Abstract Joint sensing and communications systems have gained significant research interest by merging sensing capabilities with communication functionalities. However, few works have examined the case of multiple users. This work investigates a dual‐user joint sensing and communications system, focusing on the interference between the users that explores the optimal performance trade‐offs through a time‐division approach. Bi‐static radar setting is considered. Two typical strategies under this approach are studied: one in which both users follow the same order of communications and then sensing, and the other in which the tasks are performed in opposite order at two users. In each strategy, the sum rate and the detection probability are evaluated and optimized. The results show that the opposite order strategy offers superior performance to the same order strategy, and they also quantify their performance difference. This research highlights the potential benefits of time‐division strategies and multiple users in joint sensing and communications systems.

Massive multiple-input multiple-output (MIMO) networks are highly vulnerable to an active eavesdropping attack called pilot spoofing attack. The pilot spoofing attack causes information leakage to the active eavesdropper (ED) and also weakens the strength of the signal received by the attacked legitimate user equipment (UE) during the downlink transmission. In this paper, a deep neural network, called identification network (IDNet), is proposed to detect asynchronous pilot spoofing attacks and identify the attacked UE. We show that an asynchronous pilot spoofing attack leads to increasing the signal subspace dimension by one unlike the synchronous one. This property is then exploited to improve the attack detection/identification accuracy. In the proposed IDNet, the input features are the eigenvalues of the sample covariance matrix of the received signal at the base station (BS) as well as the ratio between the power of the received signal at the BS projected onto the pilot signals and its expected value. Numerical results show the effectiveness of IDNet in identifying the attacked UE and reveal that the larger the timing and/or frequency mismatches of the ED, the higher the identification accuracy confirming that asynchronous pilot spoofing attacks can be identified more accurately than synchronous pilot spoofing attacks.

We propose a new downlink cloud radio access network (CRAN) architecture with wireless fronthaul and access links and a central unit (CU) that is equipped with a very large antenna array to serve multiple multi-antenna remote radio heads (RRHs) that in turn serve a number of user equipments (UEs). The use of a very large antenna array at the CU allows to improve the fronthaul capacity leading to improved capacity of the whole network. We propose to minimize the total transmit power at the CU and RRHs subject to maximum powers allowed at the CU and RRHs and rate constraints of UEs via jointly optimizing the power allocation at the CU, the precoders at the RRHs, and the quantization noise covariance matrices. Both independent and joint compression schemes are considered. An iterative algorithm is proposed via reformulating the non-convex optimization problem as a semidefinite relaxation (SDR) problem of which the solution is proved to be also optimal for the original problem. Simulation results show that the performance of the proposed system can significantly decrease the total transmit power compared to two benchmark schemes.

This paper considers secure simultaneous wireless information and power transfer (SWIPT) in cell-free massive multiple-input multiple-output (MIMO) systems. The system consists of a large number of randomly (Poisson-distributed) located access points (APs) serving multiple information users (IUs) and an information-untrusted dual-antenna active energy harvester (EH). The active EH uses one antenna to legitimately harvest energy and the other antenna to eavesdrop information. The APs are networked by a centralized infinite backhaul which allows the APs to synchronize and cooperate via a central processing unit (CPU). Closed-form expressions for the average harvested energy (AHE) and a tight lower bound on the ergodic secrecy rate (ESR) are derived. The obtained lower bound on the ESR takes into account the IUs' knowledge attained by downlink effective precoded-channel training. Since the transmit power constraint is per AP, the ESR is nonlinear in terms of the transmit power elements of the APs and that imposes new challenges in formulating a convex power control problem for the downlink transmission. To deal with these nonlinearities, a new method of balancing the transmit power among the APs via relaxed semidefinite programming (SDP) which is proven to be rank-one globally optimal is derived. A fair comparison between the proposed cell-free and the colocated massive MIMO systems shows that the cell-free MIMO outperforms the colocated MIMO over the interval in which the AHE constraint is low and vice versa. Also, the cell-free MIMO is found to be more immune to the increase in the active eavesdropping power than the colocated MIMO.

