Single Source-destination Pair Research Articles

Distributed On-Off Power Control for Amplify-and-Forward Relays with Orthogonal Space-Time Block Code

A single source-destination pair communicating via a layer of parallel relay nodes under quasi-static slow fading environment is investigated. One existing transmission protocol is considered, namely, the combination of the distributed version of the half symbol-rate complex constellation orthogonal space-time block codes (OSTBC) with adaptive amplify-and-forward (AAF) relaying strategy. We call this transmission protocol as distributed orthogonal space-time block coded adaptive amplify-and-forward (DOSTBC-AAF). To improve the performance of DOSTBC-AAF, a distributed on-off power control (OOPC) rule applied to the relays is analytically derived and is proved to achieve full diversity order. The outage performance of DOSTBC-AAF with and without power control is evaluated. Our simulation results show that DOSTBC-AAF with all relays transmitting at full power (FP) achieves no diversity gain, whereas DOSTBC-AAF with OOPC achieves full diversity order. Correspondingly, at high signal-to-noise ratio (SNR), the diversity-multiplexing tradeoff (DMT) achieved by DOSTBC-AAF (OOPC) is analytically derived and is numerically shown to outperform DOSTBC-AAF (FP) significantly.

A Digital Interface for Gaussian Relay and Interference Networks: Lifting Codes From the Discrete Superposition Model

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.

End-to-End Energy–Bandwidth Tradeoff in Multihop Wireless Networks

In this paper, energy-constrained wireless multihop networks with a single source-destination pair are considered. A network model that incorporates both the energy radiated by the transmitter and the energy consumed by the circuits that process the received signals is proposed. The rate of communication is the number of information bits transmitted (end-to-end) per coded symbol transmitted by any node in the network that is forwarding the data. The tradeoff between the total energy consumption and the end-to-end rate of communication is analyzed. The performance (either energy or rate) depends on the transmission strategy of each node, the location of the relay nodes, and the data rate used by each node. Communication strategies include the rate of transmission on each link, the scheduling of links, and the power used for each link. Strategies that minimize the total energy consumption for a given rate are found. Two communication strategies that capture the inherent constraints of some practical networks are also considered and compared with the optimum strategies. In the case of equispaced relays, analytical results for the tradeoff between the energy and the end-to-end data rate are provided. The minimum energy over all possible data rates is also obtained. Low rates incur a significant penalty because the receiver is on for a long time period while high rates require high transmission energy. At high rates routes with fewer hops minimize the energy consumption while at lower rates more hops minimize the energy consumption.

A distributed on-off amplify-and-forward protocol for the fading parallel relay channel

A single source-destination pair communicating via a layer of two parallel relay nodes under slow fading is considered. The bit error rate (BER) performance of Alamouti-Coded Amplify-and-Forward (ACAF) transmission protocol under different power control strategies is investigated. The optimal power control rule is analytically derived and two distributed approximations to this rule are proposed. The optimal rule reveals an interesting fact: The transmission of each relay is on-off in nature. Simulation results show that our proposed distributed approximations improve the BER performance significantly.

Single-symbol ML decodable distributed STBCs for partially-coherent cooperative networks

A relay network with N relays and a single source destination pair is called a partially-coherent relay channel (PCRC) if the destination has perfect channel state information (CSI) of all the channels and the relays have only the phase information of the source-to-relay channels. In this paper, first, a new set of necessary and sufficient conditions for a space-time block code (STBC) to be single-symbol decodable (SSD) for colocated multiple antenna communication is obtained. Then, this is extended to a set of necessary and sufficient conditions for a distributed STBC (DSTBC) to be SSD for a PCRC. Using this, several SSD DSTBCs for PCRC are identified. It is proved that even if a SSD STBC for a co-located MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and only coding gain is lost. It is shown that when a DSTBC is SSD for a PCRC, then arbitrary coordinate interleaving of the in-phase and quadrature-phase components of the variables does not disturb its SSD property for PCRC. Finally, it is shown that the possibility of channel phase compensation operation at the relay nodes using partial CSI at the relays increases the possible rate of SSD DSTBCs from 2/N when the relays do not have CSI to 1/2, which is independent of N.

