Compress-and-forward Research Articles

Relay‐assisted spectrum sensing

A cooperative spectrum-sensing problem has been considered here, in which a network of secondary users (SUs) assists a fusion centre (FC) in detecting the presence of a primary user (PU). Assuming communication links with unlimited capacity of the SUs and FC and known channel gains and noise variances, the optimal Neyman–Pearson detector is derived. Assuming limited capacity between the SUs and FC and unknown channel gains and noise variances, three different spectrum-sensing protocols have been studied; namely, amplify-and-forward (AF), compress-and-forward (CF) and detect-and-forward (DF), where each SU transmits an amplified or compressed version of its observed signal, or its local binary decision to the FC, respectively. The Edgeworth expansion is used to obtain novel expressions for the performance of these detectors. The theoretical analysis and numerical results show that the CF and OR detectors outperform the other proposed detectors. In addition, the simulation results show that the performance of the coded protocols (CF and DF) improves as the number of samples increases or as the noise variance at the SUs decreases, whereas such a behaviour cannot be guaranteed in the uncoded AF protocol.

A Unified Relay Framework With Both D-F and C-F Relay Nodes

Decode-and-forward (D-F) and compress-and-forward (C-F) are two fundamentally different relay strategies proposed by Cover and El Gamal in 1979. Individually, either of them has been successfully generalized to multirelay channels. In this paper, to allow each relay node the freedom of choosing either of the two strategies, we propose a unified framework, where both the D-F and C-F strategies can be employed simultaneously in the network. It turns out that, to incorporate in full the advantages of both the best known D-F and C-F strategies into a unified framework, the major challenge arises as follows: For the D-F relay nodes to fully utilize the help of the C-F relay nodes, decoding at the D-F relay nodes should not be conducted until all the blocks have been finished; however, in the multilevel D-F strategy, the upstream nodes have to decode prior to the downstream nodes in order to help, which makes simultaneous decoding at all the D-F relay nodes after all the blocks have been finished inapplicable. To tackle this problem, nested blocks combined with backward decoding are used in our framework, so that the D-F relay nodes at different levels can perform backward decoding at different frequencies. As such, the upstream D-F relay nodes can decode before the downstream D-F relay nodes, and the use of backward decoding at each D-F relay node ensures the full exploitation of the help of both the other D-F relay nodes and the C-F relay nodes. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases. It is also demonstrated through a Gaussian network example that our achievable rates are generally better than the rates obtained with existing unified schemes and with D-F or C-F alone.

MIMO Two-Way Compress-and-Forward Relaying with Approximate Joint Eigen-Decomposition

While compress-and-forward (CF) is one of the basic relay protocols in cooperative transmission, little is known about the optimal design of CF in multiple-input multiple-output (MIMO) two-way relay channels (TWRC). An intuitive method is to compress each element of the superimposed signal vector during the multiple-access (MAC) phase independently and with identical compression noise variance. In this paper, we introduce an improved compression method. The key idea is to apply approximate joint diagonalization (AJD) to realize simultaneous eigen-decomposition of the two channel matrices in the MAC phase of two-way relaying in an approximate manner. After that, a novel covariance matrix design of the compression noise vector is derived for sum-rate maximization. Numerical results show that the proposed CF design can improve the spectral efficiency, especially when the relay node is close to any of the two source nodes instead of in the midpoint.

Lattice Codes for the Gaussian Relay Channel: Decode-and-Forward and Compress-and-Forward

Lattice codes are known to achieve capacity in the Gaussian point-to-point channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that lattice codes may be used to achieve the same performance as known i.i.d. Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks. In particular, we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decode-and-forward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present two examples of how this DF scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known Gaussian random coding techniques in multisource relay channels. That is, we derive a new achievable rate region for the two-way relay channel with direct links and compare it to existing schemes, and derive a new achievable rate region for the multiple access relay channel. We furthermore present a lattice compress-and-forward (CF) scheme for the Gaussian relay channel which exploits a lattice Wyner-Ziv binning scheme and achieves the same rate as the Cover-El Gamal CF rate evaluated for Gaussian random codes. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks.

Analysis of the Generalized DF-CF for Gaussian Relay Channels: Decode or Compress?