We consider the optimization of the downlink transmission for simultaneous wireless information and power transfer (SWIPT) in multi-cell massive multiple-input multiple-output systems. The system comprises a two-antenna active energy harvester (EH) which is capable of legitimately harvesting energy via one antenna, and illegitimately and actively eavesdropping the signal intended for certain information user(s) (IU(s)) via the other antenna for the purpose of information decoding or energy harvesting. Thereby, the considered problems are: 1) when the EH eavesdrops for the purpose of information decoding, i.e., the EH is information-untrusted by the base station (BS), we propose to maximize the worst-case secrecy rate under a constraint on a worst-case average harvested energy (AHE) and 2) when the EH eavesdrops one or multiple IUs for energy harvesting, i.e., the EH is information-trusted by the BS, we propose to maximize the sum-rate of the IUs under a constraint on a worst-case AHE by the EH. We derive asymptotic expressions for a lower bound on ergodic secrecy rate (ESR) and AHE in large system limit. Subsequently, we use these results to optimize the power allocation for downlink SWIPT transmissions which include information signals, artificial noise (AN) and energy signal towards the IUs, and legitimate and illegitimate antennas of the EH, respectively. Simulation results show the accuracy of our asymptotic analysis. We show that there is a performance trade-off between the worst-case ESR and the worst-case AHE. In addition, the impact of the combined legitimate/illegitimate operation of the EH on the SWIPT performance is evaluated.

This paper considers a multiuser multiple‐input multiple‐output (MIMO) space‐time block coded system that operates at a high data rate with full diversity. In particular, they propose to use a full rate downlink algebraic transmission scheme combined with a differential space‐time scheme for multiuser MIMO systems. To achieve this, perfect algebraic space‐time codes and Cayley differential transforms are employed. Since channel state information (CSI) is not needed at the differential receiver, differential schemes are ideal for multiuser systems to shift the complexity from the receivers to the transmitter, thus simplifying user equipment. Furthermore, orthogonal spreading matrices are employed at the transmitter to separate the data streams of different users and enable simple single user decoding. In the orthogonal spreading scheme, the transmitter does not require any knowledge of the CSI to separate the data streams of multiple users; this results in a system which does not need CSI at either end. With this system, to limit the number of possible codewords, a sphere decoder is used to decode the signals at the receiving end. The proposed scheme yields low complexity transceivers while providing full rate full diversity with good performance. Simulation results demonstrate the effectiveness of the proposed scheme.

In this paper, we investigate the performance of relay selection for simultaneous wireless information and power transfer (SWIPT) systems. In particular, we consider a relay network consisting of both energy harvesting (EH) and non-EH relays. We further assume amplify-and-forward relaying and power-splitting at the EH units. We study the scenarios for both the battery-less and battery-equipped relays. The diversity and coding gains for the battery-less scenario are derived through the outage probability analysis. Our analysis indicates that the relay selection schemes achieve full diversity gain for SWIPT. We corroborate our analysis through simulations and compare the performance of the battery-less and battery-equipped relay scenarios. Moreover, we investigate the effects of the powersplitting on the system performance through simulations.

In this paper, we consider both channel state uncertainty and harvested energy state uncertainty for a source-relay-destination communication link where the source and the relay are equipped with hybrid energy sources. Taking into account these uncertainties is of important for practical energy harvesting (EH) communication. While channel state uncertainties also affect conventional communication systems and have been widely studied, harvested energy state uncertainties are specific to energy harvesting systems and have not been considered in the literature before. The considered hybrid energy sources include a constant energy source and an energy harvester. Our objective is to maximize the worst case system throughput over a finite number of transmission intervals. We propose robust optimal offline, optimal online, and suboptimal online power allocation schemes. The offline power allocation design is formulated as an optimization problem which can be solved optimally. For the online case, we propose a dynamic programming (DP) approach to compute the optimal transmit power. To alleviate the prohibitively high complexity inherent to DP, we also propose several suboptimal low-complexity online power allocation schemes. Simulation results confirm the robustness of the proposed power allocation schemes to channel and energy state uncertainties.