Distortion Control for Delay-Sensitive Sources

We investigate the problem of finding minimum-distortion policies for streaming delay-sensitive but distortion-tolerant data. We consider cross-layer approaches which exploit the coupling between presentation and transport layers. We make the natural assumption that the distortion function is convex and decreasing. We focus on a single source-destination pair and analytically find the optimum transmission policy when the transmission is done over an error-free channel. This optimum policy turns out to be independent of the exact form of the convex and decreasing distortion function. Then, for a packet-erasure channel, we analytically find the optimum open-loop transmission policy, which is also independent of the form of the convex distortion function. We then find computationally efficient closed-loop heuristic policies and show, through numerical evaluation, that they outperform the open-loop policy and have near optimal performance.

Bit Loading Algorithms for Cooperative OFDM Systems

We investigate the resource allocation problem for an OFDM cooperative network with a single source-destination pair and multiple relays. Assuming knowledge of the instantaneous channel gains for all links in the entire network, we propose several bit and power allocation schemes aiming at minimizing the total transmission power under a target rate constraint. First, an optimal and efficient bit loading algorithm is proposed when the relay node uses the same subchannel to relay the information transmitted by the source node. To further improve the performance gain, subchannel permutation, in which the subchannels are reallocated at relay nodes, is considered. An optimal subchannel permutation algorithm is first proposed and then an efficient suboptimal algorithm is considered to achieve a better complexity-performance tradeoff. A distributed bit loading algorithm is also proposed for ad hoc networks. Simulation results show that significant performance gains can be achieved by the proposed bit loading algorithms, especially when subchannel permutation is employed.

Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity–multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source–destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect. </para>

Amplify-and-Forward in Wireless Relay Networks: Rate, Diversity, and Network Size

A wireless network with fading and a single source-destination pair is considered. The information reaches the destination via multiple hops through a sequence of layers of single-antenna relays. At high signal-to-noise ratio (SNR), the simple amplify-and-forward strategy is shown to be optimal in terms of degrees of freedom, because it achieves the degrees of freedom equal to a point-to-point multiple-input multiple-output (MIMO) system. Hence, the lack of coordination in relay nodes does not reduce the achievable degrees of freedom. The performance of this amplify-and-forward strategy degrades with increasing network size. This phenomenon is analyzed by finding the tradeoffs between network size, rate, and diversity. A lower bound on the diversity-multiplexing tradeoff for concatenation of multiple random Gaussian matrices is obtained. Also, it is shown that achievable network size in the outage formulation (short codes) is a lot smaller than the ergodic formulation (long codes).

Minimum Error Probability Cooperative Relay Design

In wireless networks, user cooperation has been proposed to mitigate the effect of multipath fading channels. Recognizing the connection between cooperative relay with finite alphabet sources and the distributed detection problem, we design relay signaling via channel aware distributed detection theory. Focusing on a wireless relay network composed of a single source-destination pair with L relay nodes, we derive the necessary conditions for optimal relay signaling that minimizes the error probability at the destination node. The derived conditions are person-by-person optimal: each local relay rule is optimized by assuming fixed relay rules at all other relay nodes and fixed decoding rule at the destination node. An iterative algorithm is proposed for finding a set of relay signaling approaches that are simultaneously person-by-person optimal. Numerical examples indicate that the proposed scheme provides performance improvement over the two existing cooperative relay strategies, namely amplify-forward and decode-forward

On the Capacity of Large Gaussian Relay Networks

The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cut-set arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cut-set upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source-channel coding problem, and it is well known that the source-channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance-it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source-destination pair, capacity grows with the logarithm of the number of nodes.