Convex Optimisation for Communication Systems

Multiple Input Multiple Output(MIMO) has been in much importance in recent past because of high capacity gain over a single antenna system. In this article, analysis over the capacity of the MIMO channel systems with spatial channel with modified precoder and decoder has been considered when the channel state information (CSI) is considered partial. Due to delay in acquiring transmitted information at the receiver end, the time selective fading wireless channel often induces incomplete or partial CSI. The dynamic CSI model has also been implemented consisting channel mean and covariance which leads to extracting of channel estimates and error covariance which then further applied with the modified precoder and decoder utilizing both the parameters indicating the CSI quality since these are the functions of temporal correlation factor, and based on this, the model covers data from perfect to statistical CSI, either partially or fully blind. It is found that in case of partial and imperfect CSI, the capacity depends on the statistical properties of the error in the CSI which has been manipulated according to the precoder and decoder conditions. Based on the knowledge of statistical distribution of the deviations in CSI knowledge, a new approach which maximizes the capacity of spatial channel model with modified precoder and decoder has been tried. The interference then interactively reduced by employing the iterative channel estimation and data detection approach, where by utilizing the detected symbols from the previous iteration, multiuser/MIMO channel estimation and symbol detection is improved.

Traditional beamforming and power control algo-rithms in cognitive radio (CR) are based on the assumption of perfect channel state information (CSI) however; this may lead to performance degradation in realistic systems.In this paper, the problem of joint beamforming and power control is investigated in underlay CR networks with imperfect CSI.Our objective is to maximize the sum utility of secondary users (SUs) under the primary users (PUs) interference power constraints and the transmission power constraint of SUs.First, the joint beamforming and power control problem is formulated under game theory framework, where the SUs compete with each other over the beamforming vectors and transmission power level made available by the PUs.Moreover, the channel uncertainty is described using ellipsoid sets and the interference power constraints can be converted into robust interference power constraints.Besides, Nash equilibrium (NE) is considered as the solution of this game.Finally, simulation results show that the proposed scheme can converge to a locally optimal pair of beamforming vector and transmission power level in the presence of channel uncertainty.

Joint Beamforming and power allocation schemes are considered for cognitive radio (CR) multiple input single output (MISO) system in this paper. We considered the robust downlink beamforming and power allocation problem with per-antenna power constraints which is more realistic in practice, instead of sum-power constraint, under the imperfect channel state information (CSI). Since the given optimization problem is a non-convex problem which is difficult to handle, we transformed it into second order cone program (SOCP) problem, which can be solved efficiently. Simulation shows that the proposed scheme indeed has a better performance in CR system.

In this paper, we investigate robust beamforming to improve the energy efficiency (EE) of wireless networks when only imperfect or partial channel state information (CSI) is available at the transmitter. Due to CSI quantization errors and/or limited feedback information, CSI imperfections can be well modeled by a bounded uncertainty region. We focus on the worst case robust beamforming strategy to optimize the EE of downlink transmission under the deterministic bounded channel model, which merely assumes a maximal channel error magnitude. We start with a single-user single-cell MIMO system and obtain a closed-form design for robust beamforming. For a multicell network, robust beamforming is in a nonconvex fractional form, and the solution cannot be directly extended from the single-cell scenario. To solve this problem efficiently, we resort to a lower bound, instead of the primal problem, and cast it as a semidefinite program (SDP). The robustness and efficiency of the proposed beamforming design are confirmed by computer simulation results.

In wireless communications, the assumption that the transmitter has perfect channel state information (CSI) is often unreasonable, due to feedback delays, estimation errors, and quantization errors. In order to accurately assess system performance, a more careful analysis with imperfect CSI is needed. In this paper, the impact of partial CSI due to feedback delays in a multiuser Orthogonal Frequency Division Multiplexing (MU-OFDM) cognitive radio (CR) system is investigated. The effect of partial CSI on the bit error rate (BER) is analyzed. A relationship between the transmit power and the number of bits loaded on a subcarrier is derived which takes into account the target BER requirement. With this relationship, existing resource allocation schemes which are based on perfect CSI being available can be applied when only partial CSI is available. Simulation results are provided to illustrate how the system performance degrades with increasingly poor CSI.

