system consisting of one source, one server, and one sink. The source generates packets according to a Poisson process and the packets are served according to a generally distributed service time. We consider a system with a capacity of one packet, i.e., there is no waiting buffer in the system, and model it as an M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy and calculate the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) under the policy. According to the probabilistically preemptive policy, when a packet arrives, the possible packet in the system is replaced by the arriving packet with a fixed probability. Numerical results show the effectiveness of the packet management policy.

In this paper, we propose a deep learning method for channel estimation in OFDM systems over WINNER II channel. The approach is based on a Long Short-Term Memory (LSTM) network that takes advantage of the temporal and frequency correlation across OFDM blocks. The model is trained to predict the full channel frequency response at each block using only pilot observations from current and previous blocks. We evaluate the performance of the proposed estimator under various signal-to-noise ratio (SNR), numbers of pilot subcarriers, and temporal window sizes. Simulation results demonstrate that the LSTM-based approach consistently outperforms both LS and recent deep learning models based on super-resolution. The results show that the LSTM model achieves lower estimation error across different SNR values, making it a strong candidate for reliable channel estimation in dynamic wireless environments.

We consider an Internet of Battlefield Things (IoBT) system consisting of multiple devices that want to securely communicate with each other during a mission in the presence of an adversary with unbounded computational power. The adversary has complete access to listen/read the ciphertext without tampering with the communication line. We provide an unconditionally secure encryption scheme to exchange messages among devices in the system. The main idea behind the scheme is to provide secret keys to exchange messages using a random binary matrix that is securely shared among all the devices, and pair-wise random secret keys established between each pair of devices attempting to communicate before the mission. The scheme is implemented by using finite group modular addition. We show that the scheme is absolutely semantically secure, i.e., the scheme guarantees that an adversary with unbounded computational power cannot get even one bit of information about a message, except for an exponentially small probability in a security parameter. Besides that, we show that even if the random binary matrix is revealed to the adversary, the provided scheme is computationally secure against the key recovery attack.

The unbreakable security and higher data rates offered by quantum communication networks have made quantum communication an inevitable necessity of the future. Many quantum communication frameworks, such as quantum key distribution and super dense coding, require entangled pairs to be shared between the source and destination nodes. Communication nodes in quantum networks have a minimum fidelity requirement for the entangled pairs. If the fidelity requirement is not satisfied, the entangled pairs may not be used for the desired operations. Successful sharing of the entangled pairs between the nodes is a crucial step in making quantum communication practical. In this work, we propose a framework to maximize entanglement sharing between a source and multiple destination nodes in a fair manner. We consider a system that takes advantage of the purification process to improve the fidelity of the entangled pairs when necessary. The proposed solution framework provides the optimal number of entangled pairs required for the purification process and the optimal transmission rate at the source node to achieve the desired system objective. The non-convex problem is first transformed into a convex form, and then a Lagrangian dual-based framework is proposed to find the optimal solution values. Moreover, to optimize the number of entangled pairs for purification at each link, we derive a closed-form expression that provides the optimal value in a single step. Selected simulation results demonstrate that the proposed framework exhibits excellent performance.

Heart arrhythmia is a chronic condition characterized by irregular heartbeats without early detection, which can lead to high mortality rates. To address this critical concern and enhance the prediction of arrhythmia onset and its prevention, this paper proposes a CNN-Informer model, a deep learning approach, for long-term time series forecasting of electrocardiogram (ECG) signals. The model achieves a long-term prediction with a remarkable mean square error (MSE) of 0.8358, a short-term prediction MSE of 0.3712 on the database from Beth Israel Deaconess Medical Center and the Massachusetts Institute of Technology (MIT-BIH Arrhythmia Database) and an MSE of 0.6843 on the 12-lead ECG arrhythmia database under the auspices of Chapman University and Shaoxing People’s Hospital. These results show that the CNN-Informer model is promising for time series forecasting and computer-assisted diagnosis in clinical settings and holds the potential for improvements in patient care and management.

We provide an encryption protocol for storing highly confidential data of a user on a public cloud storage. We show that the protocol provides unconditional security. More specifically, we prove that the protocol is semantically secure against an all-powerful adversary with unbounded computational power and storage capacity who has complete access to the communication line. The provided protocol is very simple, it is implemented by exploiting finite group modular addition and XOR operations. The protocol provides a high security gain defined as the ratio of the amount of data (in bits) that can be securely stored on the public cloud and the number of secret bits required to be stored at the user end. As an illustrative example, according to the protocol, by using 40.2 Terabytes (TBs) of secret bits, a user is able to store 5.9 ×108TBs of data on a public storage with guaranteed everlasting security.

Deep neural networks (DNNs) have been widely used in recent years for wireless communication applications, including channel estimation. However, DNN performs well for environments (data) that it has been trained for. However, it is still challenging to work in a non-stationary system where the statistical characteristics of the environment change with time. This paper introduces an online adaptation approach that allows the neural network to dynamically change to cope with the non-stationary channel estimation. The idea is to use the existing detected packets to continuously update the weights of the DNN. Simulation results show that our approach can significantly improve the performance of the DNN in non-stationary environments whereas concurrent state-of-the-art algorithms fail.

In the bounded storage model introduced by Maurer, the adversary is computationally unbounded and has a bounded storage capacity. In this model, perfect secrecy is guaranteed by using a publicly available random string whose length is larger than the adversary storage capacity. The protocol proposed by Maurer is simple, from the perspective of implementation, and efficient, from the perspective of the initial secret key size and random string length. However, he provided the proof of the security for the case where the adversary can access a constant fraction of the random string and store onlyoriginal bitsof the random string. In this paper, we provide a new proof of the security of the protocol proposed by Maurer for the general bounded storage model, i.e., the adversary can access all bits of the random string, and store the output of any Boolean function on the string. We reaffirm that the protocol isabsolutely semantically securein the general bounded storage model.

Low latency and high throughput are critical features for 5G mobile communication systems and beyond, in which the support of large MIMO is essential. Signal detection in large Multiple-Input Multiple-Output (MIMO) is a paramount component of a communication system since its performance in terms of latency, error rate, and achieved throughput depends on it. In this paper, we demonstrate the ability of our proposed massively parallel non-linear detection approach to support a large number of antennas and sustain high throughput at the extreme low latency of next-generation mobile communication systems. Our proposed method operates on a search tree that models all possible combinations of the transmitted signal. It selects coefficients from different levels and navigates the tree toward the Maximum Likelihood (ML) solution. To maintain the low latency requirement, we leverage the significant computational power of the Graphics Processing Unit (GPU) by expressing operations in terms of matrix-matrix multiplications. The obtained results show the ability of our non-linear detection approach to deal with up to 120 antennas with one-millisecond latency while satisfying good error rate performance at a practical signal-to-noise ratio (SNR).

In this paper, we describe a novel cross-layer fingerprinting approach (CL-FP) that aims at uniquely identifying wireless devices by extracting inherent cross-layer device features based on the requirements of the driving network application(s). We demonstrate how our system can be applied to MAC spoofing detection. Our contributions include: (1) We propose the CL-FP framework and pipeline for detecting MAC spoofing attacks, which, to our knowledge, is the first of its kind; (2) We experimentally confirm theoretical results showing that easier-to-extract FP features can reliably represent harder-to-extract intrinsic physical characteristics of devices; (3) We test and evaluate the performance of the proposed CL-FP approach through simulations in the context of the MAC spoofing detection use case. Our preliminary results show that the proposed CL-FP pipeline provides a lightweight, scalable and reliable end-to-end cross-layer device fingerprinting framework.

In this paper, we propose a deep learning autoencoder (AE) to model and design space optical communications (SOC) systems from end-to-end performance. The proposed AE is based on multiple-decoders and a new layered structure for constructing both encoders and decoders. The use of multiple-decoders can increase the receiver diversity, which allows the gradient descent to minimize the cost function compared to state-of-the-art models and therefore improve the bit error rate (BER) performance. In addition, we utilize system tool kit (STK) simulator for a realistic SOC channel modeling in Log-normal fading and additive white Gaussian channel. Numerical results reveal that the traditional convolution codes-based SOC systems are outperformed by the proposed learning-based AE for various code rates. Moreover, the proposed AE outperforms the benchmark AE learning-based models in terms of BER performance metric.