We consider a three-node quasi-static communication system with a full-duplex relay. The goal is to determine the relaying mode that enables rate-efficient communication under given channel conditions. To achieve this goal, we consider a generalized scheme that subsumes the decode-and-forward (DF) and compress-and-forward (CF) schemes as special cases. The generalized scheme is considered when the source and relay signals are synthesized from commonly-used Gaussian codebooks, which are shown to be capacity achieving in two asymptotic cases: perfect relay-destination link and broken source-destination link. Studying the generalized DF-CF scheme, it is shown that, for two non-asymptotic cases in which the signal-to-noise ratios (SNRs) of the links satisfy certain conditions, this scheme reduces to either DF or CF. For another set of non-asymptotic SNRs, the generalized scheme is shown to yield strictly higher rates than both DF and CF. Despite the complexity of the generalized scheme, its rate advantage over DF and CF is shown to be upper bounded by 0.5 bits per channel use. This indicates that the practical benefit of the analysis of this scheme is to enable selecting the relaying mode that suits a given channel realization. Numerical results show that, under Rayleigh fading conditions, this selection yields significant gains over fixed DF and CF.

Practical analysis of codebook design and frequency offset estimation for virtual‐multiple‐input–multiple‐output systems

A virtual-multiple-input-multiple-output (MIMO) wireless system using the receiver-side cooperation with the compress-and-forward (CF) protocol, is an alternative to a point-to-point MIMO system, when a single receiver is not equipped with multiple antennas. It is evident that the practicality of CF cooperation will be greatly enhanced if an efficient source coding technique can be used at the relay. It is even more desirable that CF cooperation should not be unduly sensitive to carrier frequency offsets (CFOs). This study presents a practical study of these two issues. Firstly, codebook designs of the Voronoi vector quantisation (VQ) and the tree-structure VQ (TSVQ) to enable CF cooperation at the relay are described. A comparison in terms of the codebook design and encoding complexity is analysed. It is shown that the TSVQ is much simpler to design and operate, and can achieve a favourable performance-complexity tradeoff. Furthermore, this study demonstrates that CFO can lead to significant performance degradation for the virtual-MIMO system. To overcome this, it is proposed to maintain clock synchronisation and jointly estimate the CFO between the relay and the destination. This approach is shown to provide a significant performance improvement.

Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the simultaneous relay channel (SRC) that consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the broadcast relay channel (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on decode-and-forward (DF) and compress-and-forward (CF), must be capable of transmitting information simultaneously to all destinations in such a set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: 1) cooperation is based on DF strategy for both users, referred to as DF–DF region; 2) cooperation is based on CF strategy for both users, referred to as CF–CF region; and 3) cooperation is based on DF strategy for one destination and CF for the other, referred to as DF–CF region. These results can be seen as a generalization and hence unification of previous works. An outer bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semidegraded and degraded Gaussian SRCs. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.

The Multiway Relay Channel

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multiway relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, such that the users within the same cluster wish to exchange messages among themselves, i.e., each user multicasts its message to all the other users in its own cluster. It is assumed that the users cannot receive each other's signals directly. Hence, the relay terminal in this model is the enabler of communication. In particular, restricted encoders are considered, such that the encoding function of each user depends only on its own message and the received signal is used only for decoding the messages of the other users in the cluster. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of the exchange rate, the symmetric rate point in the capacity region in a symmetric Gaussian mRC scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the optimal exchange rate, independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding-based achievable schemes, a nested lattice coding-based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.

Capacity Bounds and Mapping Design for Binary Symmetric Relay Channels

Capacity bounds for a three-node binary symmetric relay channel with orthogonal components at the destination are studied. The cut-set upper bound and the rates achievable using decode-and-forward (DF), partial DF and compress-and-forward (CF) relaying are first evaluated. Then relaying strategies with finite memory-length are considered. An efficient algorithm for optimizing the relay functions is presented. The Boolean Fourier transform is then employed to unveil the structure of the optimized mappings. Interestingly, the optimized relay functions exhibit a simple structure. Numerical results illustrate that the rates achieved using the optimized low-dimensional functions are either comparable to those achieved by CF or superior to those achieved by DF relaying. In particular, the optimized low-dimensional relaying scheme can improve on DF relaying when the quality of the source-relay link is worse than or comparable to that of other links.

