Two-hop Channel Research Articles

On the Capacity of M-ary ASK Two-Hop Channel With Finite Battery Energy Harvesting Relay

On the Capacity of <i>M</i>-ary ASK Two-Hop Channel With Finite Battery Energy Harvesting Relay

Estimation of Dispersive High-Doppler Channels in the RIS-Aided mmWave Internet of Vehicles

Reconfigurable intelligent surfaces (RISs) have emerged as a promising candidate for improving the spectral-and energy-efficiency of millimeter-wave (mmWave) Internet of vehicles (IoV) communications, but the conception of their accurate channel estimation poses. Hence the existing estimation methods mainly focus on time-invariant channels, while ignoring the Doppler effect induced by the high-velocity vehicles, which will lead to significant performance degradation. In this paper, we investigate the problem of channel estimation in RIS-aided mmWave IoV systems considering the deleterious Doppler effect. Firstly, we derive the expression of the time-varying cascaded two-hop multiple-path channels, where each delay tap is subject to multiple paths instead of having a simple one-to-one correspondence. In order to decouple the paths, the problem is formulated in the delay-domain by a series of transformations and the cascaded two-hop channel can be estimated at each delay tap. Then we propose a pair of estimation strategies by considering different hardware constraints depending on the number of receiver antennas at the base station (BS). When a large receiver array is employed at the BS, we can exploit its high angular selectivity for distinguishing each resolvable path at a certain delay tap because they arrive from different directions. However, this cannot be achieved for small arrays, given their more limited angular resolution. Thus, the RIS reflection patterns are delicately designed for distinguishing multiple resolvable paths. After separating the paths, Doppler estimation can be performed by calculating the phase difference of the adjacent symbols. Our simulation results demonstrate the superior performance of the proposed methods within a wide range of Doppler shifts.

Wideband Channel Estimation for IRS-Aided Systems in the Face of Beam Squint

Intelligent reflecting surfaces (IRSs) improve both the bandwidth and energy efficiency of wideband communication systems by using low-cost passive elements for reflecting the impinging signals with adjustable phase shifts. To realize the full potential of IRS-aided systems, having accurate channel state information (CSI) is indispensable, but it is challenging to acquire, since these passive devices cannot carry out transmit/receive signal processing. The existing channel estimation methods conceived for wideband IRS-aided communication systems only consider the channel's frequency selectivity, but ignore the effect of beam squint, despite its severe performance degradation. Hence we fill this gap and conceive wideband channel estimation for IRS-aided communication systems by explicitly taking the effect of beam squint into consideration. We demonstrate that the mutual correlation function between the spatial steering vectors and the cascaded two-hop channel reflected by the IRS has two peaks, which leads to a pair of estimated angles for a single propagation path, due to the effect of beam squint. One of these two estimated angles is the frequency-independent `actual angle', while the other one is the frequency-dependent `false angle'. To reduce the influence of false angles on channel estimation, we propose a twin-stage orthogonal matching pursuit (TS-OMP) algorithm.

Tensor-Based Algebraic Channel Estimation for Hybrid IRS-Assisted MIMO-OFDM

We consider the channel estimation problem in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems assisted by intelligent reconfigurable surfaces (IRSs). To avoid the inherent estimation ambiguities of the two-hop channels from mobile stations (MS) to the base station (BS), we adopt a hybrid IRS architecture composed of passive reflectors and active sensors, and establish two independent subproblems of estimating the MS-to-IRS and BS-to-IRS channels. By leveraging the sparse characteristics of high-frequency propagation, we model the training signals as multi-dimensional canonical polyadic decomposition (CPD) tensors with missing fibers or slices. We develop algebraic algorithms to solve the tensor completion problems and recover channel multipath parameters, i.e., angles of arrival, time delays and path gains. Our methods require neither random initialization nor iterative operations, and for these reasons they can perform robustly with a low computational complexity. Moreover, we investigate the uniqueness condition of CPD tensor completion, which can be utilized to inform both the physical design of hybrid IRSs and the time-frequency resource allocation of training strategies. Simulation results indicate that the proposed schemes outperform the traditional counterparts in terms of accuracy, robustness and complexity, especially for the case of low-complexity IRSs with limited number of active sensing elements.

