Second-hop Channel Research Articles

Outdoor-to-Indoor mmWave Relaying with Massive MIMO: Impact of Imperfect Channel Estimation

Assuming incomplete knowledge of the channel state information (CSI), we investigate two scenarios involving millimeter wave (mmWave) relaying to support outdoor-to-indoor communications. We proceed to derive the average signal-to-noise ratio (SNR) expressions for two relaying scenarios and quantify the asymptotic SNR. The performance of the two relaying scenarios is evaluated using the outage probability—for which we have derived closed-form equations—the end-to-end channel capacity, and the energy efficiency. The obtained results are compared with those derived assuming complete knowledge of the CSI. The effect of the imperfect CSI is therefore assessed in relation to the reference of perfect CSI. In these scenarios, an outside base station (BS) in an urban cellular network serves several indoor users. In the context of a two-hop full-duplex (FD) relaying scheme, we initially suggest a method in which the base station (BS) utilizes zero-forcing (ZF) precoding, and we take into account the overall channel response. Furthermore, we make the assumption that the base station (BS) engages in precoding only depending on the response of the channel in the first hop; in this second design, the relay precodes (using the response of the second-hop channel), amplifies, and sends the signals. Both techniques utilize massive multiple-input–multiple-output (mMIMO) arrays to permit transmission. We also present Monte Carlo simulation results to assess the accuracy of our analytical results. Finally, the two systems are compared in terms of channel estimation and precoding complexity, the number of antennas, as well as the number of users. Practical deployment recommendations are formulated at the end of this work.

On the Physical Layer Security of Untrusted Millimeter Wave Relaying Networks: A Stochastic Geometry Approach

The physical layer security (PLS) of millimeter wave (mmWave) communication systems is investigated, where the secure source-to-destination communication is assisted by an untrusted relay selected from a group of them and there are also several passive eavesdroppers (Eves) in the network. In the considered system model, while the distributions of the untrusted relays and Eves follow a homogeneous Poisson Point Process (PPP). To maximize the instantaneous secrecy rate, a novel joint relay selection and power allocation (JRP) method is developed where the destination and source aim for jamming the reception of both the untrusted relays and passive Eves. New expressions of the optimal power allocation (OPA) are derived for both non-colluding Eves (NCE) and colluding Eves (CE). Subsequently, by considering the impact of potential blockages, new closed-form equations are derived for analyzing the system’s ergodic secrecy rate (ESR) and secrecy outage probability (SOP) for transmission over fading mmWave channels. Finally, numerical examples are provided for demonstrating the superiority of our proposed JRP method over the relevant benchmarks found in the literature. Interestingly, the ESR increases with the density of untrusted relays for both the NCE and CE scenarios, which is a benefit of the improved probability of selecting a relay with a stronger second-hop channel. Furthermore, in the low transmit power regime, employing relatively low mmWave frequencies achieves better ESR, while in the high transmit power regime, high mmWave frequencies provide higher ESR.

Relay Selection for Energy-Harvesting Relays With Finite Data Buffer and Energy Storage

Buffer-aided relaying can fully utilize the available selection gain of relay channels by allowing relays to store the received packets in the data buffers when the first-hop and second-hop channels are mismatched in quality. For energy-constrained Internet-of-Things (IoT) networks, some relays may lack sufficient energy to forward the buffered packets even their relay-to-destination channels are strong enough, leading to significant performance loss. This work studies buffer-aided relaying for relays that accumulate the energy harvested from source signal using finite-size energy buffers. A relay selection scheme considering both data buffer and energy buffer status is proposed and its performance is theoretically analyzed through Markov-chain modeling. Due to the complex behavior of dual buffers, the power consumption for reporting buffer status is first ignored in the theoretical analysis, which is then extended to, including feedback energy consumption. We validate the accuracy of the theoretical analysis and extensively discuss the performance of the proposed relay selection scheme subject to numerous key parameters. Numerical results demonstrate that the proposed relay selection scheme can fully exploit the diversity gain of multiple relays when ignoring energy consumption of feedback. With nonnegligible feedback energy consumption, the proposed relay selection scheme still significant outperforms some existing buffer-aided relay selection schemes.

