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Buffer-Aided Relaying with Adaptive Link Selection

Nikola Zlatanov, Robert Schober, Petar Popovski

arXiv:1202.5349v2cs.IT

TL;DR

The paper studies how to improve relaying performance under transmission constraints. It proposes adaptive link selection with buffering, derives optimal policies for delay-unconstrained transmission, and reports significant throughput gains.

  • Problem

    The paper investigates how transmission constraints affect the performance of a proposed relaying protocol and seeks to maximize throughput through adaptive link selection and power allocation.

  • Method

    The paper proposes adaptive link selection that selects the node with the stronger link and derives optimal policies for delay-unconstrained transmission with fixed and variable transmit powers.

  • Results

    Analytical and simulation results show that buffer-aided relaying with adaptive link selection can significantly increase throughput.

  • Takeaways & Limitations

    Selecting the stronger involved link makes the optimal policies attractive for implementation.

  • Takeaways & Limitations

    The paper identifies searching for other protocols with possibly superior performance as future work.

Abstract

from arXiv · show

In this paper, we consider a simple network consisting of a source, a half-duplex decode-and-forward relay, and a destination. We propose a new relaying protocol employing adaptive link selection, i.e., in any given time slot, based on the channel state information of the source-relay and the relay-destination link a decision is made whether the source or the relay transmits. In order to avoid data loss at the relay, adaptive link selection requires the relay to be equipped with a buffer such that data can be queued until the relay-destination link is selected for transmission. We study both delay constrained and delay unconstrained transmission. For the delay unconstrained case, we characterize the optimal link selection policy, derive the corresponding throughput, and develop an optimal power allocation scheme. For the delay constrained case, we propose to starve the buffer of the relay by choosing the decision threshold of the link selection policy smaller than the optimal one and derive a corresponding upper bound on the average delay. Furthermore, we propose a modified link selection protocol which avoids buffer overflow by limiting the queue size. Our analytical and numerical results show that buffer-aided relaying with adaptive link selection achieves significant throughput gains compared to conventional relaying protocols with and without buffers where the relay employs a fixed schedule for reception and transmission.

I. INTRODUCTION

The paper replaces fixed reception-transmission schedules in half-duplex relaying with buffer-aided adaptive link selection based on channel conditions. It analyzes delay-constrained and delay-unconstrained operation, optimizing selection and power allocation while evaluating throughput gains over conventional relaying.

  • Motivation: Conventional half-duplex protocols receive at the relay in one slot and forward in the next under a fixed schedule.Earlier buffer-aided approaches still fixed when the source transmitted, limiting the flexibility of relay buffers.
  • Contribution: Adaptive link selection lets the source or relay transmit in each slot according to the source-relay and relay-destination CSI.The relay buffer queues decoded data until the relay-destination link is selected.
  • Contribution: The paper studies both delay-constrained and delay-unconstrained transmission.For unconstrained delay, it optimizes link selection and source-relay power allocation; for constrained delay, it proposes alternative protocols and an average-delay upper bound.
  • Results: The optimal unconstrained policy requires only instantaneous CSI for the current slot and statistical CSI of the involved links.Past and future channel states and the relay-buffer state are not required for optimal selection.
  • Results: Buffer-aided adaptive selection can achieve large performance gains over conventional relaying with or without buffers when some delay is tolerated.The paper supports this conclusion with analytical and simulation results in good agreement.
  • System model: The system is a three-node half-duplex decode-and-forward network without a direct source-destination link, with time-varying source-relay and relay-destination channels.The source is assumed always to have data to transmit, and link SNRs depend on transmit powers and instantaneous channel gains.

B. Link Adaptive Transmission Protocol

The protocol assigns a central node to decide whether the source or relay transmits in each slot, then adapts transmission rates and manages the relay buffer according to the selected link. CSI requirements are distributed among the central node and communicating endpoints.