On Uplink Performance of Multiuser Massive MIMO Relay Network With Limited RF Chains

This paper considers a multiuser massive multiple-input multiple-output uplink with the help of an analog amplify-and-forward relay. The base station equips a large array of $N_d$ antennas but is supported by a far smaller number of radio-frequency chains. By first deriving new results for a cascaded phase-aligned two-hop channel, we obtain a tight bound for the ergodic rate in closed form for both perfect and quantized channel phase information. The rate is characterized as a function of a scaled equivalent signal-to-noise ratio of the two-hop channel. It implies that the source and relay powers can be respectively scaled down as $1/N_d^a$ and $1/N_d^{1-a}\, (0\!\leq \!a\!\leq \!1)$ for an asymptotically unchanged sum rate. Then for the rate maximization, the problem of power allocation is optimized with closed-form solutions. Simulation results verified the observations of our derived results.

Jamming-Resilient Frequency Hopping-Aided Secure Communication for Internet-of-Things in the Presence of an Untrusted Relay

In this paper, we propose a light-weight jamming-resistant scheme for the Internet-of-Things (IoT) in 5G networks to ensure high-quality communication in a two-hop cooperative network. In the considered system model, a source communicates with a destination in the presence of an untrusted relay and a powerful multi-antenna adversary jammer. The untrusted relay is an authorized necessary helper who may wiretap the confidential information. Meanwhile, the jammer is an external attacker who tries to damage both the training and transmission phases. Different from traditional frequency hopping spread spectrum (FHSS) techniques that require a pre-determined pattern between communicating nodes, in our scheme, the source and destination enjoy the local observations of the two-hop channels. Then they exploit the measured channel as the source of common randomness to generate shared secret keys. By collecting multiple time slots into a frame, the sequence of channels observed in each frame is utilized to specify the adopted FHSS sequence in the next frame. Based on the derived FHSS sequence from the key generation phase, the source starts to transmit its message supporting by the the destination-assisted cooperative jamming (DACJ) technique which prevents the untrusted relay from discovering the secret message. For the mentioned system model, we present new closed-form expressions for characterizing the achievable secret key rate (SKR) and ergodic secrecy rate (ESR) to highlight the efficiency of our proposed scheme compared to the state-of-the-art. We next determine the optimal power allocation (OPA) between the pilot and data transmission phases that maximizes the ESR performance while escaping from jamming attack. Finally, several numerical examples and discussions are presented to gain engineering insights behind the studied communication scenario.

Security Optimization of Two-Hop AF Cooperative Relay Network

In a two-hop cooperative relay network under eavesdropping environment, selecting the appropriate relay node forwarding information can improve the security performance of the system. Traditional relay selection depends on the channel condition of the two-hop link acquired through feedback to select the optimal relay node, ignoring the possible feedback delay of the system during relay selection moment and data transmission moment and inevitably causing the system security performance decline. With this in mind, this paper aims at improving the security transmission performance of the system, considering the condition of two-hop link channel of AF secure cooperative network combined with the maximum posterior probability criterion to weaken the influence of feedback delay to the relay selection, thus improving the security performance of the system. The simulation results shows that, with the improved optimal relay selection strategy based on the maximum posterior probability criterion, the reliability of relay selection is improved, and the system security performance is better.

Two-Stage Single-Relay Channel Model for In-Home Broadband PLC Systems

This paper discusses the two-stage single-relay channel model for in-home broadband power line communication links with up to two hops. This channel model consists of the concatenation of two single-relay channels that can result in eight configurations; however, only five of them are analyzed in this work since they cover up to one relay availability. In this context, a discussion addressing both amplify-and-forward and decode-and-forward cooperative protocols at relay node and maximal ratio combining at destination node is carried out. As the power line channels are frequency selective, the attenuation profile increases along with both distance and frequency, and the additive noise is colored, we discuss achievable data rate analyses using a data set covering the frequency band from 1.7 to 100 MHz, under sum power constraint. Based on the attained results, we state that the two-stage single-relay channel model is the best option for in-home broadband power line communication systems when the source-to-destination link is severely degraded (e.g., high signal attenuation and/or high-power noise presence), while the two-hop channel model is more appropriate when the channel degradation is not severe. Moreover, we show that the single-relay channel model may be remarkably outperformed by the two-stage single-relay channel model.