Electrocardiogram (ECG), one of the most popular cardiac tests, is a quick and painless tool for early diagnosis. Machine learning algorithms have been advocated as a promising tool to facilitate ECG signals' analysis. However, current ECG classification algorithms confront various obstacles, including high model complexity, time-consuming training, and low ac-curacy. To close this gap, we develop a convolutional neural network (CNN) model for classifying the data collected from the Beth Israel Deaconess Medical Center and the Massachusetts Institute of Technology (MIT-BIH Arrhythmia Database). The proposed CNN model is designed to classify 3 super-classes, 5 sub-classes, and 6 sub-classes, respectively, to significantly improve arrhythmia classification. It uses a pre-processing denoising approach prior to classification, which is capable of enhancing the Signal-to-Noise Ratio (SNR) by around 13.6 dB, to achieve an average classification accuracy of 99.11%, 99.1 %, and 98.88 %, respectively.

This work presents a deep-Q reinforcement learning (DQ-RL) framework to achieve fairness in multi-access cognitive radio (CR) systems. The proposed framework provides fast solution and is robust to channel dynamics. Further, to remove the computational overhead and the burden to feedback thousands of weights from the secondary receiver (SR), we propose a solution where the process of learning is carried out at the secondary transmitters (STs). The simulations show that by using the proposed technique, a good level of fairness is achievable with an outage probability of the primary system less than 0.04. We also provide the comparison of the proposed technique with a brute-forcing optimization method, and show the fairness gain of the proposed framework compared to the rate maximization model.

This paper addresses the degraded discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communication system based on intensity modulation and direct detection (IM-DD). Subject to nonnegativity, average-intensity, and bandwidth constraints, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with a countably infinite number of mass points, but with finitely many mass points in any bounded interval. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the regimes where the average intensity constraint either tends to zero (low-intensity) or tends to infinity (high-intensity). In the low-intensity regime, we observe that: when the channel gains of the legitimate receiver and the eavesdropper are identical, the secrecy capacity scales linearly in the average-intensity ε; whereas when the channel gains are different, the secrecy capacity scales, to within a constant, like$(\alpha_{B}-\alpha_{E})\mathcal{E}\log\log\frac{1}{\mathcal{E}}$, where αBand αEare the legitimate receiver's and the eavesdropper's channel gains, respectively. In the high-intensity regime, we establish that the secrecy capacity does not scale with the average intensity constraint.

In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a b -bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.

In optical wireless communication (OWC) systems, channel estimation and detection of the transmitted symbols have been conventionally performed using analytical methods assuming that the optical channel follows a certain model, e.g., free-space model, input-dependent noise model, or Poisson model. In practical OWC systems, channels do not necessarily follow a specific model. Hence, it is difficult, if not impossible, to derive analytical models that provide optimal performance in realistic optical channels. Motivated by the success of neural networks in estimation and classification in various fields, we propose a neural network-based methodology for detection and estimation for OWC that does not rely on a channel model. Simulation results show that the proposed learning-based estimation and detection schemes achieve the optimal performance of the maximum likelihood detector under different channel state information assumptions.

This paper addresses the discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communications system based on intensity modulation and direct detection. Subject to nonnegativity and peak intensity as well as bandwidth constraints imposed on the channel input, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with a finite support. In general, the number of mass point of the optimal distributions are greater than two. This is in contrast with the continuous-time PWC where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions when the signaling bandwidth is not restricted. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the low intensity regime and observe that the secrecy capacity scales quadratically with the peak intensity constraint. Finally, Our numerical results indicate that there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously.

This paper investigates the secrecy performance of the multiple-input single-output visible light communication (VLC) wiretap channel. The considered system model comprises three nodes: a transmitter (Alice) equipped with multiple fixtures of LEDs, a legitimate receiver (Bob), and an eavesdropper (Eve), each equipped with one photo-diode. The VLC channel is modeled as a real-valued amplitude-constrained Gaussian channel. Eve is assumed to be randomly located in the same area as Bob. Due to this, artificial noise-based beamforming is adopted as a transmission strategy in order to degrade Eve's signal-to-noise ratio. Assuming discrete input signaling, we derive an achievable secrecy rate in a closed-form expression as a function of the beamforming vectors and the input distribution. We investigate the average secrecy performance of the system using stochastic geometry to account for the location randomness of Eve. We also adopt the truncated discrete generalized normal (TDGN) as a discrete input distribution. We present several examples through which we confirm the accuracy of the analytical results via Monte Carlo simulations. The results also demonstrate that the TDGN distribution, albeit being not optimal, yields performance close to the secrecy capacity.

This paper focuses on performance analysis of millimeter wave (mmWave) communications. We investigate how the interference behaves in the outdoor mesh network operating at 60-GHz when blockage and shadowing are present, using probability of collision as a metric, under both protocol model and physical model. In contrast with reported results in mmWave mesh network at 60-GHz advocating that the interference has only a marginal effect, our results show that for a short-range link of 100 m, the collision probability gets considerably large (beyond 0.1) at signal-to-interference-plus-noise ratio (SINR) of interest. Compensation or compromise should be made in order to maintain a low probability of collision, either by reducing transmitter node density which is at the cost of network connectivity, or by switching to a compact linear antenna array with more flat-top elements, which places a more stringent requirement in device integration techniques.

The capacity of the intensity-modulation direct-detection (IM-DD) multiple-input multiple-output channel is studied under average and peak intensity constraints. We focus on the low signal-to-noise ratio (SNR) regime where the constraints proportionally vanish, or alternatively, where the noise power is large. A general upper bound on the capacity of this channel is derived. Then, this bound is shown to be tight at low SNR, where it coincides with the achievable rate of (i) on-off keying (OOK), spatial repetition coding, and maximum-ratio combining under individual average constraint and (ii) OOK with maximally-correlated inputs under a sum average constraint. This leads to a low-SNR capacity characterization of the channel.

This paper addresses a two-user intensity-modulation direct-detection discrete memoryless free space optical broadcast channel (DM-FSOBC) with nonnegativity, peak and average intensity constraints at the transmitter. It is shown that superposition coding along with generating the codebooks of both users according to discrete distributions with a finite number of mass points, achieve the capacity region of the DM-FSOBC. Although the capacity-achieving distributions are not necessarily unique, it is established that only discrete distributions with a finite number of mass points can achieve the points on the boundary of the capacity region.

The low-SNR asymptotic capacity of the multiple-input multiple-output (MIMO) optical intensity channel is studied under both average and peak intensity constraints. We focus on low SNR, which can be modeled as the scenario where both constraints proportionally vanish, or where the peak constraint is held constant while the average constraint vanishes. A capacity upper bound is derived and is shown to be tight at low SNR under both scenarios. The capacity achieving input distribution at low SNR is shown to be a maximally correlated vector-binary input distribution. Consequently, the low-SNR capacity of the channel is characterized. As a byproduct, it is shown that for a channel with peak intensity constraints only, or with peak intensity constraints and individual (per aperture) average intensity constraints, a simple scheme composed of coded ON-OFF keying, spatial repetition, and maximum-ratio combining is optimal at low SNR.

An optical wireless intensity-modulation direct-detection multiple-input multiple-output communication system is considered. The performance of $M$ -PAM rate-1 direct current offset space-time block codes is studied in terms of average worst-case pairwise error probability (WC-PEP) in quasi-static channels. It is shown that within this code class, the average WC-PEP is minimized by repetition coding (RC) under both electrical and optical individual power constraints, irrespective of channel statistics. This agrees with previously published results related to ON-OFF keying RC. This is further extended to sum power constraints, where it is shown that spatial beamforming minimizes the average WC-PEP within this code class, which simplifies to RC if the channel matrix has independent and indentically distributed columns and a sum electrical power constraint. Under a sum optical power constraint, this also holds true at high signal-to-noise ratio (SNR), but not at low SNR. Generally, the time dimension of this code class is redundant from an average WC-PEP perspective. Numerical results are provided to support the theoretical findings and to show that the average WC-PEP leads to a good approximation of the actual error probability at high SNR.