  • Decision process: A central node decides whether the source or relay transmits in a given time slot and broadcasts that decision.Which node is central depends on the network architecture.
  • Transmission: Selected source and relay transmissions adapt their rates to the corresponding link capacity using codewords spanning one slot.The protocol assumes capacity-achieving codes and requires CSI for link selection and rate adaptation.
  • CSI requirements: The central node needs both instantaneous channel gains, while the communicating nodes need the selected link's channel information for adaptation and decoding.For source-relay transmission, source and relay require hS(i); for relay-destination transmission, relay and destination require hR(i).
  • Power information: With power allocation, source and relay compute their transmit powers from instantaneous channel gains and statistical CSI.With fixed powers, the relevant nodes instead require the fixed source and relay powers.
  • Buffer dynamics: When the source transmits, decoded data is appended to the relay buffer; when the relay transmits, departures are limited by its queued data and instantaneous link capacity.The queue remains non-negative, and half-duplex operation disables the opposite link in each slot.

C. Throughput

The paper formulates throughput as the average destination arrivals and optimizes adaptive link selection and transmit powers. It compares the proposed buffer-aided scheme with conventional relaying under fixed schedules, showing throughput gains but highlighting delay and buffer-size costs.

  • Throughput τ is the average number of bits arriving at the destination per time slot, optimized through link selection and source-relay power allocation.The source is assumed always to have data, and transmission rates adapt to the selected link capacity.
  • Baseline schemes: τconv,2 ≥ τconv,1 holds for the two conventional baselines, but realizing the buffered baseline gain requires an infinite relay buffer and introduces infinite delay.The comparison uses the average-throughput expressions in (6) and (7).
  • Numerical setting: The numerical analysis considers Rayleigh-faded S-R and R-D links and compares the resulting conventional-relaying throughputs with the proposed protocol.For Rayleigh fading, the link SNR densities are parameterized by ΩS and ΩR.
  • Main comparison: Adaptive link selection provides substantial throughput gains over conventional relaying with and without buffers using fixed schedules.The paper also develops optimal power allocation and discusses the effect of limited buffer size.
  • The proposed protocol selects either the S-R or R-D link in each slot using a binary decision variable based on instantaneous channel information.d_i = 0 selects source transmission, while d_i = 1 selects relay transmission.

B. Optimal Link Selection Policy

The optimal policy operates the relay queue at the boundary between non-absorbing and absorbing behavior. It uses a threshold rule based only on current link SNRs, while the threshold itself depends on both links’ statistics.

  • The throughput-maximizing policy must keep the relay queue at the edge of non-absorption: non-absorbing but at the boundary of absorption.This condition links the optimal policy to balanced long-term arrival and departure behavior.
  • For the optimal policy, average source-to-relay arrivals equal average relay-to-destination departures, yielding the throughput expression in Theorem 2.The queue is non-absorbing and typically contains more bits than can be transmitted over the R-D link in a slot.
  • The optimal adaptive link-selection rule is a threshold policy parameterized by decision threshold ρ, with ρopt chosen to satisfy the queue-balance condition.Theorem 3 gives the optimal decision function and states that ρopt must satisfy (15).
  • The decision at slot i depends only on the instantaneous SNRs s(i) and r(i), not on queue state or past or future channel states.Non-causal instantaneous CSI is unnecessary because the relay operates in the practically fully backlogged regime.
  • The optimal threshold depends on statistical CSI from both links, and maximum throughput can also be achieved with long codewords and constant transmission rates.Long codewords introduce ideally infinitely long delays, making extension to delay-constrained transmission difficult.
  • The paper therefore uses adaptive-rate transmission with one codeword spanning one time slot for the delay-constrained setting.This contrasts with the long-codeword alternative, whose delay is inherently long.

C. Generalization of the Decision Function and Optimal Decision Threshold

The threshold framework is generalized from the logarithmic capacity function to any smooth, increasing invertible decision function. This flexibility can simplify analysis, although the optimal function may yield complicated expressions.

  • Alternative functions such as F(x) = x can be analytically preferable because they generally provide similar performance to the logarithmic choice while producing more tractable expressions.The paper presents this as a motivation for studying generalized decision functions.
  • The decision function F(x) is generalized to any non-negative, smooth, increasing function with an existing inverse.The condition F(x+ε) > F(x) for ε > 0 ensures strict increase.
  • For a given decision function, the optimal threshold ρopt is computed from the condition equating average source arrivals and relay departures.The resulting integrals use the link SNR densities and threshold-dependent boundaries G(r) and H(s).
  • The optimal threshold depends on the statistical properties of both involved links.This dependence is revealed by the threshold equation and the corresponding link-density integrals.