The bidirectional relay channel, in which two users communicate with each other through a relay node, is a simple but fundamental and practical network architecture. In this paper, we consider the block fading bidirectional relay channel with a decode-and-forward relay and propose efficient transmission strategies that exploit the block fading property of the channel. We assume that a direct link between the two users is not present and consider two transmission modes: 1) the multiple-access mode (both users transmit to the relay) and 2) the broadcast mode (the relay transmits to both users). Most existing relaying protocols assume a fixed schedule for using these transmission modes. In contrast, we abandon the restriction of having a fixed and predefined schedule and propose to optimize the selection of the transmission modes and the associated transmission rates based on the instantaneous channel state information (CSI) of the involved links. Thereby, we consider two different types of transmit power constraints: 1) a fixed transmit power for each node and 2) a per-node long-term power constraint. To enable the use of a nonpredefined schedule for transmission mode selection, the relay has to be equipped with two buffers for storage of the information received from both users. We develop new relaying protocols based on adaptive mode selection and provide the corresponding achievable long-term rate regions. In particular, based on the CSI of the involved links, the optimal transmission mode as well as the optimal transmission rates and/or the transmit powers of the nodes are chosen in each time slot to maximize the weighted sum rate of both users. By varying the weights assigned to the users, the boundary surface of the achievable long-term rate region of the proposed protocol can be obtained. In addition, we discuss and address two practical challenges for the implementation of the proposed protocols, namely, the availability of the knowledge of the channel statistics required for the implementation of the optimal protocols, and the increase of the end-to-end delay due to the data buffering. Numerical results confirm the superiority of the proposed buffer-aided protocols compared with existing bidirectional relaying protocols.

In this paper, we consider optimal power allocation for conventional and buffer-aided link adaptive energy harvesting (EH) relay systems, where an EH source communicates with the destination via an EH decode-and-forward relay {over fading channels}. In conventional relaying, source and relay transmit signals in consecutive time slots whereas in buffer-aided link adaptive relaying, the state of the source-relay and relay-destination channels {as well as the amounts of energy available at source and relay} determine whether the source or the relay is selected for transmission. Our objective is to maximize the system throughput over a finite number of transmission time slots for both relaying protocols. In case of conventional relaying, we propose an offline and several online joint source and relay transmit power allocation schemes. For offline power allocation, we formulate {a convex optimization problem} whereas for the online case, we propose a dynamic programming (DP) approach to compute the optimal online transmit power. To alleviate the complexity inherent to DP, we also propose several suboptimal online power allocation schemes. For buffer-aided link adaptive relaying, we show that the joint offline optimization of the source and relay transmit powers along with the link selection results in a mixed integer non-linear program which we solve optimally using the spatial branch-and-bound method. We also propose efficient online power allocation schemes for buffer-aided link adaptive relaying. Simulation results show that buffer-aided link adaptive relaying provides significant performance gains compared to conventional relaying but requires a higher complexity for computation of the power allocation solution. We also show that buffer-aided link adaptive relaying is more robust to changes in the EH rate than conventional relaying.

We jointly optimize the source and relay precoders for multi—antenna multi—relay networks employing a prefixed receiver. Prefixed receivers are of practical interest since they enable low complexity at the end—user's receiver as well as backward compatibility. To compute the source and relay precoders, we consider two different criteria. The objective of the first criterion is to maximize the worst stream signal—to—interference—plus—noise ratio (SINR) at the output of the receiver subject to source and relay transmit power constraints. Under the second criterion, we minimize the source and relay transmit powers subject to a certain quality—of—service constraint. Both optimization problems are non—convex. To solve them, we propose iterative alternating algorithms, where, in each iteration, we compute the precoders alternately, i.e., for each precoder optimization, we fix all the precoders except the one which is optimized. For both criteria, we formulate the optimization problem for the computation of the source precoder as a second order cone programming (SOCP) problem, for which the optimal solution can be found using interior point algorithms. For each relay precoder, we formulate the optimization problem as a semidefinite relaxation (SDR) problem for which ready—to—use solvers exist. If the solution to the SDR problem is not of rank one, matrix rank—one decomposition or randomization is applied. We also provide sufficient conditions for the convergence of the proposed iterative alternating algorithms to a fixed point. Simulation results show that the performance of the proposed algorithms is close to the performance achieved if the source, relay, and receiver filters are jointly optimized.