Performance Analysis over Slow Fading Channels of a Half-Duplex Single-Relay Protocol: Decode or Quantize and Forward

In this work, a static relaying protocol, called Decode or Quantize and Forward (DoQF), is introduced for half duplex single-relay networks, and its performance is studied in the context of communications over slow fading wireless channels. The proposed protocol is inspired by the so-called Compress-and-Forward (CF) but only needs statistical Channel State Information at the Transmitter (CSIT). First, we analyze the behavior of the outage probability P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> of the proposed protocol as the SNR p tends to infinity. In this case, we prove that ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> converges to a constant ξ. We refer to this constant as the outage probability gain and we derive its closed-form expression for a general class of wireless channels that includes Rayleigh and Rice. We furthermore prove that the DoQF protocol has the best achievable outage gain in the wide class of half-duplex static relaying protocols and we minimize ξ w.r.t the power allocation to the source and the relay and the durations of the slots. Next, we focus on Rayleigh channels to derive the Diversity-Multiplexing Tradeoff (DMT) of the DoQF. Our results show that the DoQF achieves the 2 by 1 MISO DMT upper-bound for multiplexing gains r <; 0.25.

On the Achievable Rates of the Diamond Relay Channel with Conferencing Links

We consider the half-duplex diamond relay channel, which consists of one source-destination pair and two relay nodes connected with two-way rate-limited out-of-band conferencing links. Three basic coding schemes are studied: For the decode-and-forward (DF) scheme, we obtain an achievable rate by letting the source send a common message and two private messages; for the compress-and-forward (CF) scheme, we exploit the conferencing links to help with the compression of the received signals, or to exchange messages intended for the second hop to introduce different levels of cooperations; for the amplify-and-forward (AF) scheme, we study the optimal combining strategy between the received signals from the source and the conferencing link. Moreover, we show that these schemes could achieve the capacity upper bound under certain conditions. Finally, we evaluate various achievable rates for the Gaussian case with numerical results.

Performance assessment of virtual multiple-input multiple-output systems with compress-and-forward cooperation

A cooperative virtual multiple-input multiple-output (MIMO) system using two transmit antennas that implements bit-interleaved coded modulation (BICM) transmission and compress-and-forward (CF) relay cooperation among two receiving nodes is presented here. To perform CF cooperation, we propose to use standard source-coding techniques for virtual MIMO detection, based on the analysis of its expected rate bound and the tightness of the bound. Since the relay and the destination are closely spaced, the authors first assume an error-free conference link between them, to focus on investigating the achievable gain from the CF cooperation. Then the system throughput expression and upper bounds on the system error probabilities over block fading channels are derived. The results show that the relay enables the proposed cooperative virtual-MIMO system to achieve almost ideal MIMO performance with low source-coding rates. Furthermore, when we consider a non-ideal cooperation link for practical considerations, a channel-aware adaptive CF scheme is proposed, so that the relay could always adapt its source-coding rate to meet the data rate on the non-ideal link. Owing to the short-range communication and the proposed scheme, the impact of the non-ideal link is too slight to impair the system performance significantly.

Achievable Rate Regions and Performance Comparison of Half Duplex Bi-Directional Relaying Protocols

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achievable rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, our protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay. The relay may forward information in one of four manners; we outline existing amplify and forward (AF), decode and forward (DF), lattice based, and compress and forward (CF) relaying schemes and introduce the novel mixed forward scheme. The latter is a combination of CF in one direction and DF in the other. We derive achievable rate regions for the CF and Mixed relaying schemes for the two and three phase protocols. We provide a comprehensive treatment of eight possible half-duplex bi-directional relaying protocols in Gaussian noise, obtaining their relative performance under different SNR and relay geometries.

Compress-and-Forward Strategy for Cognitive Interference Channel with Unlimited Look-Ahead

This study investigates the Causal Cognitive Interference Channel (CC-IFC) with unlimited look-ahead, in which the cognitive user non-causally knows its entire received sequence. A coding scheme is proposed which combines the Compress-and-Forward (CF) strategy and Marton coding at the cognitive user. Using this scheme, a new inner bound on the capacity region (achievable rate region) is established for the CC-IFC with unlimited look-ahead. Further, the derived achievable rate region is extended to the Gaussian case and is compared with the previously obtained results via numerical examples, which are based on the Decode-and-Forward (DF) strategy.

