Estimate-and-forward Research Articles

Generalized Khatri-Rao and Kronecker space-time coding for MIMO relay systems with closed-form semi-blind receivers

In this paper, we propose two new space-time (ST) coding schemes for multiple-antenna signalling based on multiple Khatri-Rao and Kronecker products of symbol matrices, denoted MKRST and MKronST codings, respectively. These new coding schemes generalize the standard Khatri-Rao coding by introducing extra space/time diversities due to a mutual space-time spreading of the transmitted data streams, induced by Khatri-Rao and Kronecker products between symbol matrices. Parallel non-iterative decoding methods are proposed for estimating each symbol matrix. We consider a one-way two-hop multi-input multi-output (MIMO) relay system using the MKRST and MKronST codings at both the source and relay nodes, and three different relaying protocols, namely, amplify-and-forward (AF), decode-and-forward (DF) and estimate-and-forward (EF). For the DF and EF protocols, the channel and symbol estimation is split into two successive phases, one at the relay and the other one at the destination. Exploiting parallel factor (PARAFAC) models for the tensors of signals received at the relay and the destination, closed-form semi-blind receivers are derived for joint symbol and channel estimation. System parameters identifiability is also discussed, and the computational cost of the proposed receivers and decoders is detailed. Monte Carlo simulation results are provided to assess the performance of the proposed coding schemes, and semi-blind receivers.

Estimate-and-Forward Relaying in Diffusion-Based Molecular Communication Networks: Performance Evaluation and Threshold Optimization

In this paper, we propose and investigate an estimate-and-forward (EF) relaying scheme with half-duplex transmission protocol in a two-hop diffusion-based molecular communication (DMC) system under the influence of both residual and counting noises. The proposed relaying scheme forwards an estimate of the transmitted number of molecules, which is derived using maximum likelihood principle. Based on this estimate, we assess the performance of EF relaying in terms of molecular throughput and end-to-end error probability. Further, we calculate energy consumption in synthesizing the information molecules at the relay nanomachine. Thereafter, we optimize the detection threshold by solving the convex optimization problem using logarithmic barrier followed by modified Karush-Kuhn-Tucker conditions, Newton Raphson method, and finally rounding the solution to the nearest integer value. Numerical and simulation results show the improvement in molecular throughput when EF relaying scheme is employed in contrast to the baseline direct communication scheme. The systematic comparisons reveal the scenarios where EF scheme can be beneficial over the existing amplify-and-forward and decodeand-forward relaying schemes. Moreover, we examine the effect of various parameters on error performance of the considered DMC system. Eventually, we demonstrate the effectiveness of our optimization solution in terms of accuracy and convergence time.

Joint Estimation of Time, Frequency Offsets, and Channel Gains With ICIs in EF Multi-relay DMIMO-OFDM System

The cooperative communication or distributed multiple-input multiple-output (DMIMO) system, combined with orthogonal frequency division multiplexing (OFDM), is considered as an emerging paradigm for link reliability, high data rate, and coverage extension in fifth-generation (5G) wireless communication systems. The DMIMO system employs multiple relays with single or multiple antennas that opportunistically form virtual antenna array (VAA) in between the source and destination. Moving to the DMIMO-OFDM system from the conventional network with uncoordinated nodes requires robust synchronization and tracking. The signal received at the destination is characterized by multiple timing offsets (MTOs), multiple carrier frequency offsets (MCFOs), and frequency-selective channel gains. In this paper, we address the issue of joint time frequency and channel gain estimation for the estimate-and-forward (EF) relaying protocol. EF is a cost-effective solution but provides coarse estimation at the relays introducing intercarrier interferences (ICIs). OFDM system is very sensitive to the ICIs. We propose two iterative estimators: expectation conditional maximization (ECM) and space-alternating generalized expectation maximization (SAGE) to jointly estimate MTOs, MCFOs, and channel gains in the presence of ICIs. The robustness of the estimators is analyzed through mathematical formulation and simulations. The performances of the estimators are measured in terms of mean square error (MSE) and bit error rate (BER). The MSE performance is further verified with the theoretical Cramer–Rao lower bound (CRLB) derived. Simulation results show that the proposed estimators provide a significant performance gain in the DMIMO-OFDM system with MIMO configuration at the relays compared to the single-input single-output (SISO) system.