In this paper, we consider a multisource multirelay network where relays employ buffers to store the received user data packets before forwarding them to a common destination. The transmission schedule, i.e., when each source and each relay transmit, is not a priori fixed, but rather depends on the link qualities. In particular, we consider adaptive link selection and adaptive rate transmission for the considered network. For simple three node relay networks, it was shown before that buffer-aided relaying with adaptive link selection yields significant throughput gains compared to conventional relaying protocols using a fixed transmission schedule. In this work, we consider a general multisource multirelay framework where operations are more complex and analysis is more involved. First, we consider average sum rate maximization for adaptive rate transmission and derive an adaptive link selection policy which exploits the channel state information. As fairness is an important issue in multisource networks, we also consider max-min fairness constrained throughput optimization and derive the corresponding link selection policy. Numerical results show that the proposed link selection policies yield significantly higher throughputs compared to conventional relaying schemes where source and relay transmission schedules are a-priori fixed.

In this paper, we consider the problem of sum rate maximization in a bidirectional relay network with fading. Hereby, user 1 and user 2 communicate with each other only through a relay, i.e., a direct link between user 1 and user 2 is not present. In this network, there exist six possible transmission modes: four point-to-point modes (user 1-to-relay, user 2-to-relay, relay-to-user 1, relay-to-user 2), a multiple access mode (both users to the relay), and a broadcast mode (the relay to both users). Most existing protocols assume a fixed schedule of using a subset of the aforementioned transmission modes, as a result, the sum rate is limited by the capacity of the weakest link associated with the relay in each time slot. Motivated by this limitation, we develop a protocol which is not restricted to adhere to a predefined schedule for using the transmission modes. Therefore, all transmission modes of the bidirectional relay network can be used adaptively based on the instantaneous channel state information (CSI) of the involved links. To this end, the relay has to be equipped with two buffers for the storage of the information received from users 1 and 2, respectively. For the considered network, given a total average power budget for all nodes, we jointly optimize the transmission mode selection and power allocation based on the instantaneous CSI in each time slot for sum rate maximization. Simulation results show that the proposed protocol outperforms existing protocols for all signal-to-noise ratios (SNRs). Specifically, we obtain a considerable gain at low SNRs due to the adaptive power allocation and at high SNRs due to the adaptive mode selection.

In this work, we consider a point-to-point link where the transmitter has a hybrid supply of energy, i.e., the energy is supplied by a constant energy source and an energy harvester, which harvests energy from its surrounding environment. Our goal is to jointly minimize the power consumed by the constant energy source and any possible waste of the harvested energy to ensure their optimum utilization for transmission of a given amount of data in a given number of time intervals. Two scenarios are considered for packet arrival. In the first scenario, we assume that all data packets have arrived before the transmission begins, whereas in the second scenario, we assume that data packets are arriving during the course of data transmission. For both scenarios, we propose optimal offline transmit power allocation schemes which provide insight on how to efficiently consume the energy supplied by the constant energy source and the energy harvester.

In this paper, we consider the problem of joint source and relay precoder design for multi-antenna multi-relay networks with a prefixed receiver. Prefixed receivers are of practical interest since they enable low complexity at the end-user's receiver as well as backward compatibility. To compute the source and relay precoders, we propose to maximize the worst stream signal-to-interference-plus-noise ratio (SINR) at the output of the receiver subject to source and relay transmit power constraints. The problem is a non-convex optimization problem. To solve it, we propose an iterative alternating algorithm, where, in each iteration, we compute the precoders alternately. We formulate the resulting optimization problems for the computation of the source and relay precoders as second order cone programming (SOCP) and semidefinite relaxation (SDR) problems, respectively. Moreover, we provide sufficient conditions for the convergence of the proposed iterative alternating algorithm to a fixed point. Simulation results show that the performance of the proposed algorithm is close to the performance achieved if the source, relay, and receiver filters are jointly optimized.