Millimeter wave (mmWave) technology has been advocated as a promising infrastructure to provide reliable communications, both in indoor and outdoor environments. In this paper, we extend the application of mmWave to the uplink communication between smart meters (SMs) and a gateway. Such a communication is subject to interference from SMs belonging to adjacent networks and blockage caused by human bodies. Using a 3-D stochastic blockage model, we derive the outage probability. When human-body blockage is neglected, the high signal-to-noise-ratio (SNR) analysis shows a diversity gain of (mLM), where mLis the Nakagami-fading parameter of the line of sight (LOS) of the reference transmitter's channel, and M is the number of receive antennas at the gateway. Accounting for human-body blockage, the diversity gain reduces to (mNM), where mNis the Nakagami-fading parameter of the non LOS of the reference transmitter's channel. Our analysis shows that the probability that an SM is in LOS decays exponentially with the link length and the density of blockages. Although at high SNR blockage reduces the diversity gain, our numerical results show that blockage may decrease the outage probability at finite SNR.

This paper studies the optical wiretap channel with input-dependent Gaussian noise, in which the main distortion is caused by an additive Gaussian noise whose variance depends on the current signal strength. Subject to nonnegativity and peak-intensity constraints on the channel input, we first present a practical optical wireless communication scenario for which the considered wiretap channel is stochastically degraded. We then study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. Moreover, we show that the entire rate-equivocation region of this wiretap channel is also obtained by discrete input distributions with a finite support. Similar to the case of the Gaussian wiretap channel under a peak-power constraint, here too, we observe that under nonnegativity and peak-intensity constraints, there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously. Furthermore, we prove the optimality of discrete input distributions in the presence of an additional average intensity constraint. Finally, we shed light on the asymptotic behavior of the secrecy capacity in the low- and high-intensity regimes. In the low-intensity regime, the secrecy capacity scales quadratically with the peak-intensity constraint. On the other hand, in the high-intensity regime, the secrecy capacity does not scale with the constraint.

The capacity of the intensity modulation direct detection multiple-input-multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precoding-free schemes: channel inversion and orthogonal-upper triangular matrix product decomposition. The achievable rate of a dc-offset singular-value decomposition-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived.

In this work, we investigate the ergodic secrecy rate region of a block-fading spectrum-sharing system, where a D2D communication is underlying a cellular channel. We consider that both the primary and the secondary transmissions require their respective transmitted messages to be kept secret from a common eavesdropper under a joint secrecy constraint. The presented results are for three different scenarios, each corresponding to a particular requirement of the cellular system. First, we consider the case of a fair cellular system, and we show that the impact of jointly securing the transmissions can be balanced between the primary and the secondary systems. The second scenario examines the case when the primary network is demanding and requires the secondary transmission to be at a rate that is decodable by the primary receiver, while the last scenario assumes a joint transmission of artificial noise by the primary and the secondary transmitters. For each scenario, we present an achievable ergodic secrecy rate region that can be used as an indicator for the cellular and the D2D systems to agree under which terms the spectrum will be shared.

Visible light communication (VLC) is an effective alternative technology to overcome the limitations related to the radio frequency (RF) spectrum. In the modern day of communication systems, the energy harvesting (EH) technique is considered as a promising technology to design more energy efficient communication systems. Integrating VLC with the EH technology in wireless networks guaranties the reliability of these networks. In this paper, we consider a dual-hop VLC/RF wireless communication, composed of two Light Emitting Diodes (LEDs) and two receivers, assisted by a decode-and-forward (DF) relaying system operating with EH in order to boost the coverage of VLC systems. Using successive interference cancellation, we derive achievable rates of both users. Afterwards, we determine the achievable rate-region for this communication system where we show that this region can take four shapes depending on the communication scenario. Then, we formulate the achievable rate-region maximization problem, and we develop solution to find the optimal design for the EH time switching protocol. Further, we show that EH enhances the performance of the communication system in a certain regime of its initial power. We finally present selected numerical result to verify the analytic results.

The capacity of MIMO intensity modulation channels is studied. The non-negativity of the transmit signal (intensity) poses a challenge on the precoding of the transmit signal, which limits the applicability of classical schemes in this type of channels. To resolve this issue, capacity lower bounds are developed by using precoding-free schemes. This is achieved by channel inversion or QR decomposition to convert the MIMO channel to a set of parallel channels. The achievable rate of a DC-offset SVD based scheme is also derived as a benchmark. Then, a capacity upper bound is derived and is shown to coincide with the achievable rate of the QR decomposition based scheme at high SNR, consequently characterizing the high-SNR capacity of the channel. The high-SNR gap between capacity and the achievable rates of the channel inversion and the DC-offset SVD based schemes is also characterized. Finally, the ergodic capacity of the channel is also briefly discussed.

We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the Karush-Kuhn-Tucker (KKT) condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in a multidimensional setting as Rnis not an open subset of Cn.

In this paper, an optical wireless multiple-input single-output communication system employing intensity-modulation direct-detection is considered. Subject to a per transmit-aperture power constraint, the performance of direct current (DC) offset space-time block codes (STBC) is studied in terms of pairwise error probability (PEP). It is shown that among the class of DC-STBCs, the worst case PEP, i.e., the one corresponding to the minimum distance between two codewords, is minimized by repetition coding (RC) for any channel state. Therefore, it follows that among all DC-STBCs, RC is optimal in terms of worst case PEP under any turbulence statistics. This result agrees with previously published numerical results showing the superiority of RC in such systems. It also agrees with previously published analytical results on this topic under lognormal turbulence and further extends it to arbitrary turbulence statistics. Numerical results provided to verify this indicate that RC is not only optimal in terms of worst case PEP, but also in terms of average error probability.

We analyze the achievable rates of a cognitive radio MIMO system assisted by an unmanned aerial vehicle (UAV) relay. The primary user (PU) and the secondary user (SU) aim to communicate to the closest primary base station (BS) via a multi-access channel through the same UAV relay. The SU message is then forwarded from the primary BS to the secondary network with a certain incentive reward as a part of the cooperation protocol between both networks. We propose a special linear precoding scheme to enable the SU to exploit the PU free eigenmodes. We, also, present the expression of the power maximizing both primary and secondary rates under power budget, relay power, and interference constraints. In the numerical results, we evaluate the PU and SU rates of proposed scheme with respect to various problem parameters. We also highlight the effect of the UAV altitude on the SU and PU rates. Finally, we show that the relay matrix variation affects both rates that reach their peaks at different values of the matrix.

In this paper, we propose a new cellular network operation scheme fulfilling the 5G requirements related to spectrum management and green communications. We focus on cognitive radio cellular networks in which both the primary network (PN) and the secondary network (SN) are maximizing their operational profits. The PN and the SN are required to respect a CO2emissions threshold by switching off one or more lightly loaded base stations (BSs). In addition, the PN accepts to cooperate with the SN by leasing its spectrum in the cells where the PN is turned off. In return, the corresponding SN BSs host the PN users and impose extra roaming fees to the PN. We propose a low-complexity algorithm that maximizes the profit per CO2emissions metric while switching on/off the BSs. In the simulations, we show that our proposed algorithm achieves performances close to the exhaustive search method. In addition, we find that the roaming price is a key parameter that affects both PN and SN profits1.

We study the deployment of unmanned aerial vehicles (UAV) based cognitive system in an area covered by the primary network (PN). An UAV shares the spectrum of the PN and aims to maximize its energy efficiency (EE) by optimizing the transmit power. We focus on the case where the UAV simultaneously communicates with the ground receiver (G), under interference limitation, and with another relaying UAV (A), with a minimal required rate. We analytically develop the power allocation framework that maximizes the EE subject to power budget, interference, and minimal rate constraints. In the numerical results, we show that the minimal rate may cause a transmission outage at low power budget values. We also highlighted the existence of optimal altitudes given the UAV location with respect to the different other terminals.

In this paper, we study the achievable secrecy rate of visible light communication (VLC) links for discrete input distributions. We consider single user single eavesdropper multiple-input single-output (MISO) links. In addition, both beamforming and robust beamforming are considered. In the former case, the location of the eavesdropper is assumed to be known, whereas in the latter case, the location of the eavesdropper is unknown. We compare the obtained results with those achieved by some continuous distributions including the truncated generalized normal (TGN) distribution and the uniform distribution. We numerically show that the secrecy rate achieved by the discrete input distribution with a finite support is significantly improved as compared to those achieved by the TGN and the uniform distributions.

Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user time-division multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multi-output OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/post-coding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, this paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the Karush-Kuhn-Tucker conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints.

In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper, and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. On the other hand, the transmitter is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically, as the capacity of the feedback link becomes large, i.e., B→∞, hence fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high signal-to-noise ratio, and evaluate the gap between the bounds.

Device-to-device (D2D) communications underlying the cellular infrastructure are a technology that have been proposed recently as a promising solution to enhance cellular network capabilities. It improves spectrum utilization, overall throughput, and energy efficiency while enabling new peer-to-peer and location-based applications and services. However, interference is the major challenge, since the same resources are shared by both systems. Therefore, interference management techniques are required to keep the interference under control. In this paper, in order to mitigate interference, we consider centralized and distributed power control algorithms in a one-cell random network model. Existing results on D2D underlay networks assume perfect channel state information (CSI). This assumption is usually unrealistic in practice due to the dynamic nature of wireless channels. Thus, it is of great interest to study and evaluate achievable performances under channel uncertainty. Differently from previous works, we are assuming that the CSI may be imperfect and include estimation errors. In the centralized approach, we derive the optimal powers that maximize the coverage probability and the rate of the cellular user while scheduling as many D2D links as possible. These powers are computed at the base station (BS) and then delivered to the users, and hence the name “centralized”. For the distributed method, the ON-OFF power control and the truncated channel inversion are proposed. Expressions of coverage probabilities are established in the function of D2D links intensity, pathloss exponent, and estimation error variance. Results show the important influence of CSI error on achievable performances and thus how crucial it is to consider it while designing networks and evaluating performances.

We study the secrecy capacity of the multiple- input single-output (MISO) Gaussian wiretap visible light communication (VLC) channel. We study a typical VLC scenario with one transmitter, one legitimate receiver, and one eavesdropper. Specifically, we compute the achievable secrecy rate for various input signaling distributions, including the truncated generalized normal (TGN) and uniform distributions. The transmitter is equipped with multiple light sources, while the legitimate and unauthorized receivers are each equipped with a single photodetector. We analyze the achievable secrecy rates via transmit beamforming and artificial noise. In addition, both zero-forcing beamforming and robust beamforming are considered. In the former case, the location of the eavesdropper is assumed to be known, whereas in the latter case, the location of the eavesdropper is unknown. Our numerical results show that the secrecy rate achieved by the TGN distribution is significantly improved as compared to those achieved by the truncated Gaussian and uniform distributions, for both zero-forcing beamforming and robust beamforming. We also derive an upper bound on the achievable secrecy capacity that we used to assess the closeness of the achievable secrecy rates to the derived bound.

In this work, we examine the secrecy capacity region of the block-fading broadcast channel with confidential messages (BCC) when the transmitter has limited knowledge of the channel. In particular, we consider a two-user communication system where the transmitter has one common message to be transmitted to both users and one confidential message intended to only one of them. The confidential message has to be kept secret from the other user to whom the information is not intended. The transmitter is not aware of the channel state information (CSI) of neither channel and is only provided by limited CSI feedback sent at the beginning of each fading block. Assuming an error-free feedback link, we characterize the secrecy capacity region of this channel and show that even with a 1-bit CSI feedback, a positive secrecy rate can still be achieved. Then, we look at the case where the feedback link is not error- free and is rather a binary erasure channel (BEC). In the latter case, we provide an achievable secrecy rate region and show that as long as the erasure event is not a probability 1 event, the transmitter can still transmit the confidential information with a positive secrecy rate.

We improve upon our previous upper bound on the secrecy capacity of the wiretap channel with multiple transmit antennas and single-antenna receivers, with noisy main channel state information (CSI) at the transmitter (CSI-T). Specifically, we show that if the main CSI error does not scale with the power budget at the transmitter P̅, then the secrecy capacity is )bounded above essentially by log log (P̅ yielding a secure degree of freedom (sdof) equal to zero. However, if the main CSI error scales as O(P̅-β), for β ∈ [0,1], then the sdof is equal to β.

In energy harvesting communications, the transmitters have to adapt transmission to the availability of energy harvested during communication. The performance of the transmission depends on the channel conditions which vary randomly due environmental changes. In this paper, we consider the problem of power allocation taking into account the energy arrivals over time and imperfect channel state information (CSI) available at the transmitter, in order to maximize the throughput. Differently from previous work, the CSI at the transmitter is not perfect and may include estimation errors. We solve this problem with respect to energy harvesting constraints. We determine the optimal power policy in the case where the channel is perfectly known at the receiver. Furthermore, a study of the asymptotic behavior of the communication system is proposed. Specifically, we analyze the average throughput (AT) in a system where the average recharge rate (ARR) is asymptotically small and when it is very high. Selected numerical results are provided to illustrate our analysis.

A system consisting of parallel intensity-modulation direct-detection optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. If channel-state information is available at the transmitter, the bounds have to be optimized with respect to intensity allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the Karush-Kuhn-Tucker conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose a low-complexity intensity allocation algorithm which is nearly optimal. The optimized capacity lower bound coincides with the capacity at high signal-to-noise ratio.

In energy harvesting communications, the transmitters have to adapt transmission to availability of energy harvested during the course of communication. The performance of the transmission depends on the channel conditions which vary randomly due to mobility and environmental changes. In this paper, we consider the problem of power allocation taking into account the energy arrivals over time and the degree of channel state information (CSI) available at the transmitter, in order to maximize the throughput. Differently from previous work, the CSI at the transmitter is not perfect and may include estimation errors. We solve this problem with respect to the causality and energy storage constraints. We determine the optimal offline policy in the case where the channel is assumed to be perfectly known at the receiver. Also, we obtain the power policy when the transmitter has no CSI. Furthermore, we analyze the asymptotic average throughput in a system where the average recharge rate goes asymptotically to zero.

In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we look at the independent messages case, where the transmitter broadcasts multiple independent messages to the legitimate receivers. For this case, we present lower and upper bounds on the ergodic secrecy sum-capacity. In both scenarios, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback links becomes large, hence, fully characterizing the secrecy capacity in this case.

In this paper, we study the energy efficiency (EE) of orthogonal frequency-division multiple access (OFDMA) cellular networks. Our objective is to present a power allocation scheme that maximizes the EE of downlink communications. We propose a novel explicit expression of the optimal power allocation to each subcarrier. We also present the power control when the transmit power is limited by power budget constraint or/and minimal rate constraint and we highlight the occurrence of some transmission outage events depending on the constraints' parameters. In the numerical results, we show that our proposed power control improves the EE especially at high power budget regime and low minimal rate regime. In addition, we show that having a higher number of subcarriers enhances the OFDMA EE.

Due to the massive data traffic in wireless networks, energy consumption has become a crucial concern, especially with the limited power supply of the mobile terminals and the increasing $CO_2$ emission of the cellular industry. In this context, we study the energy efficiency (EE) of MIMO spectrum sharing cognitive radio (CR) systems under power and interference constraints. We present an energy-efficient power allocation framework based on maximizing the average EE per parallel channel resulting from the singular value decomposition (SVD) eigenmode transmission. We also present a sub-optimal low-complexity power allocation scheme based on the water-filling power allocation. In the numerical results, we show that the sub-optimal power allocation achieves at least $95\%$ of the optimal performance. In addition, we show that adopting more antennas is more energy efficient for a given power budget. Finally, we show that the interference threshold has a significant effect on both the EE and the spectral efficiency at high-power regime.

Outage performance of the M-block fading with additive white Gaussian noise (BF-AWGN) is investigated in the low-power regime. We consider delay-constrained constant-rate communications with perfect channel state information (CSI) at both the transmitter and the receiver (CSI-TR), under a short-term power constraint (STPC) and a long-term power constraint (LTPC). Subject to STPC, we show that selection diversity that allocates all the power to the strongest block is asymptotically optimal. Then, we provide a simple characterization of the outage probability in the regime of interest. We quantify the reward due to CSI-TR over the constant-rate constant-power scheme and show that this reward increases with the delay constraint. For instance, for Rayleigh fading, we find that a power gain up to 4.3 dB is achievable. Subject to LTPC, we show that the above guidelines still holds and that the outage performance improves due to the flexibility of the LTPC over the STPC. More interestingly, we prove that LTPC allows zero-outage communication even at low SNR and characterize the delay-limited capacity at low SNR in a simple form. More precisely, we establish that the delay-limited capacity scales linearly with the power constraint, for a given M <; ∞. Our framework highlights the benefit of fading at low SNR as the delay-limited capacity may outperform the AWGN capacity. For instance, for Rayleigh fading and with M = 3, the delay-limited capacity is 16% higher than the capacity of an AWGN channel.

