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Opportunistic Cooperation in Cognitive Femtocell Networks

Rahul Urgaonkar, Michael J. Neely

arXiv:1103.1401v3math.OCcs.SYeess.SY

TL;DR

In cooperative cognitive networks, secondary-user actions affect primary-channel state, making throughput optimization a constrained MDP for which conventional approaches require system-dynamics knowledge or slow learning. The paper uses Lyapunov drift-plus-penalty-ratio control to obtain an online algorithm without dynamics knowledge or explicit learning; its throughput approaches optimality within O(1/V), with a queue-backlog tradeoff.

  • Problem

    Because secondary-user actions affect primary-channel state, opportunistic cooperation creates a constrained MDP that conventional methods address with extensive dynamics knowledge or learning that may converge slowly.

    Source: §I · p. 2, B. Control Objective · p. 4

  • Method

    The paper uses a drift-plus-penalty-ratio method to design an online control algorithm requiring neither network-dynamics knowledge nor explicit learning.

    Source: §I · p. 2

  • Results

    O(1/V) bounds the gap between time-average secondary-user throughput and optimality, with a trade-off in worst-case queue backlog.

    Source: §V · p. 8

  • Takeaways & Limitations

    By Little’s Theorem, the throughput-backlog trade-off yields an O(1/V, V) utility-delay trade-off.

    Source: §V · p. 8

Abstract

from arXiv · show

We investigate opportunistic cooperation between unlicensed secondary users and legacy primary users in a cognitive radio network. Specifically, we consider a model of a cognitive network where a secondary user can cooperatively transmit with the primary user in order to improve the latter's effective transmission rate. In return, the secondary user gets more opportunities for transmitting its own data when the primary user is idle. This kind of interaction between the primary and secondary users is different from the traditional dynamic spectrum access model in which the secondary users try to avoid interfering with the primary users while seeking transmission opportunities on vacant primary channels. In our model, the secondary users need to balance the desire to cooperate more (to create more transmission opportunities) with the need for maintaining sufficient energy levels for their own transmissions. Such a model is applicable in the emerging area of cognitive femtocell networks. We formulate the problem of maximizing the secondary user throughput subject to a time average power constraint under these settings. This is a constrained Markov Decision Problem and conventional solution techniques based on dynamic programming require either extensive knowledge of the system dynamics or learning based approaches that suffer from large convergence times. However, using the technique of Lyapunov optimization, we design a novel greedy and online control algorithm that overcomes these challenges and is provably optimal.

I. INTRODUCTION

The paper reframes cognitive-radio resource allocation as opportunistic cooperation: a secondary user helps primary transmissions to gain later idle-channel opportunities while managing its own power. It formulates the control problem around queueing and power decisions in a frame-based one-primary/one-secondary model.

I. INTRODUCTION

  • Unlike dynamic spectrum access, which targets vacant channels, opportunistic cooperation uses secondary-user resources to improve primary transmissions in exchange for more idle-channel opportunities.Source: §I · p. 1
  • Because secondary-user actions affect primary-channel state evolution, the problem is a constrained MDP; dynamic programming needs extensive dynamics knowledge or learning can converge slowly.Source: §I · p. 2
  • The drift-plus-penalty ratio method yields an online control algorithm that needs neither network-dynamics knowledge nor explicit learning and is stated to be optimal.It minimizes a drift-plus-penalty ratio over each renewal frame by solving a sequence of unconstrained stochastic shortest-path problems.Source: §I · p. 2

II. BASIC MODEL

  • Each frame begins with a geometrically distributed PU Idle period and then a PU Busy period whose duration depends on secondary-user control decisions.The idle-period geometric distribution has parameter λpu.Source: §II · p. 2

A. Control Decisions and Queueing Dynamics

  • During busy slots, cooperation can improve primary transmission success and shorten the busy period, but power spent cooperating may leave less for the secondary user's own transmissions.The formulation maximizes secondary-user throughput subject to a time-average power constraint, with an instantaneous peak-power constraint as well.Source: §I · p. 2, §II · p. 3, A. Control Decisions and Queueing… · p. 3

B. Control Objective

The control objective is to maximize secondary-user throughput under average and peak power and scheduling constraints. The proposed frame-based drift-plus-penalty method makes online admission and resource-allocation decisions using queue state.