Mixed-Timescale Channel Estimation for MIMO Relay Multi-User Systems Based on the PARAFAC Decomposition

This letter presents novel mixed-timescale channel estimation algorithms for uplink multiple-input multiple-output (MIMO) relay multi-user systems, considering the mixed-timescale property of practical dual-hop channel. With the one-stage training (OST) scheme, we formulate the channel estimation problem based on the parallel factor (PARAFAC) decomposition using the received pilots at multiple time slots, where the second-hop channel is viewed as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-timescale</i> variable and the first-hop channel is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short-timescale</i> . Then, the alternating least-square (LS) fitting method in batch mode (Batch-ALS) and online recursive alternating LS (Online-RALS) algorithms are proposed for mixed-timescale channel estimation. Simulation results show that the proposed algorithms improve the estimation performance significantly compared to the existing single-timescale channel estimation algorithms.

Design of Cooperative MIMO Wireless Sensor Networks With Partial Channel State Information

Wireless sensor networks (WSNs) play a key role in automation and consumer electronics applications. This paper deals with joint design of the source precoder, relaying matrices, and destination equalizer in a multiple-relay amplify-and-forward (AF) cooperative multiple-input multiple-output (MIMO) WSN, when partial channel-state information (CSI) is available in the network. In particular, the considered approach assumes knowledge of instantaneous CSI of the first-hop channels and statistical CSI of the second-hop channels. In such a scenario, compared to the case when instantaneous CSI of both the first- and second-hop channels is exploited, existing network designs exhibit a significant performance degradation. Relying on a relaxed minimum-mean-square-error (MMSE) criterion, we show that strategies based on potential activation of all antennas belonging to all relays lead to mathematically intractable optimization problems. Therefore, we develop a new joint relay-and-antenna selection procedure, which determines the best subset of the available antennas possibly belonging to different relays. Monte Carlo simulations show that, compared to conventional relay selection strategies, the proposed design offers a significant performance gain, outperforming also other recently proposed relay/antenna selection schemes.

Optimal Streaming Erasure Codes Over the Three-Node Relay Network

This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the source to the relay and the second-hop channel from the relay to the destination are subject to packet erasures. Every source message generated at a time slot must be recovered perfectly at the destination within the subsequent T time slots. In any sliding window of $ {T}+1$ time slots, we assume no more than $ {N}_{1}$ and ${N}_{2}$ erasures are introduced by the first-hop channel and second-hop channel respectively. We fully characterize the maximum achievable rate in terms of T , $ {N}_{1}$ and $ {N}_{2}$ . The achievability is proved by using a symbol-wise decode-forward strategy where the source symbols within the same message are decoded by the relay with different delays. The converse is proved by analyzing the maximum achievable rate for each channel when the erasures in the other channel are consecutive (bursty). In addition, we show that traditional message-wise decode-forward strategies, which require the source symbols within the same message to be decoded by the relay with the same delay, are sub-optimal in general.

Two-Hop AF MIMO Relay System Optimization With Own Information From the Relay Node

In this paper, we consider precoding matrices optimization for a new two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, where in addition to forwarding the source signals, the relay node concurrently transmits its own signals to the destination node. Compared with conventional AF MIMO relay systems where the relay node only forwards the source signals, the transceiver optimization problem in the new system is more challenging to solve. We prove that for all Schur-concave objective functions, the optimal source and relay matrices jointly diagonalize the source-relay-destination and relay-destination channels, which simplifies the matrices optimization problem to a joint subchannel and power allocation problem with scalar variables. It is shown that to achieve a maximal sum mutual information (MI) of both the source and relay links, the strongest subchannels of the second-hop channel should be allocated for transmitting signals from the relay node. With additional quality-of-service constraints in terms of the lower bounds of the MI of both links, the optimal subchannel allocation problem is NP-hard. In this case, we propose a suboptimal channel allocation algorithm with a low computational complexity. For a given subchannel allocation, we develop a primal decomposition based algorithm to efficiently solve the power allocation problem. Simulation results show that compared with the exhaustive search based channel allocation approach and the general nonlinear programming based power allocation algorithm, the proposed subchannel and power allocation algorithms have a much lower computational complexity with only a small performance loss.

Optimization of Links With a Battery-Assisted Time-Switching Wireless Energy Harvesting Relay

In this paper, we analyze the performance of a two-hop network in which a multiantenna source communicates with a single-antenna destination through a decode-and-forward single-antenna energy harvesting (EH) relay. We assume a novel practical system framework in which the EH relay has the option of augmenting the wireless energy harvested by drawing energy from a supplementary battery, thereby improving link performance. Assuming use of the time-switching relaying (TSR) EH protocol, the outage and throughput performance are analyzed. We optimize the fraction of time devoted to EH (the TSR parameter) so as to maximize throughput for fixed supplementary battery energy. We also optimize the TSR parameter to minimize supplementary battery energy consumption for target throughput performance. We further show that exploiting second-hop channel knowledge at the relay can dramatically reduce the energy drawn from the supplementary battery. These insights are of fundamental importance to system designers. Simulation results validate the derived analytical expressions and corroborate our findings.