D. Rayleigh Fading

For Rayleigh fading, the paper derives throughput expressions for alternative decision functions and compares adaptive link selection with conventional buffer-aided relaying. The optimal threshold is numerically determined in the general case, with especially large gains when the links are highly asymmetric.

  • For F(x) = x, the optimal threshold ρopt,1 is obtained from a one-dimensional optimization, with maximal throughput then evaluated from the selected decisions.
  • The optimal threshold ρopt,2 is found numerically, and the corresponding maximum throughput follows from the resulting optimization.
  • The gain ratio τmax/τconv,2 increases monotonically from 1 to 1.5 as Ω decreases from infinity to zero, with minimum gain at ΩS = ΩR.
  • When ρ = 1, F(x) = x and F(x) = log2(1 + x) produce identical decisions and throughputs.
  • For unequal average link gains, the two decision functions are no longer equivalent, and τmax,2 exceeds τmax,1.
  • The section also formulates joint optimization of link selection and normalized transmit powers under average power constraints, summarized by Theorem 4.

B. Finding the Optimal λ and ρ

The optimal power-allocation solution is characterized through coupled conditions for the threshold parameters λ and ρ. For Rayleigh fading, these conditions simplify, and the resulting maximum throughput is obtained from the same equations.

  • Lemma 2 specifies coupled equations that optimal λ and ρ must satisfy when adaptive link selection and power allocation jointly maximize throughput.
  • The maximum throughput equals the left- and right-hand sides of the equation defining the optimal parameters.
  • The parameters λopt and ρopt can be computed offline from link statistics and updated at a low rate because those statistics vary more slowly than instantaneous gains.
  • For Rayleigh fading, the coupled optimality equations simplify, with the maximum throughput still given by their common value.
  • The delay-constrained analysis assumes fixed transmit powers and examines practical constraints on relay delay and buffer size.

A. Satisfying an Average Delay Constraint by “Starving” the Buffer

The delay-constrained protocols control relay buffering either by reducing arrivals below the throughput-optimal rate or by forcing relay transmission when the queue is full. The first approach has an analytical delay bound, while the second avoids dropped bits but is difficult to analyze theoretically.

  • A. Satisfying an Average Delay Constraint by “Starving” the Buffer: Choosing ρ < ρopt starves the buffer by intentionally reducing the arrival rate, enabling control of the average delay.
  • A. Satisfying an Average Delay Constraint by “Starving” the Buffer: Under uncorrelated fading and ξ < 1, Theorem 5 provides an upper bound on average delay, while throughput equals E{(1 − di)S(i)}.
  • A. Satisfying an Average Delay Constraint by “Starving” the Buffer: A desired average delay can be met by increasing ρ from zero until the analytical delay expression reaches the target.
  • B. Satisfying the Delay Constraint by Limiting the Queue Size: With finite buffer capacity, arriving bits can still be dropped when the queue is full, even under buffer starving.
  • B. Satisfying the Delay Constraint by Limiting the Queue Size: The queue-size-limiting protocol forces relay transmission when available space cannot accommodate possible source arrivals, thereby avoiding overflow.
  • B. Satisfying the Delay Constraint by Limiting the Queue Size: The queue-size-limiting protocol is evaluated by simulation because arrival rates and buffer-emptying frequency depend mutually on each other.
  • Both delay-constrained protocols are heuristic, and finding potentially superior alternatives remains future work.

VI. NUMERICAL AND SIMULATION RESULTS

Numerical and simulation results show substantial throughput gains from adaptive link selection, with the largest fixed-power gains under strongly asymmetric links. Power allocation also helps, while delay and finite-buffer constraints introduce distinct trade-offs.