B. Control Objective

  • The policy maximizes secondary-user throughput subject to average and peak power constraints and the model’s scheduling constraints.The objective is posed as a stochastic optimization problem.Source: B. Control Objective · p. 4
  • The primary queue backlog is the control state because cooperation affects its dynamics and its zero/nonzero status changes the available actions.This makes the problem a constrained Markov decision problem.Source: B. Control Objective · p. 4
  • Conventional dynamic-programming methods require extensive system-dynamics knowledge or learning approaches with large convergence times.Source: B. Control Objective · p. 4

III. SOLUTION USING THE “DRIFT-PLUS-PENALTY” RATIO METHOD

  • The frame-based algorithm chooses admission control and power allocation by minimizing an upper bound on drift-plus-penalty per expected frame length.It observes the secondary-user queue and virtual power queue at each frame’s start, then updates the queues after the policy is applied.Source: §III · pp. 4–5
  • Its admission decision is threshold-based, while power allocation maximizes a frame-based ratio subject to power and idle-versus-cooperation scheduling constraints.The decisions use queue values observed at the beginning of the frame.Source: §III · p. 5

IV. THE MAXIMIZING POLICY OF (16)

The maximizing policy uses separate powers for the secondary user’s own transmissions and cooperative transmissions. These powers are computed from the frame’s queue weights, without arrival-rate knowledge.

IV. THE MAXIMIZING POLICY OF (16)

  • P*_0 and P*_1 are obtained from separate single-variable optimization problems that can be solved efficiently.P*_0 is defined by one optimization problem and P*_1 by another.Source: §IV · p. 5
  • On every slot t of frame k, the policy chooses power P(t), using constant power P*_0 for the secondary user’s own transmission during the frame’s PU-idle period and P*_1 for cooperative transmission.Source: §IV · p. 5
  • The powers depend on the secondary-user queue weights and do not require knowledge of the primary or secondary arrival rates.Source: §IV · p. 6

A. Proof Details

The proof recasts the frame-based ratio optimization as an infinite-horizon Markov decision problem under a primary-queue stability assumption. It then reduces the optimizing policy to separate choices for idle and nonempty primary-queue states.

A. Proof Details

  • Maximizing the frame-based ratio is equivalent, by renewal theory, to an infinite-horizon Markov decision problem over primary-queue backlog states.The proof considers stationary randomized power allocations for each state.Source: A. Proof Details · p. 6
  • Under λpu < φnc, the primary queue remains stable even without cooperation, allowing the ratio problem to be treated using steady-state probabilities.The proof uses this assumption to establish recurrent-system steady-state probabilities for the stationary policies considered.Source: A. Proof Details · p. 6
  • The proof shows it suffices to use the same power distribution in every state with positive primary backlog, reducing the policy to separate idle-state and nonempty-state choices.The birth-death chain represents the primary-user queue backlog, and the proof’s alternate policy preserves the objective while imposing this common distribution.Source: A. Proof Details · pp. 6–7, Figure 3 · p. 6
  • The nonempty-state power optimization can be solved without knowing either arrival rate; with P = {0, Pmax}, it yields a threshold-based rule.Source: A. Proof Details · p. 7
  • Implementation requires the secondary user’s own queue values and whether the slot is PU-idle or PU-busy, not the primary queue backlog value.Source: A. Proof Details · p. 7

V. PERFORMANCE ANALYSIS

The Frame-Based-Drift-Plus-Penalty-Algorithm is compared with a stationary randomized policy, and its throughput approaches the optimum as the control parameter grows. This comes with a worst-case queue-backlog trade-off.

V. PERFORMANCE ANALYSIS

  • The algorithm’s performance is analyzed by comparing its Lyapunov drift with the optimal stationary randomized policy STAT.The analysis also introduces ALT to compare admission-control decisions; resource-allocation decisions are the same under both algorithms.Source: §V · pp. 7–8
  • At each frame, the algorithm admits packets and selects resource allocation by maximizing a ratio, then updates its queues.The ratio minimizes an upper bound on drift plus penalty divided by expected frame length.Source: §V · p. 8
  • The theorem states that the secondary-user queue is bounded and the virtual power queue is mean rate stable.The throughput guarantee is stated for all K > 0.Source: §V · p. 8
  • Theorem 1 bounds secondary-user throughput within O(1/V) of optimal, with a worst-case queue-backlog trade-off.By Little’s Theorem, the stated utility-delay trade-off is O(1/V, V).Source: §V · p. 8

VI. EXTENSIONS TO BASIC MODEL

The paper considers two extensions to the basic model.

VI. EXTENSIONS TO BASIC MODEL

  • The section introduces two extensions to the basic model.Source: §VI · p. 9

A. Multiple Secondary Users

The multiple-user extension allows secondary users to cooperate with the primary user or transmit their own data during primary-idle periods. It describes a sum-throughput objective and a frame-based control algorithm.