Performance of EH Protocols in Two-Hop Networks With a Battery-Assisted EH Relay

In this paper, we compare the performance of time-switching relaying (TSR) and power-splitting relaying (PSR) protocols in two-hop networks with a battery-assisted energy-harvesting (EH) amplify-and-forward relay. In this battery-assisted relay framework, the EH relay augments the harvested energy with energy drawn from a battery. Using expressions derived for throughput and average battery energy consumption, we investigate maximization of throughput for given battery energy availability per time slot and minimization of battery energy consumption for target throughput requirement. When only statistical channel knowledge is available, PSR results in better throughput performance at practical signal-to-noise ratios. However, in the typical low battery energy and low target throughput regime, it is TSR that is more battery energy efficient. When second-hop instantaneous channel knowledge is available, we observe dramatical energy savings that increases lifetime of nodes. Simulation results are presented to demonstrate accuracy of the derived expressions.

Individual Channel Estimation Based on Blind Interference Cancellation for Two-Way MIMO Relay Networks

In this paper, we investigate an individual channel estimation problem for multiple-input multiple-output (MIMO) two-way amplify-and-forward (AF) relay networks. To avoid self-interference during the estimation of the individual MIMO channels, a novel blind interference cancellation (BIC) approach is proposed based on an orthogonal preceding framework, where a pair of orthogonal precoding matrices is utilized at the source nodes. By designing an optimal decoding scheme, we propose to decompose the bidirectional transmission into a pair of unidirectional transmissions. Unlike most existing approaches, we make the practical assumption that the nonreciprocal MIMO channel and the mutual interference of multiple antennas are both taken into consideration. Under the precoding framework, we employ an orthogonal superimposed training strategy to obtain the individual MIMO channels. However, the AF strategy causes the noise at the terminal to be the sum of the local noise and the relay-propagated noise. To remove the relay-propagated noise during the estimation of the second-hop channel, a partial noise-nulling method is designed. We also derive a closed-form expression for the total mean square error (MSE) of the MIMO channel from which we compute the optimal power allocation. The simulation results demonstrate that the analytical and simulated curves match fully.

Exploiting cooperative relays to enhance the performance of energy-harvesting systems over Nakagami-m fading channels

This paper investigates a time-switching energy-harvesting system in which a source communicates with a destination via energy-constrained amplify-and-forward relays. To exploit the benefit of using multiple relays, we propose a relay scheduling called consecutive relay selection (CRS), which allows all relays to assist the source-to-destination communication, to improve the transmission efficiency of the time-switching policy. The partial relay selection (PRS) is examined for performance comparison. The selected relay in the PRS protocol is considered in two cases: in one, it is selected based on the first-hop channel gains (PRS-1 protocol), and in the other, it is selected based on the second-hop channel gains (PRS-2 protocol). For performance evaluation, the analytical expressions of the outage probability and throughput for Nakagami-m fading channel are derived. Our results show that the CRS protocol outperforms the PRS protocol in terms of throughput, the PRS-1 protocol achieves better performance than the PRS-2 protocol. Moreover, we discuss the effects of various key system parameters on system performance, such as the energy-harvesting ratio, source transmission rate, and locations of relays, to provide insights into the various design choices.

Channel Estimation for OFDM-Based Amplify-and-Forward Cooperative System Using Relay-Superimposed Pilots

For the OFDM-based Amplify-and-Forward cooperative system, a novel relay-superimposed pilot strategy is proposed, where the source pilot symbols are frequency division multiplexed to estimate the cascaded channel while relay pilot sequence is superimposed onto the top of the cooperative data stream for second-hop channel estimation. This method avoids the loss of data rate for additional pilot subcarriers but results in the interference of unknown cooperative data. To remove the interference of cooperative data during the estimation of second-hop channel, the Cooperative Interference Cancelation scheme assisted by cooperative data from direct link is proposed. We derive the approximated lower bound for the MSE of second-hop channel estimation. Simulation results are presented to validate the performance of the proposed schemes.