  • Adaptive link selection produces substantial throughput gains over conventional relaying for both considered decision functions.
  • The ratio τmax/τconv,2 approaches 2 as ΩR/ΩS tends to zero or infinity, yielding nearly twice conventional throughput in either extreme.
  • At Γ = 0 dB, adaptive link selection with power allocation achieves a throughput gain of 95 % over conventional buffered relaying with power allocation.
  • At Γ = 20 dB, adaptive link selection yields a throughput gain of 1 bit/slot compared to conventional relaying with buffer.
  • The delay upper bound is tight especially for large delays, whereas buffer starving becomes inefficient at very small delays.
  • For the starved-buffer protocol, throughput increases with tolerable delay and approaches the optimal delay-constrained threshold at large delays.
  • The dropped-bit probability decreases rapidly with increasing buffer size and decreasing average delay, although the analytical Markov bound is relatively loose.

2) Limiting the Queue Size:

The paper develops adaptive buffer-aided relaying for both delay-unconstrained and delay-constrained transmission, including queue-size control. The proposed protocols generally improve throughput, but conventional relaying can perform better at very small delays.

  • Numerical comparison: For large delays, both delay-constrained protocols approach the delay-unconstrained protocol’s performance.The limiting-buffer protocol yields higher throughput than buffer starving at comparable delays.
  • Numerical comparison: At very small delays, conventional relaying with or without a buffer may outperform both proposed delay-constrained protocols.This identifies a practical boundary for the proposed delay-control methods.
  • Delay-unconstrained transmission: The delay-unconstrained policy selects the node with the stronger link and depends on instantaneous and statistical CSI.The policy is derived for fixed and variable source and relay transmit powers.
  • Delay-constrained transmission: Two protocols control delay by starving the relay buffer or limiting its size, with the latter avoiding buffer overflow.The buffer-starving method also has an upper bound on average delay.
  • Overall conclusion: Adaptive link selection significantly increases throughput compared with conventional relay-assisted transmission using a predefined schedule.The paper also identifies extensions involving larger networks, imperfect CSI, and fixed-rate outage analysis.

APPENDIX

The appendix proves the optimality condition for adaptive link selection by analyzing queue absorption and flow conservation. It shows that the optimum lies at the boundary between absorbing and non-absorbing queues.

  • Queue optimality: Flow conservation gives throughput equal to arrival rate when the relay queue is non-absorbing.The proof uses τ = E{(1 − d_i)S(i)} for this case.
  • Queue optimality: An absorbing queue has arrival rate greater than throughput, so its long-run queue grows and cannot characterize the optimum.The proof improves such policies by reallocating selected time slots until flow balance is reached.
  • Boundary condition: Therefore, an optimal policy must be non-absorbing but lie at the edge where a small perturbation would make the queue absorbing.This boundary condition is used to derive the optimal selection rule.
  • Threshold derivation: The Lagrangian optimization yields binary decisions governed by a threshold parameter ρ chosen to satisfy the flow constraint.The derivation establishes 0 < μ < 1 and sets ρ = μ/(1−μ).

D. Proof of Theorem 4

Theorem 4 is proved by applying Lagrangian optimization to the power-allocation and link-selection problem, then evaluating the resulting ergodic expectations. The proof also bounds queue size and average delay under the non-absorbing condition.

  • Optimization: The Lagrangian conditions produce closed-form expressions for source power, relay power, and link selection.The parameters ρ and λ are chosen so the relevant constraints hold with equality.
  • Expectation form: Ergodicity converts the normalized constraint sums into expectations over the channel processes.The source and relay transmission regions are obtained by integrating over the corresponding CSI domains.
  • Expectation form: The relay-transmission contribution is likewise obtained by integrating over the region where d_i and γ_R(i) are jointly nonzero.This yields the right-hand side of the throughput constraint.
  • Queue bound: When ξ = E{(1−d_i)S(i)}/E{d_iR(i)} < 1, the queue is non-absorbing and its average size can be upper-bounded.The bound uses slot-by-slot uncorrelated arrivals and departures together with the queue recursion.
  • Delay bound: Little’s law converts the average queue-size bound into the stated upper bound on average delay.The queue evolves as Q(i) = max {Q(i−1) − d_iR(i) + (1−d_i)S(i), 0}.
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