The knowledge of the impact of imperfect channel state information (CSI) on data transmission techniques is helpful to improve the performance of wireless communication systems. In this paper, based on the proposed cooperative downlink (DL) transmission scheme applying adaptive scheduling of mobile stations (MSs), significant channel selection, and joint transmission (JT) with partial CSI, i.e., JT considering only part of the useful channels and the interference channels, a novel performance assessment is performed taking imperfectness of the CSI into consideration. The performance degradation caused by the imperfectness of the CSI which is used in the adaptive scheduling, the significant channel selection and the JT with partial CSI is investigated. The question about how much CSI should be taken into consideration as a function of the extent of imperfectness of the CSI in order to achieve optimum system performance is answered based on numerical results.

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

In this paper, a single input multiple output system is considered with L receive antennas and the underlying channels are assumed to be time varying with temporal correlation coefficient a and spatially correlated with correlation coefficient $$\rho $$ . Further, the channel is assumed to be identically distributed using Rayleigh fading channels and characterized by first order autoregressive model. For the detection, we assume partial channel state information (CSI) available at the receiver. The partial CSI is in the form of a known preamble (one symbol) only before beginning of a frame of size N symbols. Further, the preamble is imperfectly known with a variance of error $$\sigma _e^2$$ . For the assumed system, closed form expressions of symbol error rate (SER) are derived for M-PSK and M-QAM constellations under the compound effect of spatially correlated channels, temporally correlated channels and partial CSI at the Receiver. The derived expressions are functions of average SNR per symbol, $$\rho $$ , a, $$\sigma _e^2$$ , N, L and modulation order M. Further, these expressions are reduced for some special cases and compared with prevailing results in literature. The analytical expressions are also validated by comparing them with the corresponding simulation results. The derived expressions are very useful to select N, L and M to overcome the deterioration in SER due to adverse effects of $$\rho $$ , a and $$\sigma _e^2$$ .

In this paper, a comprehensive comparison analysis in terms of outage probability and average symbol error ratio (SER) is presented for cooperative cognitive multiple-input and multiple-output (CC-MIMO) multiuser systems with amplify-and-forward (AF) protocol. Specially, we consider two scenarios where the CC-MIMO multiuser systems have the perfect and imperfect channel state information (CSI). The CC-MIMO multiuser systems consist of one multi-antenna source, one single-antenna relay, and multiple multi-antenna destinations. At the secondary source and destinations, the maximal ratio transmission (MRT) and maximal ratio combining (MRC) are employed, respectively. For such CC-MIMO multiuser systems, we first obtain the exact closed-form expressions of outage probability under the two cases where the CC-MIMO multiuser systems have the perfect and imperfect CSI. Then, to reduce the implementation complexity, the tight lower bounds of outage probability and average SER are derived. Finally, to obtain insight, by using the high signal-to-noise ratio (SNR) approximation, the asymptotic estimations of outage probability are achieved. The numerical results show that the derivations are agreed with the simulations, which validate our derivations. At the same time, the results show that, for the systems without perfect CSI, the achievable diversity order reduces to one, regardless of the number of antennas at the cognitive source and destinations as well as the number of the cognitive destinations. Nevertheless, these key parameters affect the coding gain of the CC-MIMO multiuser systems. When the systems have the perfect CSI (or without feedback delay), the achievable diversity gain is determined by the minimum between the number of source’s antennas and the product of the number of destinations and the number of destination’s antennas. For the effect of PU’s parameters, our results indicate that primary systems only affect the coding gain but not the diversity gain.

Efficient design of cognitive radios (CRs) calls for secondary users implementing adaptive resource allocation schemes that exploit knowledge of the channel state information (CSI), while at the same time limiting interference to the primary system. This paper introduces stochastic resource allocation algorithms for both interweave (also known as overlay) and underlay cognitive radio paradigms. The algorithms are designed to maximize the weighted sum-rate of orthogonally transmitting secondary users under average-power and probabilistic interference constraints. The latter are formulated either as short- or as long-term constraints, and guarantee that the probability of secondary transmissions interfering with primary receivers stays below a certain pre-specified level. When the resultant optimization problem is non-convex, it exhibits zero-duality gap and thus, due to a favorable structure in the dual domain, it can be solved efficiently. The optimal schemes leverage CSI of the primary and secondary networks, as well as the Lagrange multipliers associated with the constraints. Analysis and simulated tests confirm the merits of the novel algorithms in: i) accommodating time-varying settings through stochastic approximation iterations; and ii) coping with imperfect CSI.