Robust MMSE Transceiver Design for Nonregenerative Multicasting MIMO Relay Systems

In this paper, we investigate the transceiver design for nonregenerative multicasting multiple-input multiple-output (MIMO) relay systems, where one transmitter broadcasts common message to multiple receivers with the aid of a relay node. The transmitter, relay, and receivers are all equipped with multiple antennas. We assume that the true (unknown) channel matrices have Gaussian distribution, with the estimated channels as the mean value, and the channel estimation errors follow the well-known Kronecker model. We first develop an iterative robust algorithm to jointly design the transmitter, relay, and receiver matrices to minimize the maximal mean-squared error (MSE) of the signal waveform estimation among all receivers. Then, we derive the optimal structure of the relay precoding matrix and show that the MSE at each receiver can be decomposed into the sum of the MSEs of the first-hop and second-hop channels. Based on this MSE decomposition, we develop a simplified transceiver design algorithm with a low computational complexity. Numerical simulations demonstrate the improved robustness of the proposed transceiver design algorithms against the mismatch between the true and estimated channels. Interestingly, compared with the iterative algorithm, the simplified transceiver design has only negligible performance loss with significantly reduced computational complexity.

Wireless Information and Power Transfer in Kth Best Relay Selection Systems with Energy Beamforming over Nakagami-m Fading Channels

In this paper, we propose and analyze an amplify-and-forward relaying energy harvesting system with Kth best partial relay selection and energy beamforming over Nakagami-m fading channels. The Kth best relay is selected based on criteria such as the Kth best first-hop channel gains (KBFC scheme) and the Kth best second-hop channel gains (KBSC scheme). Both the time-switching relaying and power-splitting relaying protocols are examined. To evaluate the system performance, we derive analytical expressions for the outage probability and throughput in both the delay-limited transmission (DLT) and delay-tolerant transmission (DTT) modes. Then the optimal values of these throughput are determined. The DLT mode is considered in two optimal cases: global-optimal DLT (GODLT), where an optimal pair of the source rate and energy-harvesting ratio is employed, and local-optimal DLT (LODLT), where only optimal energy-harvesting ratio is used. Monte Carlo simulations are presented to corroborate our analysis. The results in terms of throughput show the following. (1) For the LODLT mode, at relatively low SNRs, the KBSC scheme outperforms the KBFC scheme except for \(K=1\). (2) For the DTT and GODLT modes, the KBSC scheme is more efficient than the KBFC scheme at high values of K. (3) When the signal quality increases, the throughput for the DTT and GODLT modes is significantly enhanced, whereas that for the LODLT mode reaches an upper limit.

Channel Estimation of MIMO Relay Systems With Multiple Relay Nodes

In this paper, we consider the channel estimation problem for multiple-input multiple-output wireless relay communication systems with multiple relay nodes. In particular, all individual channel matrices of the first-hop and second-hop links are estimated at the destination node by applying the superimposed channel training algorithm, where training sequences are superimposed at the relay nodes to assist the estimation of the relays-destination channel matrices. To improve the performance of channel estimation, we consider the estimation error inherited from the second-hop channel estimation and develop a new minimal mean-squared error-based algorithm to estimate the first-hop channel matrices. Furthermore, we derive the optimal power allocation and training sequences at the source and relay nodes. Numerical examples demonstrate a better performance of the proposed superimposed channel training algorithm.

Channel Estimation for Time-Varying MIMO Relay Systems

In this paper, we investigate the channel estimation problem for multiple-input multiple-output (MIMO) relay communication systems with time-varying channels. The time-varying characteristic of the channels is described by the complex-exponential basis expansion model (CE-BEM). We propose a superimposed channel training algorithm to estimate the individual first-hop and second-hop time-varying channel matrices for MIMO relay systems. In particular, the estimation of the second-hop time-varying channel matrix is performed by exploiting the superimposed training sequence at the relay node, while the first-hop time-varying channel matrix is estimated through the source node training sequence and the estimated second-hop channel. To improve the performance of channel estimation, we derive the optimal structure of the source and relay training sequences that minimize the mean-squared error (MSE) of channel estimation. We also optimize the relay amplification factor that governs the power allocation between the source and relay training sequences. Numerical simulations demonstrate that the proposed superimposed channel training algorithm for MIMO relay systems with time-varying channels outperforms the conventional two-stage channel estimation scheme.

Opportunistic Cooperative Channel Access in Distributed Wireless Networks With Decode-and-Forward Relays

This letter studies distributed opportunistic channel access in a contention-based wireless network with decode-and-forward relays. If a source wins a contention, the channel state information in the first-hop channel is estimated, and a decision is made for the winner source to either give up the transmission opportunity and let all sources start a new contention, or transmit to the relay. Once the relay gets the traffic, it may have a sequence of probings of the second-hop channel. The optimal decision strategies for the two hops are derived in this letter. Simulation results show that our scheme is beneficial when second-hop channels have larger average signal-to-noise ratio.