In this work, we consider a point-to-point communication link where the transmitter has a hybrid supply of energy. Specifically, the hybrid energy is supplied by a constant energy source and an energy harvester, which harvests energy from its surrounding environment and stores it in a battery which suffers from energy leakage. Our goal is to minimize the power consumed by the constant energy source for transmission of a given amount of data in a given number of time intervals. Two scenarios are considered for packet arrival. In the first scenario, we assume that all data packets have arrived before transmission begins, whereas in the second scenario, we assume that data packets are arriving during the course of data transmission. For both scenarios, we propose an optimal offline transmit power allocation scheme which provides insight into how to efficiently consume the energy supplied by the constant energy source and the energy harvester. For offline power allocation, we assume that causal and non-causal information regarding the channel and the amount of harvested energy is available a priori. For optimal online power allocation, we adopt a stochastic dynamic programming (DP) approach for both considered scenarios. For online power allocation, only causal information regarding the channel and the amount of harvested energy is assumed available. Due to the inherent high complexity of DP, we propose suboptimal online algorithms which are appealing because of their low complexity. Simulation results reveal that the offline scheme performs best among all considered schemes and the suboptimal online scheme provides a good performance-complexity tradeoff.

In this paper, we study a cooperative diversity scheme for wireless systems where the relay is equipped with a buffer. We consider practical frequency—selective channels and adopt the combination of bit interleaved coded modulation and orthogonal frequency division multiplexing (BICM—OFDM). We propose a novel link selection protocol for BICM—OFDM systems where the relay either transmits or receives in a given time slot depending on the quality of the links. We derive a closed—form upper bound for the asymptotic worst—case pairwise error probability (PEP) and the diversity gain of the considered buffer—aided relaying scheme for both infinite and finite buffer size. We show that significant diversity gains can be achieved with buffer—aided relaying compared to conventional relaying at the expense of larger packet delays. In fact, for buffers of infinite (or very large) size, the diversity gain is doubled for links with identical frequency diversity, and an even higher diversity gain advantage is possible for links with non—identical frequency diversities. Furthermore, we perform an exact closed—form average delay analysis for buffers of both finite and infinite size which provides important insight into the achieved delay—performance tradeoff. The derived analytical results and performance gains are corroborated by extensive simulation results.

In this paper, a new relaying scheme, referred to as space full-duplex max-max relay selection (SFD-MMRS) is proposed. SFD-MMRS uses relay selection and half-duplex (HD) relays with buffers to mimic full-duplex (FD) relaying. It allows the selection of different relays for reception and transmission, which in turn enables simultaneous reception and transmission. With SFD-MMRS the pre-log factor 1 over 2 is removed from the capacity expression and better performance in terms of throughput is achieved compared to the existing schemes. We provide a comprehensive analysis of the capacity of the proposed scheme for a decode-and-forward (DF) protocol in Rayleigh fading. Our simulation results show that the capacity of the proposed scheme with HD relays exceeds twice the capacity of the best relay selection (BRS) scheme with HD relays.

In this paper, we study a cooperative diversity scheme for wireless systems where the relay is equipped with a buffer. We consider practical frequency-selective channels and adopt the combination of bit interleaved coded modulation and orthogonal frequency division multiplexing (BICM-OFDM). We propose a novel link selection protocol for BICM-OFDM systems where the relay either transmits or receives in a given time slot depending on the quality of the links. We derive closed-form upper bounds for the asymptotic worst-case pairwise error probability and the diversity gain of the considered buffer-aided relaying scheme for infinite buffer size. We show that impressive diversity gains can be achieved with buffer-aided relaying compared to conventional relaying at the expense of packet delay. In fact, for buffers of infinite (or very large) size, the diversity gain is doubled for links with identical frequency diversity, and even a higher diversity gain advantage is possible for non-identical diversity links. The derived analytical results and performance gains are corroborated by simulation results, where we also show that for buffers of moderate size, a significant coding gain can be achieved, if not any diversity gain.