In this paper, we study a multiple-antenna two-way relaying (TWR) cognitive radio (CR) system. A space alignment (SA) technique is adopted by the secondary users (SUs) to avoid interference with the primary users (PUs). We derive the optimal power allocation that maximizes the TWR achievable SU sum-rate while respecting the total power budget and the relay power constraints. We also analyze the case in which the relay is able to optimize its gain matrix structure to enhance the SU sum-rate. In the numerical results, we quantify the sum-rate gain of using the SA in the TWR CR and we show that the SU sum-rate is very limited when the relay power is low or the PU power and its resulting interference are high. In addition, we optimize the relay gain using an iterative algorithm and compare between different relay matrix structures.

The capacity of the intensity-modulation direct-detection optical broadcast channel (OBC) is investigated, under both average and peak intensity constraints. An outer bound on the capacity region is derived by adapting Bergmans' approach to the OBC. Inner bounds are derived by using superposition coding with either truncated-Gaussian (TG) distributions or discrete distributions. While the discrete distribution achieves higher rates, the TG distribution leads to a simpler representation of the achievable rate region. At high signal-to-noise ratio (SNR), it is shown that the TG distribution is nearly optimal. It achieves the symmetric-capacity within a constant gap (independent of SNR), which approaches half a bit as the number of users grows. It also achieves the capacity region within a constant gap. At low SNR, it is shown that on-off keying (OOK) with time-division multiple-access (TDMA) is optimal. This is interesting in practice since both OOK and TDMA have low complexity. At moderate SNR (typically [0,8] dB), a discrete distribution with a small alphabet size achieves fairly good performance.

We investigate the problem of secure broadcasting over fast fading channels with imperfect main channel state information (CSI) at the transmitter. In particular, we analyze the effect of the noisy estimation of the main CSI on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. Besides, we consider the realistic case where the transmitter is only aware of the statistics of the eavesdropper's CSI and not of its channel's realizations. First, we discuss the common message transmission case where the source broadcasts the same information to all the receivers, and we provide an upper and a lower bound on the ergodic secrecy capacity. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link and we prove that a nonzero secrecy rate can still be achieved even when the CSI at the transmitter is noisy. Then, we look at the independent messages case where the transmitter broadcasts multiple messages to the receivers, and each intended user is interested in an independent message. For this case, we present an expression for the achievable secrecy sum-rate and an upper bound on the secrecy sum-capacity and we show that, in the limit of large number of legitimate receivers K, our achievable secrecy sum-rate follows the scaling law log ((1-α)log(K)), where α is the estimation error variance of the main CSI. The special cases of high SNR, perfect and no-main CSI are also analyzed. Analytical derivations and numerical results are presented to illustrate the obtained expressions for the case of independent and identically distributed Rayleigh fading channels.

A Gaussian multiple-input single-output (MISO) fading channel is considered. We assume that the transmitter, in addition to the statistics of all channel gains, is aware instantaneously of a noisy version of the channel to the legitimate receiver. On the other hand, the legitimate receiver is aware instantaneously of its channel to the transmitter, whereas the eavesdropper instantaneously knows all channel gains. We evaluate an achievable rate using a Gaussian input without indexing an auxiliary random variable. A sufficient condition for beamforming to be optimal is provided. When the number of transmit antennas is large, beamforming also turns out to be optimal. In this case, the maximum achievable rate can be expressed in a simple closed form and scales with the logarithm of the number of transmit antennas. Furthermore, in the case when a noisy estimate of the eavesdropper's channel is also available at the transmitter, we introduce the SNR difference and the SNR ratio criterions and derive the related optimal transmission strategies and the corresponding achievable rates.

We study the problem of secret-key agreement between two legitimate parties, Alice and Bob, in the presence of an eavesdropper Eve. There is a public channel with unlimited capacity that is available to the legitimate parties and is also observed by Eve. Our focus is on Rayleigh fading quasistatic channels. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge of their channels. We study the system in the high-power regime. First, we define the secret-key diversity gain and the secret-key multiplexing gain. Second, we establish the secret-key diversity multiplexing tradeoff (DMT) under no channel state information (CSI) at the transmitter (CSI-T). The eavesdropper is shown to “steal” only transmit antennas. We show that, like the DMT without secrecy constraint, the secret-key DMT is the same either with or without full channel state information at the transmitter. This insensitivity of secret-key DMT toward CSI-T features a fundamental difference between secret-key agreement and the wiretap channel, in which secret DMT depends heavily on CSI-T. Finally, we present several secret-key DMT-achieving schemes in case of full CSI-T. We argue that secret DMT-achieving schemes are also key DMT-achieving. Moreover, we show formally that artificial noise (AN), likewise zero-forcing (ZF), is DMT-achieving. We also show that the public feedback channel improves the outage performance without having any effect on the DMT.

In this paper, we consider a cognitive radio system in which a block-fading channel is assumed. Each transmission frame consists of M blocks and each block undergoes a different channel gain. Instantaneous channel state information about the interference links remains unknown to the primary and secondary users. We minimize the secondary user's targeted outage probability over the block-fading channels. To protect the primary user, a statistical constraint on its targeted outage probability is enforced. The secondary user's targeted outage region and the corresponding optimal power are derived. We also propose two sub-optimal power strategies and derive compact expressions for the corresponding outage probabilities. These probabilities are shown to be asymptotic lower and upper bounds on the outage probability. Utilizing these bounds, we derive the exact diversity order of the secondary user outage probability. Selected numerical results are presented to characterize the system's behavior.

We study the ergodic secrecy capacity of a block- fading wiretap channel when there are multiple antennas at the transmitter, the legitimate receiver and the eavesdropper. We consider that the receivers are aware of their respective channel matrices while the transmitter is only provided by a B-bits feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error free public link with limited capacity. Assuming an average transmit power constraint, we provide an upper and a lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback link becomes large; hence, fully characterizing the secrecy capacity in this case.

We study delay-limited (also called zero-outage) capacity region of the fading multi-access channel (MAC) with Gaussian noise and perfect channel state information (CSI) at the receiver and at the transmitters (CSI-TR), in the low-power regime. We show that for fading channels where the MAC capacity region is strictly positive, it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power, the boundary surface of the capacity region shrinks to a single point corresponding to the sum-rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Using the duality of the Gaussian MAC and broadcast channels (BC), we show that time-sharing (or time division multiple access (TDMA)) is asymptotically optimal.

We study a multiple-antenna two-way relaying (TWR) spectrum sharing system. A space alignment (SA) technique is adopted by the secondary users (SU's) to avoid interference with the primary users (PU's). We derive the optimal power allocation that maximizes the TWR achievable sum-rate of the SU while respecting the total power budget and the relay power constraints. In the numerical results, we quantify the sum-rate gain of using the SA in the TWR CR and we show that the SU sum-rate is very limited when the relay power is low or the PU's power and its resulting interference is high.

We consider secret-key agreement with public discussion over multiple-input multiple-output (MIMO) Rayleigh fast-fading channels under correlated environment. We assume that transmit, legitimate receiver and eavesdropper antennas are correlated. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the correlation matrices. First, we derive the expression of the secret-key capacity under the considered setup. Then, we prove that the optimal transmit strategy achieving the secret-key capacity consists in transmitting independent Gaussian signals along the eingenvectors of the transmit correlation matrix. The powers allocated to each channel mode are determined as the solution to a numerical optimization problem that we derive. A necessary and sufficient condition for beamforming (i.e., transmitting along the strongest channel mode) to be capacity-achieving is derived. Finally, we analyze the impact of correlation matrices on the system performance and provide closed-form expressions of the gain/loss due to correlation in the high power regime.