A novel forwarding method for full-duplex two-way relay networks

An estimate-and-forward (EF) scheme for single-input single-output (SISO) and multiple-input multiple-output (MIMO) full-duplex two-way relay networks is proposed and analyzed. The relay estimates the received signal from two terminal nodes by a minimum mean squared error (MMSE) estimation and forwards a scaled version of the MMSE estimate to the destination. The proposed EF outperforms conventional amplify- and-forward (AF) and decode-and-forward (DF) across all signal-to-noise ratio (SNR) region. Because its computational complexity is high for relays with a large number of antennas (large MIMO) and/or high order constellations, an approximate EF scheme, called list EF, are thus proposed to reduce the computational complexity. The proposed list EF computes a candidate list for the MMSE estimate by using a sphere decoder, and it approaches the performance of the exact EF relay at a negligible performance loss. The proposed forwarding approach also could be used to other relay networks, such as half-duplex, one-way or massive MIMO relay networks.

Joint Frequency Offset and Channel Estimation in Distributed MIMO-OFDM Systems

In recent times, cooperative communications or distributed multi-input multi-output (DMIMO) systems are being considered as key enabler for increasing spectral efficiency and coverage area in 4G and beyond wireless communication system. DMIMO system employs multiple relays each with single or multiple antennas in between the source and destination to form a virtual antenna array. However, a few of the fundamental difficulties in deployment of DMIMO networks with coherent communications are synchronization, tracking of independent oscillators, and channel estimation. The signal received at the destination is characterized by multiple carrier frequency offsets (MCFOs) and MIMO channel effects due to sparsely distributed relay nodes. In this paper, we address the issue of joint estimation of frequency offset and channel gains in a DMIMO orthogonal frequency division multiplexing (OFDM) systems deploying multiple antennas at the relays. We consider estimate-and-forward (EF) protocol for relaying where the coarse estimation process at the low cost relays generates inter carrier interference (ICI) in a multi-carrier system resulting in severe performance degradation and decrease in reliability of the network. The two iterative estimators, expectation conditional maximization (ECM) and space-alternating generalized expectation maximization (SAGE), are proposed to jointly estimate MCFOs and channel in the presence of ICI. The robustness of the estimators are evaluated through mathematical analysis and validated using simulations. The performance of the estimators is measured in terms of mean square error (MSE) and bit error rate (BER). Simulation results show that the proposed estimators provide a significant performance gain in DMIMO-OFDM systems with MIMO configuration at the relays compared to single-input single-output (SISO) system.

A Hybrid EF/DF Protocol With Rateless Coded Network Code for Two-Way Relay Channels

In this paper, we investigate a rateless code design for a two-time slot two-way relay channel (TWRC), where network coding operation is employed at the relay. Rateless codes are used at both users and the relay nodes as they can cope with various channel conditions. We consider a general TWRC framework, where the two users may use different rateless code generator matrices, thus, the relay cannot directly recover the physical-layer network coded (PNC) message of the two users. We propose a hybrid estimate and forward (EF)/decode and forward (DF) protocol with rateless codes for the TWRC. In the proposed scheme, the relay uses a joint belief propagation decoding process to decode the messages of two users. Depending on whether the relay recovers both users’ messages, only one user’s message or no users’ messages, the relay will generate three different types of signals, namely, NC, soft NC, and soft PNC, respectively. We design the degree distributions of the rateless codes for the three nodes of the TWRC, to make them suitable not only for decoding at two users at high signal-to-noise ratio (SNR), but also for decoding at the relay at low SNR. We show that the proposed hybrid EF/DF protocol with the designed rateless codes outperforms other schemes significantly in terms of bit error rate performance.