Using energy harvesting nodes can be a viable solution for energy limited cooperative communication systems. In this paper, we consider the optimization of an energy harvesting (EH) relay system, where an EH source communicates with the destination via an EH decode-and-forward (DF) relay. Our objective is to maximize the system throughput over a finite number of transmission intervals. To this end, we propose an offline and several online joint source and relay transmit power allocation schemes. For offline power allocation, we formulate a convex optimization problem which can be solved either in closed form or using standard optimization tools. For the online case, we propose a dynamic programming (DP) approach to compute the optimal online transmit power. To alleviate the complexity inherent to DP, we propose several suboptimal online power allocation schemes. Our simulation results show that the developed suboptimal schemes provide a good complexity-performance tradeoff compared to optimal online power allocation.

In this paper, we propose a new relay selection scheme for half-duplex relays with buffers. The proposed scheme is referred to as max-max relay selection (MMRS) since the relays with the best source-relay and the best relay-destination channels are selected for reception and transmission, respectively, which is only possible without data loss if the relays have buffers of infinite size. To relax this idealized assumption, we propose hybrid relay selection (HRS) for relays with buffers of finite size. HRS is a combination of conventional best relay selection (BRS) and MMRS and takes into account both the channel state and the buffer state for relay selection. We provide a comprehensive analysis of the outage and symbol error probabilities of both MMRS and HRS for a decode-and-forward protocol in Rayleigh fading. This analysis reveals that BRS, HRS, and MMRS achieve the same diversity gain. However, for N relays, MMRS achieves a signal-to-noise ratio (SNR) gain of 3(1-1/N) dB compared to BRS, and HRS closely approaches the SNR gain of MMRS for moderate buffer sizes (e.g. 30 transmission intervals).

We show that the performance of relay selection can be improved by employing relays with buffers. Under the idealized assumption that no buffer is full or empty, the best source-relay and the best relay-destination channels can be simultaneously exploited by selecting the corresponding relays for reception and transmission, respectively. The resulting relay selection scheme is referred to as max-max relay selection (MMRS). Since for finite buffer sizes, empty and full buffers are practically unavoidable if MMRS is employed, we propose a hybrid relay selection (HRS) scheme, which is a combination of conventional best relay selection (BRS) and MMRS. We analyze the outage probabilities of MMRS and HRS and show that both schemes achieve the same diversity gain as conventional BRS and a superior coding gain. Furthermore, our results show that for moderate buffer sizes (e.g. 30 packets) HRS closely approaches the performance of idealized MMRS and the performance gain compared to BRS approaches 3 dB as the number of relays increases.

In this paper, we consider filter-and-forward beamforming (FF-BF) for two-way relay networks employing single-carrier transmission over frequency-selective channels. In FF-BF, the relay nodes filter the received signal using finite impulse response (FIR) or infinite impulse response (IIR) filters. For the processing at the transceivers, we investigate two different cases: (1) simple slicing without equalization and (2) linear equalization. For both cases, we optimize FF-BF filters for maximization of the minimum transceiver signal-to-interference-plus-noise ratio (SINR) subject to a relay transmit power constraint. For case (1), we show that the optimization problem for FIR filters can be transformed into a convex second-order cone programming problem, which can be efficiently solved using standard tools. For case (2), leveraging results from IIR FF-BF for one-way relaying, we establish an upper and an achievable lower bound for the max-min problem. Since the gap between the upper and the lower bound is small, a close-to-optimal solution is obtained. Our simulation results reveal that the performance of FF-BF without equalization at the transceivers crucially depends on the slicer decision delay and transceivers with slicers can closely approach the performance of transceivers with equalizers provided that the FIR FF-BF filters are sufficiently long.