Cooperative Transmission for a Vector Gaussian Parallel Relay Network

In this paper, we consider a parallel relay network where two relays cooperatively help a source transmit its message to a destination. We assume the source and the destination nodes are equipped with multiple antennas. Three basic schemes and their achievable rates are studied: Decode-and-Forward (DF), Amplify-and-Forward (AF), and Compress-and-Forward (CF). For the DF scheme, the source transmits two private signals, one for each relay, where dirty paper coding (DPC) is used between the two private streams, and a common signal for both relays. The relays make efficient use of the common information to introduce a proper amount of correlation in the transmission to the destination. We show that the DF scheme achieves the capacity under certain conditions. We also show that the AF and CF schemes are asymptotically optimal in the high relay power limit if the relays-to-destination channel is full rank. The relative advantages of the three schemes are discussed with numerical results.

Capacity of a Class of Diamond Channels

We study a special class of diamond channels which was introduced by Schein in 2001. In this special class, each diamond channel consists of a transmitter, a noisy relay, a noiseless relay and a receiver. We prove the capacity of this class of diamond channels by providing an achievable scheme and a converse. The capacity we show is strictly smaller than the cut-set bound. Our result also shows the optimality of a combination of decode-and-forward (DAF) and compress-and-forward (CAF) at the noisy relay node. This is the first example where a combination of DAF and CAF is shown to be capacity achieving. Finally, we note that there exists a duality between this diamond channel coding problem and the Kaspi-Berger source coding problem.

A Singular-Value-Based Adaptive Modulation and Cooperation Scheme for Virtual-MIMO Systems

This paper presents a practical virtual multiple-input-multiple-output (MIMO) system that implements bit-interleaved coded modulation (BICM) and compress-and-forward (CF) cooperation. A minimum mean square error (MMSE) receiver is considered since it has low complexity and allows good performance when combined with BICM techniques. A closed-form upper bound for the system error probability is derived, and based on this we prove that the smallest singular value of the cooperative channel matrix determines the system error performance. Accordingly, an adaptive modulation and cooperation scheme is proposed, which uses the smallest singular value as the threshold strategy. Depending on the instantaneous channel conditions, the system could therefore adapt to choose a suitable modulation type for transmission and an appropriate quantization rate to perform CF cooperation. It is shown that the adaptive modulation and cooperation scheme not only enables the system to achieve comparable performance to the case with fixed quantization rates but eliminates unnecessary complexity for quantization operations and conference link communication as well.

Multiple Multicasts With the Help of a Relay

The problem of simultaneous multicasting of multiple messages with the help of a relay terminal is considered. In particular, a model is studied in which a relay station simultaneously assists two transmitters in multicasting their independent messages to two receivers. The relay may also have an independent message of its own to multicast. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a “cognitive” relay is characterized, including the cases of partial and rate-limited cognition. Then, achievable rate regions for the cMACr model are presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case, called the cMACr without cross-reception, in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. The capacity region is characterized for a binary modulo additive cMACr without cross-reception, showing the optimality of binary linear block codes, and thus highlighting the benefits of physical layer network coding and structured codes. Results are extended to the Gaussian channel model as well, providing achievable rate regions for DF and CF, as well as for a structured code design based on lattice codes. It is shown that the performance with lattice codes approaches the upper bound for increasing power, surpassing the rates achieved by the considered random coding-based techniques.

An Achievable Rate Region for the Cognitive Interference Channel With Causal Bidirectional Cooperation

In this paper, we consider a two-transmitter-two-receiver cognitive interference channel with causal bidirectional cooperation (CIFC-CBC), where the transmitters operate in a full-duplex mode and cooperate with each other in a causal way. Cooperation between the transmitters is realized using a strategy that combines both decode-and-forward (DF) and compress-and-forward (CF) schemes. We derive an achievable rate region for the considered system based on a proposed coding scheme that jointly implements rate splitting, block Markov coding, superposition coding, Gel'fand-Pinsker coding, and backward decoding. We then apply the derived rate region result to Gaussian channels and show via numerical results that the derived rate region extends the rate regions achieved by pure DF- and pure CF-based cooperation.

An achievable rate for relay networks based on compress-and-forward strategy

Compress-and-Forward (CF) is a well-known coding strategy proposed for relay channels. Few works which were done about the generalization of the CF strategy to the relay networks, are based on irregular encoding/successive decoding. In this paper, a new generalization of the CF strategy to the relay networks based on regular encoding/backward decoding is presented. In general, backward decoding has been shown to yield higher rates in comparison with successive decoding. Here we will investigate the performance of backward decoding in our problem and show that our achievable rate includes the previously proposed rates.