In this paper, we propose a new cognitive cellular network architecture based on the coexistence of primary and secondary networks, (PN) and (SN), respectively. The PN aims to minimize its energy consumption by switching off the maximum number of its BSs and offloading its users to the SN's infrastructure to maintain its QoS. In return, the PN pays a roaming price and permits the SN to share or lease the spectrum at a certain price. We propose a low-complexity algorithm allowing the PN to minimize its energy consumption by selecting a suboptimal combination of active base stations. Our algorithm also optimizes the resource allocation of the SN to maximize its total sum-rate while respecting the minimal profit constraints for both networks. In the numerical results, we show that our proposed algorithm achieves close performances to the optimal exhaustive search algorithm. In addition, we investigate the impact of various system parameters in the collaboration decision.

We consider a two-user interference channel assisted by a relay. Treating interference as noise at the receivers, and adopting an amplify and forward (AF) strategy at the relay, we derive achievable rates of both users, for given powers. Next, we solve the optimal power allocation problem maximizing the weighted sum rate of both users with and without relay power optimization. In particular, we propose a simple iterative line search algorithm solving the joint optimization problem over the three transmit powers and show that optimizing the relay power enhances the performance of the system. Then, considering the first user as a primary user, we determine the maximum instantaneous rate that the secondary user can achieve subject to an outage constraint with respect to the primary user and a peak power constraint. We show that, likewise the first part, jointly optimizing the secondary user and the relay transmit powers enhances the secondary user performance.

In this paper, two resource allocation schemes for energy efficient cognitive radio systems are proposed. Our design considers resource allocation approaches that adopt spectrum sharing combined with soft-sensing information, adaptive sensing thresholds, and adaptive power to achieve an energy efficient system. An energy per good-bit metric is considered as an energy efficient objective function. A multi-carrier system, such as, orthogonal frequency division multiplexing, is considered in the framework. The proposed resource allocation schemes, using different approaches, are designated as sub-optimal and optimal. The sub-optimal approach is attained by optimizing over a channel inversion power policy. The optimal approach utilizes the calculus of variation theory to optimize a problem of instantaneous objective function subject to average and instantaneous constraints with respect to functional optimization variables. In addition to the analytical results, selected numerical results are provided to quantify the impact of soft-sensing information and the optimal adaptive sensing threshold on the system performance.

We investigate the spectral efficiency gain of an uplink cognitive radio (CR) multi-input-multi-output system in which the secondary user (SU) is allowed to share the spectrum with the primary user (PU) using a specific precoding scheme to communicate with a common receiver. The proposed scheme exploits, at the same time, the free eigenmodes of the primary channel after a space alignment procedure and the interference threshold tolerated by the PU. At the common receiver, we adopt a successive interference cancellation (SIC) technique to eliminate the effect of the detected primary signal transmitted through the exploited eigenmodes. Furthermore, we analyze the SIC operation inaccuracy as well as the CSI estimation imperfection on the PU and SU throughputs. Numerical results show that our proposed scheme enhances considerably the cognitive achievable rate. For instance, in case of a perfect detection of the PU signal, the CR rate remains non-zero for high signal to noise ratio, which is usually impossible when we only employ a space alignment technique. We show that a modified water-filling power allocation policy at the PU can increase the secondary rate with a marginal degradation of the primary rate. Finally, we investigate the behavior of the PU and SU rates through the study of the rate achievable region.

In this paper, we consider secure broadcasting over fast fading channels. Assuming imperfect main channel state information (CSI) at the transmitter, we first provide an upper and a lower bounds on the ergodic secrecy capacity when a common message is broadcasted to multiple legitimate receivers in the presence of one eavesdropper. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link. Then, we present an expression for the achievable secrecy sum-rate when each legitimate receiver is interested in an independent message. The special cases of high SNR, perfect and no-main CSI are also analyzed. Numerical results are presented to illustrate the obtained results for the case of independent but not necessarily identically distributed Rayleigh fading channels.

We consider a wiretap channel consisting of a source with multiple antennas, a legitimate receiver and an eavesdropper with a single antenna each. The channels between the source and the receivers undergo fast fading. We assume that the transmitter, in addition to the statistics of both channels, is only aware of a noisy version of the CSI to the legitimate receiver referred to as main channel. The legitimate receiver is aware of both its instantaneous channel gain and the transmitter's estimate of the main channel. On the other hand, the eavesdropper's receiver, in addition to its instantaneous channel realization, is aware of the actual main CSI and the transmitter's estimate as well. While the capacity of this channel is still open even with perfect CSI at the transmitter, we provide in this paper upper and lower bounds on the secrecy capacity. The upper bound is tighter than the one corresponding to perfect main CSI and the gap between the two upper bounds is characterized in function of the channel estimation error variance, at high-SNR. Furthermore, we show that our upper and lower bounds coincide in the case of no main CSI providing a trivial secrecy capacity.

In this paper we consider a cognitive radio multi-input multi-output environment in which we adapt our beamformer to maximize both energy efficiency and signal to interference plus noise ratio (SINR) metrics. Our design considers an underlaying communication using adaptive beamforming schemes combined with the sensing information to achieve an optimal energy efficient system. The proposed schemes maximize the energy efficiency and SINR metrics subject to cognitive radio and quality of service constraints. Since the optimization of energy efficiency problem is not a convex problem, we transform it into a standard semi-definite programming (SDP) form to guarantee a global optimal solution. Analytical solution is provided for one scheme, while the other scheme is left in a standard SDP form. Selected numerical results are used to quantify the impact of the sensing information on the proposed schemes compared to the benchmark ones.

Outage performance of the M-block fading with additive white Gaussian noise (BF-AWGN) is investigated at low-power regime. We consider delay-constrained constant-rate communications with perfect channel state information (CSI) at both the transmitter and the receiver (CSI-TR), under a short-term power constraint. We show that selection diversity that allocates all the power to the strongest block is asymptotically optimal. Then, we provide a simple characterization of the outage probability in the regime of interest. We quantify the reward due to CSI-TR over the constant-rate constant-power scheme and show that this reward increases with the delay constraint. For instance, for Rayleigh fading, we find that a power gain up to 4.3 dB is achievable.

Recently, the energy efficiency (EE) has become an important factor when designing new wireless communication systems. Due to economic and environmental challenges, new trends and efforts are oriented toward “green” communication especially for energy-constrained applications such as wireless sensors network and cognitive radio. To this end, we analyze the power allocation scheme that maximizes the EE defined as rate over the total power including circuit power. We derive an explicit expression of the optimal power with instantaneous channel gain based on EE criterion. We show that the relation between the EE and the spectral efficiency (SE) when the optimal power is adopted is strictly increasing in contrast with the SE-EE trade-off discussed in the literature. We also solve a non-convex problem and compute explicitly the optimal power for ergodic EE under either a peak or an average power constraint. When the instantaneous channel is not available, we provide the optimal power equation and compute simple sub-optimal power. In the numerical results, we show that the sup-optimal solution is very close to the optimal solution. In addition, we show that the absence of the channel state information (CSI) only affects the EE and the SE performances at high power regime compared to the full CSI case.

In this paper we propose an energy efficient cognitive radio system. Our design considers an underlaying resource allocation combined with soft sensing information to achieve a sub-optimum energy efficient system. The sub-optimality is achieved by optimizing over a channel inversion power policy instead of considering a water-filling power policy. We consider an Energy per Goodbit (EPG) metric to express the energy efficient objective function of the system and as an evaluation metric to our system performance. Since our optimization problem is not a known convex problem, we prove its convexity to guarantee its feasibility. We evaluate the proposed scheme comparing to a benchmark system through both analytical and numerical results.

In this paper, we present a simple way to compute the ergodic capacity of cascaded channels with perfect channel state information at both the transmitter and the receiver. We apply our generic results to the Rayleigh-double fading channel, and to the free-space optical channel in the presence of pointing errors and we express their low signal-to-noise ratio capacities. We mainly focus on the low signal-to-noise ratio range.