Most of the existing literature on cooperative relay networks has focused on frequency-nonselective channels or frequency-selective channels with multi-carrier transmission. However, several practical systems employ single-carrier transmission over frequency-selective channels and the design of corresponding relaying schemes is a largely under-explored topic. In this paper, we investigate filter-and-forward beamforming (FF-BF) for relay networks employing single-carrier transmission over frequency-selective channels. In contrast to prior work, we assume that the destination node is equipped with a simple linear or decision feedback equalizer. The FF-BF filters at the relays are optimized for maximization of the signal-to-noise ratio at the equalizer output under a joint relay power constraint. For infinite impulse response (IIR) FF-BF filters, we derive a unified expression for the filter frequency response valid for linear equalization, decision feedback equalization, and an idealized matched filter receiver. A numerical algorithm with guaranteed convergence is developed for optimization of the power allocation factor included in the expression for the IIR FF-BF filter frequency response. We also provide an efficient gradient algorithm for recursive calculation of near-optimal finite impulse response (FIR) FF-BF filters. Simulation results show that, in general, short FIR FF-BF filters are sufficient to closely approach the performance of IIR FF-BF filters even in severely frequency-selective channels and that the proposed FF-BF scheme with equalization at the destination achieves substantial performance gains compared to a previously proposed FF-BF scheme without equalization.

In this paper, we consider filter-and-forward beamforming (FF-BF) for two-way relay networks employing single-carrier transmission over frequency-selective channels. In FF-BF, the relay nodes filter the received signal using finite impulse response (FIR) or infinite impulse response (IIR) filters. For the processing at the transceivers, we investigate two different cases: (1) simple slicing without equalization and (2) linear equalization (LE) or decision-feedback equalization (DFE). For the first case, we optimize FIR FF-BF filters, respectively, for maximization of the minimum transceiver signal-to-interference-plus-noise ratio (SINR) subject to a relay transmit power constraint and for minimization of the total relay transmit power subject to two quality of service (QoS) constraints. We show that both problems can be transformed into a convex second-order cone programming (SOCP) problem, which can be efficiently solved using standard tools. For the second case, we optimize IIR and FIR FF-BF filters for max-min optimization of the SINR, and for transceivers with zero-forcing LE, also for minimization of the sum mean-squared error (MSE) at the equalizer outputs of both transceivers. Leveraging results from FF-BF for one-way relaying, we establish an upper and an achievable lower bound for the max-min problem and an exact solution for the sum MSE problem. Since the gap between the upper and the lower bound for the max-min problem is small, a close-to-optimal solution is obtained. Our simulation results reveal that the performance of FF-BF without equalization at the transceivers crucially depends on the slicer decision delay and transceivers with slicers can closely approach the performance of transceivers with equalizers provided that the FF-BF filters are sufficiently long and a sufficient number of relays is deployed.

In this paper, we investigate filter-and-forward beamforming (FF-BF) for relay networks employing single-carrier transmission over frequency-selective channels. In contrast to prior work, we assume that the destination node is equipped with a simple linear equalizer. The FF-BF filters at the relays are optimized for maximization of the signal-to-noise ratio at the equalizer output under a joint relay power constraint. For infinite impulse response (IIR) FF-BF filters, we derive a closed-form expression for the filter frequency response, and a numerical algorithm with guaranteed convergence is developed for optimization of the power allocation factor included in the expression. We also provide an efficient gradient algorithm for recursive calculation of near-optimal finite impulse response (FIR) FF-BF filters. Simulation results show that, in general, short FIR FF-BF filters are sufficient to closely approach the performance of IIR FF-BF filters even in severely frequency-selective channels and that the proposed FF-BF scheme with equalization at the destination achieves substantial performance gains compared to a previously proposed FF-BF scheme without equalization.

In this paper, we propose a new iterative algorithm for the minimization of the constant modulus (CM) criterion. It is composed of two stages: Prewhitening followed by complex Givens rotations, whence the name Givens CMA (GCMA). Initially, prewhitening reduces the channel matrix into a unitary matrix. Subsequently, this unitary matrix is computed via complex Givens rotations by minimizing the CM criterion. The proposed algorithm provides similar or even better performance than the Analytical CMA (ACMA) algorithm at reduced computational cost. Some simulation results are provided to illustrate the effectiveness of the proposed algorithm.