ECM and SAGE based joint estimation of timing and frequency offset for DMIMO–OFDM system

Distributed multiple-input multiple-output (DMIMO) technology is a key enabler of coverage extension and enhancement of link reliability in wireless networks through distributed spatial diversity. DMIMO employs classic relay channels in between the source and the destination to opportunistically form a virtual antenna array (VAA) for emulating cooperative diversity. Use of multiple antennas at the relays further increases capacity and reliability of the relay–destination channel through multiplexing and diversity of MIMO antennas respectively. In such network, the signal received at the destination is characterized by multiple timing offsets (MTO) due to different propagation delay and multiple carrier frequency offsets (MCFO) due to independent oscillators of the relays. Hence, synchronization becomes a crucial issue in DMIMO in order to realize the distributed coherence. In this paper, we address joint estimation of MCFO and MTO in DMIMO orthogonal frequency division multiplexing (OFDM) with MIMO configuration at the relays for estimate-and-forward (EF) relaying protocol. Two iterative algorithms, based on expectation conditional maximization (ECM) and space alternating generalized expectation–maximization (SAGE) are proposed for joint estimation in presence of inter carrier interference (ICI). The robustness of both the estimators to ICI is evaluated by mathematical analysis and supported by extensive simulations. The performance of the proposed estimators is assessed in terms of mean square error (MSE) and bit error rate (BER). The theoretical Cramer–Rao lower bound (CRLB) of estimator error variance is also derived.

Compressive Soft Forwarding in Network-Coded Multiple-Access Relay Channels

In this paper, we design a novel estimate-and-forward (EF) protocol in multiple-access relay channels (MARCs) where two correlated sources transmit their information to the common destination with the help of a relay. With the application of network coding (NC) at the relay, the network-coded soft symbols contain redundant information due to the correlated sources, which can be compressed before being forwarded. Specifically, we first derive the value of the network-coded soft symbol by considering the correlation of the two sources. Due to this correlation, the majority of soft symbol values are close to one. Then, we convert network-coded soft symbol vector into a sparse vector, which is suitable for compression by using the compressive sensing (CS). Next, we analyze the performance of the proposed EF protocol by comparing the soft symbol value and received signal-to-noise ratio (SNR) with the conventional EF protocol. Simulations show that our protocol can achieve the same bit error rate (BER) as the conventional EF protocol with proper compression rates, and it consumes much less transmission time due to the compression.

Half-Duplex Relaying Strategy Suitable for a Relay with Mobility

We propose a new time-division half-duplex estimate-and-forward (EF) relaying strategy suitable for a relay with mobility. We reconfigure EF relaying to guarantee a strong relay-destination link which is required to achieve a high rate using EF relaying. Based on the reconfigured model, we optimize the relaying strategy to attain a high rate irrespective of the relay position with preserving the total transmit bandwidth and energy. The proposed relaying strategy achieves high communication reliability for any relay position, which differs from conventional EF and decode-and-forward (DF) relaying schemes.

Detectors for Estimate-and-Forward Wireless Relay Networks

Relay radios are used to improve the quality of point-to-point wireless links with respect to achievable rates and symbol error rates (SER). Under these metrics, the estimate-and-forward (EF) protocol has the best performance in a wide variety of cases. The EF protocol is defined as the relaying protocol in which the relay forwards an estimate of its received information. Although optimal estimates have been identified in the literature, an implementable detector at the receiver still remains to be found. In this paper, we solve this open problem by using a piecewise linear approximation of the minimum mean square error (MMSE) estimate (pLAM) of the received symbol at the relay. In the three-node cooperative wireless relay network, this new piecewise linear approximation leads to an analytical form of the detector at the destination. Furthermore, we show that the symbol error rates of this new framework closely approximate the true performance of EF when using a MMSE estimate of the received symbol at the relay. Finally, we provide several examples where we apply this new pLAM approach to multiple modulation schemes such as BPSK and 16-QAM, in both one- and two-way relay networks.

Soft forwarding technique for unitary space‐time modulation

The authors propose two soft forwarding schemes for unitary space-time modulation, namely estimate-and-forward (EF) and mutual information-based forwarding (MIF), which are ideally suited for rapid piecewise-constant fading scenarios with no channel state information both at transmitters and receivers. In the EF scheme, the relay regenerates signal via the conditional expectation of the source unitary space-time (UST) signal given the received matrix at the relay node instead of hard decisions. The MIF scheme employs the instantaneous mutual information between the source UST signal and received matrix at the relay node as a measurement for maximum-likelihood detection. The authors provide the relay forwarding functions, the normalisation factors, and the detection methods at the destination firstly. Above all, the generalised signal-to-noise ratio (SNR) at the destination for our unitary space-time modulated relaying system is analysed and simulated firstly. Simulation results reveal that the proposed EF and MIF schemes can outperform the existing amplify-and-forward (AF) and detect-and-forward (DF) schemes in terms of bit-error-rate performances in most scenarios. For a parallel relay network with two relays, the proposed EF scheme achieves 2 and 3 dB SNR gain over AF and DF schemes, respectively. Moreover, the MIF scheme can further give about 1.5 dB SNR gain.