The capacity of Multiple Input Multiple Output (MIMO) Rayleigh fading channels with full knowledge of channel state information (CSI) at both the transmitter and the receiver (CSI-TR) has been shown recently to scale at low Signal-to-Noise Ratio (SNR) essentially as SNR log(1=SNR), independently of the number of transmit and receive antennas. In this paper, we investigate the ergodic capacity of MIMO Rayleigh fading channel with estimated channel state information at the transmitter (CSI-T) and possibly imperfect channel state information at the receiver (CSI-R). Our framework can be seen as a generalization of previous works as it can capture the perfect CSI-TR as a special case when the estimation error variance goes to zero. In our work, we mainly focus on the low SNR regime and we show that the capacity scales as (1-α) SNR log(1=SNR), where α is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel state information at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can also be extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.

We study the achievable rate of a multiple antenna relay-assisted cognitive radio system where a secondary user (SU) aims to communicate instantaneously with the primary user (PU). A special linear precoding scheme is proposed to enable the SU to take advantage of the primary eigenmodes. The used eigenmodes are subject to an interference constraint fixed beforehand by the primary transmitter. Due to the absence of a direct link, both users exploit an amplify-and-forward relay to accomplish their transmissions to a common receiver. After decoding the PU signal, the receiver employs a successive interference cancellation (SIC) to estimate the secondary message. We derive the optimal power allocation that maximizes the achievable rate of the SU respecting interference, peak and relay power constraints. Furthermore, we analyze the SIC detection accuracy on the PU throughput. Numerical results highlight the cognitive rate gain achieved by our proposed scheme without harming the primary rate. In addition, we show that the relay has an important role in increasing or decreasing PU and SU rates especially when varying its power and/or its amplifying gain.

The capacity of multiple-input multiple-output (MIMO) Rayleigh fading channels with full knowledge of channel state information (CSI) at both the transmitter and the receiver (CSI-TR) has been shown recently to scale at low signal-to-noise ratio (SNR) essentially as SNR log(1/SNR), independently of the number of transmit and receive antennas. In this paper, we investigate the ergodic capacity of MIMO Rayleigh fading channel with estimated channel state information at the transmitter (CSI-T) and possibly imperfect channel state information at the receiver (CSI-R). Our framework can be seen as a generalization of previous works as it can capture the perfect CSI-TR as a special case when the estimation error variance goes to zero. In this paper, we mainly focus on the low SNR regime, and we show that the capacity scales as (1 - α) SNR log(1/SNR), where α is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel state information at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can be also extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.

We study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and eavesdropper channels and is the best known upper bound so far. The upper and lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) is also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for i.i.d. Rayleigh fading channels.

In this paper, we consider a cognitive radio multi-input-multi-output environment, in which we adapt our beamformer to maximize both energy efficiency (EE) and signal-to-interference-plus-noise ratio (SINR) metrics. Our design considers an underlaying communication using adaptive beamforming schemes combined with sensing information to achieve optimal energy-efficient systems. The proposed schemes maximize EE and SINR metrics subject to cognitive radio and quality-of-service constraints. The analysis of the proposed schemes is classified into two categories based on knowledge of the secondary-transmitter-to-primary-receiver channel. Since the optimizations of EE and SINR problems are not convex problems, we transform them into a standard semidefinite programming (SDP) form to guarantee that the optimal solutions are global. An analytical solution is provided for one scheme, while the second scheme is left in a standard SDP form. Selected numerical results are used to quantify the impact of the sensing information on the proposed schemes compared to the benchmark ones.

We study the throughput capacity region of the Gaussian multi-access (MAC) fading channel with perfect channel state information (CSI) at the receiver and at the transmitters, at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Inspired from this result, we propose an on-off scheme, compute its achievable rate, and show that this scheme achieves single user capacity bounds of the MAC channel for a wide class of fading channels at asymptotically low power regime. We argue that this class of fading encompasses all known wireless channels for which the capacity region of the MAC channel has even a simpler expression in terms of users' average power constraints only. Using the duality of Gaussian MAC and broadcast channels (BC), we deduce a simple characterization of the BC capacity region at low power regime and show that for a class of fading channels (including Rayleigh fading), time-sharing is asymptotically optimal.

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.

We study the achievable rate of cognitive radio (CR) spectrum sharing systems at the low-power regime for general fading channels and then for Nakagami fading. We formally define the low-power regime and present the corresponding closed-form expressions of the achievable rate lower bound under various types of interference and/or power constraints, depending on the available channel state information of the cross link (CL) between the secondary-user transmitter and the primary-user receiver. We explicitly characterize two regimes where either the interference constraint or the power constraint dictates the optimal power profile. Our framework also highlights the effects of different fading parameters on the secondary link (SL) ergodic achievable rate. We also study more realistic scenarios when there is either 1-bit quantized channel feedback from the CL alone or 2-bit feedback from both the CL and the SL and propose simple power control schemes and show that these schemes achieve the previously achieved rate at the low-power regime. Interestingly, we show that the low-power regime analysis provides a specific insight into the maximum achievable rate behavior of CR that has not been reported by previous studies.

We study the impact of adopting a multi layer coding (MLC) strategy, i.e., the so-called broadcast approach (BA) on the throughput of Cognitive Radio (CR) spectrum sharing systems for general fading channels. First, we consider a scenario where the secondary transmitter, a part from the statistics, has no channel state information (CSI) of the cross link and its own link. We show that using BA improves the cognitive achievable rate compared to the outage rate provided by a single layer coding (SLC). In addition, we, also, observe numerically that 2-Layer coding achieves most of the gain. Then, we consider a situation where the secondary transmitter has a partial CSI about its own link through quantized CSI. Again, we compute the secondary achievable rate adopting the BA and highlight the improvement over SLC. Numerical results show that the advantage of MLC decreases as the rate of the feedback link increases.

We study the throughput capacity region of the Gaussian multiaccess (MAC) fading channel with perfect channel state information (CSI) at the receiver (CSI-R) and at the transmitters (CSI-T), at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Inspired from this result, we propose an on-off scheme, compute its achievable rate, and provide a necessary condition on the fading channels under which this scheme achieves single user capacity bounds of the MAC channel at asymptotically low power regime. We argue that this necessary condition characterizes a class of fading that encompasses all known wireless channels, where the capacity region of the MAC channel has a simple expression in terms of users' average power constraints only.

In this paper, we investigate the spectral efficiency gain of an uplink Cognitive Radio (CR) Multi-Input Multi-Output (MIMO) system in which the Secondary/unlicensed User (SU) is allowed to share the spectrum with the Primary/licensed User (PU) using a specific precoding scheme to communicate with a common receiver. The proposed scheme exploits at the same time the free eigenmodes of the primary channel after a space alignment procedure and the interference threshold tolerated by the PU. In our work, we study the maximum achievable rate of the CR node after deriving an optimal power allocation with respect to an outage interference and an average power constraints. We, then, study a protection protocol that considers a fixed interference threshold. Applied to Rayleigh fading channels, we show, through numerical results, that our proposed scheme enhances considerably the cognitive achievable rate. For instance, in case of a perfect detection of the PU signal, after applying Successive Interference Cancellation (SIC), the CR rate remains non-zero for high Signal to Noise Ratio (SNR) which is usually impossible when we only use space alignment technique. In addition, we show that the rate gain is proportional to the allowed interference threshold by providing a fixed rate even in the high SNR range.

In this paper, we study the ergodic capacity of Cognitive Radio (CR) spectrum sharing systems at low power regime. We focus on Nakagami fading channels. We formally define the low power regime and present closed form expressions of the capacity in the low power regime under various types of interference and/or power constraints, depending on the available channel state information (CSI) of the cross link (CL) between the secondary user transmitter and the primary user receiver. We explicitly characterize two regimes where either the interference constraint or the power constraint dictates the optimal power profile. Our framework also highlights the effects of different fading parameters on the secondary link ergodic capacity. Interestingly, we show that the low power regime analysis provides a specific insight on the capacity behavior of CR that has not been reported by previous studies.

We study the throughput capacity region of the Gaussian multi-access (MAC) fading channel with perfect channel state information (CSI) at the receiver and at the transmitters (CSI-TR), at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum-rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Using the duality of Gaussian MAC and broadcast channels (BC), we provide a simple characterization of the BC capacity region at low power regime.