Secure Transmission on the Two-Hop Relay Channel With Scaled Compute-and-Forward

In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

Channel Estimation for Full-Duplex Relay Systems With Large-Scale Antenna Arrays

The large-scale multiple-input multiple-output system with full-duplex relay is a promising candidate for future mobile communication systems, where accurate channel estimation is very challenging due to interference. In this paper, we address two channel estimation problems for such systems: individual estimation, where both the base station (BS) and the relay estimate their respective channels, and cascaded estimation, where only the BS estimates the cascaded two-hop channel. For the BS, we propose an estimator that exploits the sparsity and slowly varying nature of the channel in the beam domain. Then, we analyze the probability of correctly distinguishing the desired and interfering direct-link channels. For the relay, we present an estimator that simultaneously estimates both the source-to-relay and self-interference channels based on the expectation–maximization algorithm. The performance of this estimator is also analyzed. Numerical results demonstrate the excellent performance of the proposed channel estimators and corroborate the analysis results.

Energy Efficient Relaying in Multiantenna Two-Hop Channels With Imperfect CSI

In this letter, we investigate robust beamforming to improve the energy efficiency (EE) of a relaying system where only imperfect channel state information (CSI) is available at the relay. Specifically, from the perspective of worst-case robustness, we focus on the robust energy efficient relay beamforming optimization under the norm bounded channel error model. We equivalently transform the complicated primal robust fractional optimization problem into a one-dimensional search, which admits a unique globally optimal solution. In particular, based on this optimal solution, we further obtain explicit asymptotic closed-form results under various specific scenarios of interest.

Energy Harvesting Networks With Energy Cooperation: Procrastinating Policies

This paper considers multiterminal networks with energy harvesting transmitter nodes that are also capable of wirelessly transferring energy to or receiving energy from other nodes in the network. In particular, the jointly optimal transmit power and energy transfer policies that maximize sum-throughput for the two-way, two-hop, and multiple access channels are identified. It is shown for nodes with infinite-sized batteries that delaying energy transfers until energy is needed immediately at the receiving node is sum-throughput optimal. Focusing on such procrastinating policies without loss of optimality, the stated joint optimization problem can be decomposed into energy transfer and consumed energy allocation problems which are solved in tandem. This decomposition is shown to hold for the finite-sized battery case as well, using partially procrastinating policies that avoid battery overflows. It is observed that for the two-hop channel, the proposed algorithm has a two fluid water-filling interpretation, and for the multiple access channel, it reduces to a single transmitter problem with aggregate energy arrivals. Numerical results demonstrate the throughput improvement with bi-directional energy cooperation over no cooperation and uni-directional cooperation.

Achievable Rate Analysis and Feedback Design for Multiuser MIMO Relay with Imperfect CSI

This paper investigates a multiuser MIMO relay downlink system with imperfect channel estimation and limited feedback. We analyze the achievable rate loss due to channel state information (CSI) mismatch arising from both channel estimation and quantization feedback. We first derive an upper bound to characterize the effect of imperfect CSI, and then present a limited feedback strategy for both the two-hop channels in the relay system. This newly presented feedback strategy reveals the relationship among the CSI quantization levels, the transmit power, and the pilots for channel estimation. An optimized pilot design at the base station and the relay is also presented by applying the derived bounds for the two-hop system.

Asymptotic SEP of MIMO beamforming in two-hop AF relaying systems

This paper derives an asymptotic average symbol error probability (SEP) expression for multipleinput multiple-output (MIMO) two-hop amplify-and-forward (AF) relay systems with optimal beamforming. The analysis at high signal-to-noise ratio (SNR) quantifies the diversity order and array gain, which are valid for any antenna numbers of the terminals and arbitrary channel fading models. It is also proved that the system performance is dominated by the relatively degraded one of the two-hop channels. Our results based on the simple expressions provide valuable insights into the performance and practical design considerations of MIMO AF networks.

Relay selection with transmit precoding design for multiple-input multiple-output amplify-and-forward relay network

By employing the amplify-and-forward relaying strategy, a relay selection method with simplified precoding is proposed for two-hop multi-relay channels. The proposed method consists of two parts. In the first part, the authors present an optimal beamforming scheme with full channel state information (CSI) and derive a simplified and analytic expression for the output SNR through each relay, thereby selecting the best relay. The second part considers the transmiit precoding problem with the CSI known to the receiver only and provide a selection strategy with Grassmannian beamforming. The new algorithm chooses only one relay based on the maximal received SNR to assist in transmission. It can significantly reduce the system consumption, achieve excellent bit-error-rate and average throughput and maintain full diversity order. Simulation results demonstrate that the performance of the proposed schemes with low complexity approaches towards the optimal iteration method. For practical situations with a distance attenuation factor, the performance gain of the authors schemes is also evident.