Communication Protocols for N-way All-Cast Relay Networks

We consider communication protocols for N-way all-cast relay networks, which comprise N source terminals such that each source terminal demands messages from all other source terminals with the help of a relay. The derived protocols are characterized by the fact that physical layer network coding is employed at the relay, where each source has side information about the signals it has sent. Amplify-and-forward (AF) and decode-and-forward (DF) protocols are applied to the N-way relay network setting, where the achievable rate regions for those protocols are derived and compared with outer capacity bounds. We propose several practical space-time coding schemes for AF and DF, and introduce two new protocols denoted as denoise-and-forward (DNF) and estimate-and-forward (EF). Further, for AF and DF the fundamental diversity-multiplexing trade-off is characterized.

시분할 반이중 추정 후 전달 릴레이 시스템 설계

본 논문에서는 시분할 반이중 릴레이 통신 시스템을 위한 추정 후 전달 (EF: Estimate and Forward) 릴레이 프로토콜을 제안한다. 기존의 EF 릴레이 프로토콜은 릴레이와 수신국 간 채널 상태가 좋을 때 적용할 수 있는 방식으로 릴레이의 위치가 송신국으로 이동할수록 성능 저하가 크다. 그러나 본 논문에서 제안하는 EF 릴레이 프로토콜은 릴레이에서의 양자화 및 송신국-릴레이 간의 전력 배분 등과 같은 동작 파라미터가 채널 상태 및 변조 차수에 따라 가변적으로 정해지므로 모든 릴레이 위치에 대해 기존의 방식에 비해 낮은 전송 오류율을 보이며 릴레이가 수신국으로부터 멀리 떨어져 있는 경우에도 낮은 전송 오류율을 보인다. 따라서 본 논문에서 제안하는 방식은 릴레이의 위치가 수시로 변하는 이동 릴레이 시스템에 적합하다. 한편, 제안된 방식이 기존의 방식에 비해 모든 릴레이 위치에서 낮은 전송 오류율을 보임을 모의실험을 통해 확인하였다. In this paper, we propose a practical time-division half-duplex Estimate and Forward (EF) relaying protocol. The conventional EF relaying protocol works well only when the relay node is near the destination node. The proposed EF relaying protocol, however, determines adaptively relay parameters such as the quantization level of relay node and the power allocation between source and relay nodes according to the channel conditions. By doing so, the proposed EF relaying protocol provides low probability of bit error even when the relay node is far from the destination node. Consequently, the proposed EF protocol is suitable for the mobile relay systems. It is shown by simulations that the proposed EF relaying protocol shows lower bit error rate for all relay positions than a conventional EF protocol.

On the Diversity-Multiplexing Tradeoff of an Improved Amplify-and-Forward Relaying Strategy

The diversity-multiplexing tradeoff (DMT) is one of the most important criteria to evaluate the performance of wireless relay networks. Previous work shows that, compared to decode-and-forward (DF) and estimate-and-forward (EF) relaying protocols, amplify-and-forward (AF) achieves the worst DMT and cannot reach the DMT upper bound. In this paper, we propose a new relaying protocol, called dynamic AF (DAF), which allows the relay to adapt the receiving and forwarding time durations to the channel conditions. We show that DAF achieves the DMT upper bound when the multiplexing gain r is between 0 and α, where 0 <; α <; 0.5 is a constant set according to the relaying channel conditions.

Analysis of Instantaneous Power Distributions for Non-Regenerative and Regenerative Relaying Signals

In this paper, we analyze the instantaneous power distributions of the transmitting signals at the relay in the non-regenerative and regenerative cooperation scenarios with linear modulation. We study the following four relay function scenarios: fixed gain amplify and forward (AF) relay, variable gain AF relay, estimate and forward (EF) relay, and decode and forward (DF) relay. The analytical results show that the transmitting signals from non-regenerative relaying tend to suffer from high peak power, which is even prohibitive when the power amplifier (PA) efficiency at the relay is of primary concern.