The effective capacity have been introduced by Wu and Neji as a link-layer model supporting statistical delay QoS requirements. In this paper, we propose to study the effective capacity of a Nakagami-m fading channel with full channel state information (CSI) at both the transmitter and at the receiver. We focus on the low Signal-to-Noise Ratio (SNR) regime. We show that the effective capacity for any arbitrary but finite statistically delay Quality of Service (QoS) exponent θ, scales essentially as S NRlog(1/SNR) exactly as the ergodic capacity, independently of any QoS constraint. We also characterize the minimum energy required for reliable communication, and the wideband slope to show that our results are in agreement with results established recently by Gursoy et al. We also propose an on-off power control scheme that achieves the capacity asymptotically using only one bit CSI feedback at the transmitter. Finally, some numerical results are presented to show the accuracy of our asymptotic results.

We consider a spectrum sharing communication scenario in which a primary and a secondary users are communicating, simultaneously, with their respective destinations using the same frequency carrier. Both optimal power profile and ergodic capacity are derived for fading channels, under an average transmit power and an instantaneous interference outage constraints. Unlike previous studies, we assume that the secondary user has a noisy version of the cross link and the secondary link Channel State Information (CSI). After deriving the capacity in this case, we provide an ergodic capacity generalization, through a unified expression, that encompasses several previously studied spectrum sharing settings. In addition, we provide an asymptotic capacity analysis at high and low signal-to-noise ratio (SNR). Numerical results, applied for independent Rayleigh fading channels, show that at low SNR regime, only the secondary channel estimation matters with no effect of the cross link on the capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI. Furthermore, a practical on-off power allocation scheme is proposed and is shown, through numerical results, to achieve the full capacity at high and low SNR regimes and suboptimal rates in the medium SNR regime.

The capacity of flat Rayleigh fading channels with full channel state information (CSI) at the transmitter and at the receiver at asymptotically low SNR has been recently shown to scale essentially as SNR log (1/SNR). In this paper, we investigate the Rician fading channel capacity with full CSI, and show that the capacity of this channel scales essentially as 1/1+K SNR log (1 /SNR), where K is the Rician factor. This characterization includes perfect CSI at both the transmitter and the receiver or noisy CSI at the transmitter and perfect CSI at the receiver. We also show that one-bit CSI at the transmitter is enough to achieve this asymptotic capacity using an On-Off power control scheme. Our framework may be seen as a generalization of previous works as it captures the Rayleigh fading channel as a special case by letting K goes to zero.

The optimal transmit power of a sensor node while satisfying different rate constraints is derived. First, an optimization problem with an instantaneous transmission rate constraint is addressed. Next, the optimal power is analyzed, but now with an average transmission rate constraint. The optimal solution for a class of fading channels, in terms of system parameters, is presented and a suboptimal solution is also proposed for an easier, yet efficient, implementation. Insightful asymptotical analysis for both schemes, considering a Rayleigh fading channel, are shown. Finally, the optimal power allocation for a sensor node in a cognitive radio environment is analyzed where an optimum solution for a class of fading channels is again derived. In all cases, numerical results are provided for either Rayleigh or Nakagami-m fading channels.

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers. We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free feedback channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q = 1. We also show that the lower and the upper bounds coincide asymptotically as q → ∞. Finally, asymptotic analysis at high Signal-to-Noise Ratio (SNR) are presented where it is found that the capacity is bounded at high-SNR and present a simple suboptimal scalar quantizer that is capacity achieving, without the need of any numerical optimization, as q → ∞. When applied to Rayleigh fading channels, we show that, at high-SNR, a 4-bit feedback achieves 90% of the secrecy capacity when perfect main CSI is available at the transmitter.

In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel.

A spectrum-sharing communication system where the secondary user is aware of the instantaneous channel state information (CSI) of the secondary link, but knows only the statistics and an estimated version of the secondary transmitter-primary receiver (ST-PR) link, is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels (with continuous probability density function) under average and peak transmit-power constraints and with respect to two different interference constraints: an interference outage constraint and a signal-to-interference (SI) outage constraint. When applied to Rayleigh fading channels, our results show, for instance, that the interference constraint is harmful at high-power regime, whereas at low-power regime, it has a marginal impact and no-interference performance may be achieved.

In this paper, we study the ergodic capacity of secondary user channel in a spectrum sharing scenario in which the secondary transmitter is instantaneously aware of estimated versions of the cross link (between the secondary transmitter and the primary receiver) and the secondary link Channel State Information (CSI). The secondary link optimal power profile along with the ergodic capacity are derived for a class of fading channels, under an average power constraint and an instantaneous interference outage constraint. We also show that our framework is rather general as it encompasses several previously studied spectrum sharing settings as special cases. In order to gain some insights on the capacity behavior, numerical results are shown for independent Rayleigh fading channels where it is found for instance, that at low SNR regime, only the secondary channel estimation matters and that the cross link CSI has no effect on the ergodic capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI.

We study the noncoherent capacity of secret-key agreement with public discussion over independent identically distributed (i.i.d.) Rayleigh fading wireless channels, where neither the sender nor the receivers have access to instantaneous channel state information (CSI). We present two results. At high signal-to-noise ratio (SNR), the secret-key capacity is bounded in SNR, regardless of the number of antennas at each terminal. Second, for a system with a single antenna at both the legitimate and the eavesdropper terminals and an arbitrary number of transmit antennas, the secret-key capacity-achieving input distribution is discrete, with a finite number of mass points. Numerically we observe that at low SNR, the capacity achieving distribution has two mass points with one of them at the origin.

Abstract In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency ofRbps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gainris greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.

We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity- achieving input distribution at low signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity of a non-coherent channel is derived. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non- coherence penalty and give a more precise characterization of the sub- linear term in SNR. Finally, in order to get more insight on how the optimal input varies with SNR, upper and lower bounds on the non-zero mass point location of the capacity-achieving input are given.

The capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver, is addressed. A closed form expression of the optimal capacity-achieving input distribution at low signal-to-noise ratio (SNR) is derived, and the exact capacity of a non-coherent Single Input Single Output (SISO) channel is given. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non-coherence penalty and give a more precise characterization of the sub-linear term in SNR. Finally, upper and lower bounds on the capacity of a multiple input multiple output (MIMO) channel are derived in terms of its counterpart SISO channel capacity. We show that these bounds are sufficient to characterize the MIMO channel capacity at low SNR.

The impact of spatial correlation on the performance limits of multielement antenna (MEA) channels is analyzed in terms of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) values. A lower bound on the outage probability is first derived. Using this bound accurate finite-SNR estimate of the DMT is then derived. This estimate allows to gain insight on the impact of spatial correlation on the DMT at finite SNR. As expected, the DMT is severely degraded as the spatial correlation increases. Moreover, using asymptotic analysis, we show that our framework encompasses well-known results concerning the asymptotic behavior of the DMT.

We present tight upper bounds on the channel mutual information of spatially correlated and uncorrelated multielement antenna (MEA) channels. Using these upper bounds, accurate lower bounds on the outage probability are derived. Similarly, tight upper bounds on the outage rate are obtained. Interestingly, these bounds are even tighter as the spatial correlation increases. Simulation results show that, in a highly correlated channel, the worst gap between our outage probability lower bounds and the exact values (given by simulation) is about 0.2 and 0.3 dBs, respectively for 2 times 2 and 3 times 3 MEA systems. This tightness suggests using the derived lower bounds on the outage probability in order to characterize the performance limits of MEA in terms of the finite-SNR diversity-multiplexing tradeoff in correlated and uncorrelated spatial fading channels.

We present a tight lower bound on the outage probability of a spatially correlated multielement antenna (MEA) channel. Using this lower bound, an accurate flnite-SNR estimate of the diversity-multiplexing tradeoff over a spatially correlated Rayleigh fading channel is derived. This estimate allows gaining insight on the impact of spatial correlation on the diversity-multiplexing tradeoff at finite SNR. As expected, the diversity multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a transmission rate of R = rlog2(1+ g ldr eta) bps/Hz, where r is the multiplexing gain, g is the array gain and eta is the SNR at each receive antenna, and an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at an SNR of 10 dB in a highly correlated channel, when r ges 0.8. Another interesting point is that the maximum diversity gain is unaffected by the correlation, provided that the spatial channel correlation matrix is of full rank.