Multimode Antenna Selection for MIMO Amplify-and-Forward Relay Systems

Obtaining the most from multiple-antenna relay systems requires algorithms that configure the source and relay adaptively to instantaneous channel conditions. In this paper, we define an antenna selection mode of operation as the number of selected transmit antennas at the source (which is equal to the number of data substreams), the substream-to-antenna mapping at the source, the number of selected transmit antennas at the relay, and the substream-to-antenna mapping at the relay. We develop dualmode and multimode antenna selection algorithms to choose the mode that is most likely to deliver the lowest vector symbol error rate assuming the overall data rate is fixed. The effective condition numbers of both the two-hop channel and the relay channel are derived to give intuition on how the spatial characteristics of the constituent channels affect mode selection and to derive low complexity algorithms. Link-level simulations show that our proposed algorithms usually select the best mode, thus improving the diversity performance of spatial multiplexing relay systems and providing array gains over the existing single-stream relay transmission strategies. The two-hop multimode algorithms are shown by system-level simulations to improve the reliability of transmission and extend spatial multiplexing capability to cell-edge users in a multi-cell network.

Comparison of Channel Estimation Protocols for Coherent AF Relaying Networks in the Presence of Additive Noise and LO Phase Noise

Channel estimation protocols for wireless two-hop networks with amplify-and-forward (AF) relays are compared. We consider multiuser relaying networks, where the gain factors are chosen such that the signals from all relays add up coherently at the destinations. While the destinations require channel knowledge in order to decode, our focus lies on the channel estimates that are used to calculate the relay gains. Since knowledge of the compound two-hop channels is generally not sufficient to do this, the protocols considered here measure all single-hop coefficients in the network. We start from the observation that the direction in which the channels are measured determines (1) the number of channel uses required to estimate all coefficient and (2) the need for global carrier phase reference. Four protocols are identified that differ in the direction in which the first-hop and the second-hop channels are measured. We derive a sensible measure for the accuracy of the channel estimates in the presence of additive noise and phase noise and compare the protocols based on this measure. Finally, we provide a quantitative performance comparison for a simple single-user application example. It is important to note that the results can be used to compare the channel estimation protocols for any two-hop network configuration and gain allocation scheme.

Analog Network Coding Mappings in Gaussian Multiple-Access Relay Channels

We consider the multiple-access relay channel with two source nodes, one relay node and one destination node. For practical simplicity, we consider orthogonal transmission of the source messages and half-duplex relaying. We also assume that the relay is memoryless and is implemented based on a two-to-one deterministic mapping. Our focus is on proposing and investigating such mappings. Essentially, the proposed relaying functions combine the two incoming analog signals and forward them to the destination, thus we term them as analog network coding mappings. Both linear and non-linear relaying are investigated for the multiple-access relay channel and the special case of the multiple-access two-hop channel. In particular, we suggest to use mappings based on the Archimedean spiral for analog non-linear combining. In addition, we propose to couple spiral mappings with sawtooth-like mappings to exploit the potential side information provided by the direct links of the multiple-access relay channel. In the case of symmetric topology, our proposed scheme can be seen as an extension to the amplify-and-forward scheme, where the asymmetric input/output dimensionality in the relay node is handled before amplifying. We investigate the resulting achievable rate regions and sum rates, and demonstrate significant gains over conventional relaying schemes.

A novel channel assignment scheme for improving channel reuse efficiency in multi-channel ad hoc wireless networks

How to increase channel reuse efficiency is one of the most important issues in wireless cellular networks. Recently, many multi-channel MAC protocols have been proposed for ad hoc wireless networks. However the channel assignment schemes used in these protocols do not consider the issue of channel reuse. The channel assignment schemes only let a mobile host select a channel from the channels which are not currently being used by its one-hop neighbors. To form a channel reuse pattern, the mobile host should consider its two-hop channel usage and select a channel which is been used by its two-hop neighbors. In this paper, we propose a novel channel assignment scheme for improving the channel reuse efficiency. By overhearing control packets of one-hop neighbors, a host can easily know the channel condition within the range of two-hop hosts and then select a suitable transmitting/receiving data channel to form the better reuse pattern. To enhance the probability of forming channel reuse pattern, we propose a backoff counter adjustment scheme such that a host with more channel information can transmit control packets early than with less channel information. We verify the performance of our protocol via simulations and give some comments on the simulation results.