Practical Quantizer Design for Half-Duplex Estimate-and-Forward Relaying

We propose a quantizer design method for practical half-duplex estimate-and-forward (EF) relaying. First, we identify the regime in which EF relaying yields substantial gains where the SNR is low and the relay-destination link is strong. Then we discover design simplifications that reduce complexity with little loss in the above regime. For relay quantizer design, we first consider mean-squared distortion minimization. To illustrate the unsuitability of the approach, we present an example with AWGN links and a BPSK source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate. A distortion-minimizing quantizer attempts to preserve the received signal at the relay. The quantizer should instead preserve source information. In information theoretical terms, the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint. The above conclusion, derived from information theoretical principles, is then translated to a quantizer design method for the low SNR regime. Using LDPC codes of blocklength 100000, BPSK modulation, and quantizers designed using the proposed criterion, we observe performance less than a decibel away from the achievable rate at a BER of 10-4.

Memoryless relay strategies for two-way relay channels

We propose relaying strategies for uncoded two-way relay channels, where two terminals transmit simultaneously to each other with the help of a relay. In particular, we consider a memoryless system, where the signal transmitted by the relay is obtained by applying an instantaneous relay function to the previously received signal. For binary antipodal signaling, a class of so called absolute (abs)-based schemes is proposed in which the processing at the relay is solely based on the absolute value of the received signal. We analyze and optimize the symbol-error performance of existing and new abs-based and non-abs-based strategies under an average power constraint, including abs-based and non-abs-based versions of amplify and forward (AF), detect and forward (DF), and estimate and forward (EF). Additionally, we optimize the relay function via functional analysis such that the average probability of error is minimized at the high signal-to-noise ratio (SNR) regime. The optimized relay function is shown to be a Lambert W function parameterized on the noise power and the transmission energy. The optimized function behaves like abs-AF at low SNR and like abs-DF at high SNR, respectively; EF behaves similarly to the optimized function over the whole SNR range. We find the conditions under which each class of strategies is preferred. Finally, we show that all these results can also be generalized to higher order constellations.

On the Role of Estimate-and-Forward With Time Sharing in Cooperative Communication

In this paper, we focus on the general relay channel. We investigate the application of the estimate-and-forward (EAF) relaying scheme to different scenarios. Specifically, we study assignments of the auxiliary random variable that always satisfy the feasibility constraints. We then consider the Gaussian relay channel with coded modulation, where we show that a three-level quantization outperforms the Gaussian quantization commonly used to evaluate the achievable EAF rates in this scenario. Last, we consider the cooperative general broadcast scenario with a multistep conference between the receivers. We first apply EAF to obtain a general achievable rate region with a multistep conference. We then use an explicit assignment for the auxiliary random variables to obtain an explicit rate expression for the single common message case with a two-step conference.

Code designs for cooperative communication

The goal of this article is to discuss the implementation of two cooperative protocols - decode-and-forward (DF) and estimate-and-forward (EF). In each case, the starting point is an information theoretic random coding scheme, which motivates a practical code construction. Low-density parity check (LDPC) codes are used as components in both protocols. In DF relaying, the problem boils down to a search for multi-rate LDPC codes that simultaneously perform well for the source-relay and the source- destination links. On the other hand, in EF relaying, the challenge is to design an efficient quantizer for forming a compressed estimate at the relay. The performance of each scheme is comparable to theoretical limits.

Optimal relay functionality for SNR maximization in memoryless relay networks

We explore the SNR-optimal relay functionality in a mernoryless relay network, i.e. a network where, during each channel use, the signal transmitted by a relay depends only on the last received symbol at that relay. We develop a generalized notion of SNR for the class of memoryless relay functions. The solution to the generalized SNR optimization problem leads to the novel concept of minimum mean squared uncorrelated error (MMSUE) estimation. For the elemental case of a single relay, we show that MMSUE estimate is a scaled version of the MMSE estimate. This scheme, that we call estimate and forward (EF), performs better than the best of amplify and forward (AF) and demodulate and forward (DF) in both parallel and serial relay networks. We determine that AF is near-optimal at low transmit power in a parallel network, while DF is near-optimal at high transmit power in a serial network. For hybrid networks that contain both serial and parallel elements, the advantage of EF over the best of AF and DF is found to be significant. Error probabilities are provided to substantiate the performance gain obtained through SNR optimality. We also show that, for Gaussian inputs, AF, DF and EF are identical