In this paper, we propose combined relay selection and cooperative beamforming schemes for physical layer security. Generally, high operational complexity is required for cooperative beamforming with multiple relays because of the required information exchange and synchronization among the relays. On the other hand, while it is desirable to reduce the number of relays participating in cooperative beamforming because of the associated complexity problem, doing so may degrade the coding gain of cooperative beamforming. Hence, we propose combined relay selection and cooperative beamforming schemes, where only two of the available relays are selected for beamforming and data transmission. The proposed schemes introduce a selection gain which partially compensates for the decrease in coding gain due to limiting the number of participating relays to two. Both the cases where full and only partial channel state information are available for relay selection and cooperative beamforming are considered. Analytical and simulation results for the proposed schemes show improved secrecy capacities compared to existing physical layer security schemes employing cooperative relays.

In this paper, we explore the use of reconfigurable intelligent surface (RIS) in unmanned aerial vehicle (UAV) based multiuser downlink communications, where a flying UAV serves multiple single antenna users through multiple RISs mounted on various buildings. More specifically, we consider the selection of RISs based on the outdated and imperfect channel state information (CSI) of the composite UAV-RIS-User channels at the UAV. After selection process, the UAV communicates to the user via the selected RISs and also with the direct link. Particularly, we derive an infinite series based expression for selection probability of RISs under both the outdated and imperfect CSI of composite channels based selection scheme. We also derive the statistical distribution of instantaneously received signal-to-noise ratio (SNR) under outdated and imperfect CSI conditions of both the direct and composite links at the user. Next, using the derived statistics, we analyze the network’s performance in terms of the average coverage probability (ACP) and average bit error rate (ABER) over the complete UAV flight time. Moreover, we discuss the behavior of ACP and ABER for very small and very large values of UAV transmit power, respectively. It is depicted through numerical results that selecting more RISs from a group of small-sized RISs may not be as advantageous as selecting fewer RISs from a group of large-sized RISs. Moreover, we also demonstrate the effect of several system parameters such as number of RIS reflecting elements, number of selected RISs, the severity of UAV-RIS and RIS-User links, and the severity of imperfect and outdated CSI on the network’s performance. The analytical results are corroborated with Monte-Carlo simulations.

In multiuser multiple‐input multiple‐output/orthogonal frequency‐division multiplexing (MIMO/OFDM) systems, the EigenValue Decomposition (EVD) method was proposed to construct a number of parallel spatial channels. The beamforming technique which only exploits the spatial subchannel related to the largest eigenvalue is usually adopted in many papers to deal with adaptive resource allocation. Although these previous studies could maximise the received signal‐to‐noise ratio (SNR), they could not get the maximum system throughput. In this paper, all the spatial subchannel are investigated. With the goal of maximising the overall system throughput, we derive a simple effective criterion of subcarrier allocation and introduce an adaptive resource allocation algorithm. The proposed algorithm could get higher system throughput especially at high SNR, that is the spectral efficiency is improved about 3 bit/s/Hz at 14 dB. At the same time, in order to decrease the computational complexity, a time‐frequency blockwise loading design is suggested. In practical channel with partial channel state information (CSI), a modified algorithm based on mean feedback model is proposed. The simulation results show that under imperfect CSI, the modified algorithm could achieve optimum system throughput while guaranteeing prescribed error performance. On the other hand, in comparison to perfect CSI, the system throughput decreases. Copyright © 2008 John Wiley & Sons, Ltd.

We study robust secure transmit design in terms of input covariance matrix for Gaussian multiple-input single-output (MISO) wiretap channels in the presence of a single-antenna eavesdropper. Under the assumption that the transmitter knows partial channel state information (CSI) on the main and eavesdropper's channels, we jointly design the input covariance matrices of information-bearing signal and artificial noise (AN) to maximize the secrecy rate. Unfortunately, the secrecy rate maximization (SRM) problem is difficult to solve. We derive a safe approximation to the SRM problem and propose a tractable approach to solve it. To get more insights, we discuss the rank property of the input covariance matrix of the information-bearing signal. Finally, the simulation results are provided to verify the validity and robustness of our proposed transmit design.

In this work, we propose a robust cooperative relay beamforming (rBF) design for single-carrier frequency-division multiple access (SC-FDMA) based multiuser multi-relay systems with imperfect channel state information. We maximize a lower bound on the achievable bit rate (ABR) of the network, subject to an aggregate relay transmit power constraint. Employing the primal decomposition technique, we decompose the problem into two subproblems: the rBF coefficient optimization and the relay power allocation. For a given power allocation across the frequency tones, a closed-form solution for the rBF matrices is obtained first. Subsequently, the convexity of the remaining power allocation problem is then proved, and efficient convex optimization methods are employed to find the global optimum. Simulation results validate the excellent performance of the proposed rBF schemes and show their superiority compared to conventional non-robust designs.