Outage probability of fixed-gain dual-hop relay selection channels with heterogeneous fading

In this paper, we develop a framework that can be used to analyze the outage probability of a dual-hop fixed-gain amplify-and-forward relay system performing single relay selection. We consider three selection strategies: (1) first-hop selection, whereby the relay is chosen to maximize the signal-to-noise ratio (SNR) at the relay irrespective of the second-hop channels; (2) second-hop selection, in which the relay is chosen such that the second-hop SNR is maximized; and (3) dual-hop selection, where the end-to-end SNR is maximized. The proposed analytical framework is capable of treating systems operating in heterogeneous fading conditions, where all or a subset of the source-relay and relay-destination channels has non-identical distributions or even experience completely different fading processes. We apply the framework to calculate new exact series representations of the outage probability for the three aforementioned cases of relay selection when all channels adhere to the Nakagami-m model. Our analysis is corroborated by simulations. Finally, we provide a discussion of how the proposed framework can be applied to analyze other fading configurations using the techniques detailed herein.

Performance of Multiuser Mixed RF/FSO Relay Networks with Generalized Order User Scheduling and Outdated Channel Information

The generalized order user scheduling is among the efficient user selection schemes which can be used in conditions where the opportunistic scheduling could fail. The opportunistic scheduler could erroneously select a user other than the best user for data transmission or reception due to imperfect channel estimation or outdated channel information issues. In this paper, we study the performance of multiuser mixed radio frequency (RF)/free-space optical (FSO) relay network with generalized order user scheduling. Due to its importance on the system performance, the outdated channel information problem is also addressed in this paper. The considered system includes K sources or users, one decode-and-forward relay and one destination. The users are connected with the relay node through RF links, and the relay is connected with the destination through an FSO link. In the analysis, the first-hop channels are assumed to follow Rayleigh fading model and the second-hop channel is assumed to follow Gamma–Gamma fading model including the effect of pointing errors. Closed-form expressions are derived for the outage probability, average symbol error probability and ergodic channel capacity. Moreover, in order to get more insights about the system behavior, the system is studied at the high signal-to-noise ratio regime where the diversity order and coding gain are provided and studied. Monte Carlo simulations are given to validate the achieved exact and asymptotic results. Main findings illustrate that under weak atmospheric turbulence conditions, the system performance is dominated by the RF links and a diversity order of K − N + 1 is achieved by the system, whereas under sever atmospheric turbulence conditions, the system is dominated by the FSO link and the diversity order is related to the minimum value of the turbulence fading and pointing error parameters.

The Degrees of Freedom of Two-Unicast Layered MIMO Interference Networks With Feedback

Two-unicast layered interference networks under the Shannon feedback and limited Shannon feedback settings are studied from a degrees of freedom (DoF) perspective. The main focus is on the archetypal two-hop multiple-input, multiple-output (MIMO) $(M,N)\, \times \, (M,N) \,\times \, (M,N) $ network, denoted here as the $(M,N)^{3}$ network, which is a layered two-unicast network with two transmitters, two relays, and two receivers, with the first hop network between the transmitters and the relays, and the second hop network between the relays and the receivers, both being MIMO Gaussian interference channels. In particular, the first transmitter–receiver pair and the first relay have $M$ antennas each and the second transmitter–receiver pair and the second relay having $N$ antennas each. The (full) Shannon feedback setting for the $(M,N)^{3}$ network is one in which the transmitters have delayed knowledge of the first and second hop channel coefficients and the relay and destination outputs and the relays have delayed knowledge of the second hop channel coefficients and destination outputs. The DoF region under this setting is established. A key result in this paper shows that this Shannon feedback DoF region can in fact be achieved with much less side information—under what we refer to as the limited Shannon feedback setting—wherein the transmitters have no channel state or output feedback whatsoever and only the $M$ -antenna relay (assuming $M \geq N$ ) has delayed knowledge of the coefficients of the second-hop channel and of only the received signal of the $N$ -antenna receiver. For this limited Shannon feedback setting, the DoFs region of the $(M,N)^{3}$ network is established by introducing a retro-cooperative interference alignment scheme. These DoF region results for the $(M,N)^{3}$ network with feedback are also extended to more general layered interference networks including the two-unicast $l$ -hop layered networks as well as layered networks with more general numbers of antennas at the various terminals.