A. Multiple Secondary Users

  • At most one secondary user cooperates with the primary user per slot, and at most one transmits its own data when the primary user is idle.Source: A. Multiple Secondary Users · p. 9
  • The extension maximizes total secondary-user throughput subject to per-user average and peak power constraints and scheduling constraints.Source: A. Multiple Secondary Users · p. 9
  • The frame-based algorithm performs admission control, resource allocation, and queue updates; its allocation procedure solves separate problems for each user.The described solutions assign one user to transmit on idle slots and another to cooperate on busy slots.Source: A. Multiple Secondary Users · p. 9

B. Fading Channels

The fading extension models channel state as i.i.d. and makes primary success probability depend on both fading and cooperative power. It restricts the optimization to policies that use the same power-selection distribution across positive primary-queue states for each fading state.

B. Fading Channels

  • The fading state is i.i.d. across slots, and the known success-probability function for each state is non-decreasing in cooperative power.The secondary-user transmission rate is assumed to depend only on power.Source: B. Fading Channels · p. 9
  • A policy using the same power-selection distribution across all positive primary-queue states for each fading state achieves the optimal time-average objective.Therefore, it is sufficient to optimize over this restricted stationary-policy class.Source: B. Fading Channels · p. 10
  • The extension’s optimization can be solved using deterministic power allocations and does not require knowledge of the primary or secondary arrival rates.The passage also states that the problem can be solved efficiently for general power-allocation options.Source: B. Fading Channels · p. 11

VII. SIMULATIONS

Simulations show that the Frame-Based-Drift-Plus-Penalty-Algorithm approaches the optimal secondary throughput while respecting the average power constraint, and adapts its cooperative power use as primary traffic changes.

VII. SIMULATIONS

  • 0.25 packets/slot is the offline-optimal secondary throughput; the algorithm converges to it with an O(1/V) gap while keeping average power at or below 0.5 units/slot.The secondary queue backlog grows linearly with V, as predicted by Theorem 1.Source: §VII · p. 11
  • Average secondary queue occupancy grows linearly with V, consistent with Theorem 1.Fig. 5 plots average secondary-user queue occupancy against V.Source: §VII · p. 11, Figure 5 · p. 11
  • In the simulations, No Cooperation yielded 0.166 packets/slot, Always Cooperate yielded zero throughput because it used all secondary-user power, and Counter Based Policy reached a maximum of 0.137 packets/slot.This shows that simply satisfying the average-power constraint is not sufficient to achieve maximum throughput; under the counter policy, the running average may exceed Pavg before the next idle opportunity.Source: §VII · p. 11
  • When primary arrivals fall to 0.2 packets/slot, cooperation is unnecessary under Pavg = 0.5; when they rise to 0.55, the algorithm increases cooperative power.The simulation changes λpu after frames 350 and 700, respectively.Source: §VII · pp. 11–12

VIII. CONCLUSIONS

The conclusion frames opportunistic cooperation in a cognitive femtocell network as a constrained decision problem and presents a greedy online Lyapunov-optimization algorithm that is provably optimal.

VIII. CONCLUSIONS

  • The secondary user cooperates with the primary to increase its transmission success probability, in return gaining more chances to send its own data during primary-idle periods.The paper studies this opportunistic-cooperation setting in a cognitive femtocell network.Source: §VIII · p. 12
  • Because secondary-user actions affect system-state evolution, the problem is a constrained Markov Decision Problem.Conventional approaches require extensive system-dynamics knowledge or learning methods with long convergence times.Source: §VIII · p. 12
  • Lyapunov optimization yields a greedy online control algorithm that the authors characterize as overcoming those challenges and being provably optimal.Source: §VIII · p. 12

APPENDIX B PROOF OF THEOREM 1, PARTS 2 AND 3

The proof uses Lyapunov drift bounds and comparisons with an alternate algorithm to establish the stated theorem properties for the Frame-Based-Drift-Plus-Penalty-Algorithm.

APPENDIX B PROOF OF THEOREM 1, PARTS 2 AND 3

  • A Lyapunov drift bound under the Frame-Based-Drift-Plus-Penalty-Algorithm begins the proof of Theorem 1, parts 2 and 3.Source: Appendix B · p. 13
  • The proof compares the algorithm with ALT by considering cases above and below the secondary queue threshold V and using its resource-allocation maximization.The cases use Qsu(tk) > V and Qsu(tk) ≤ V.Source: Appendix B · p. 13
  • The argument rearranges the drift inequality, invokes Theorem 4.1 and Theorem 2.5(b) of, and sums bounds over frames to derive the theorem claims.Source: Appendix B · pp. 13–14

APPENDIX C COMPUTING D

Appendix C computes a finite bound D by analyzing random frame durations and moments of the primary user’s idle and busy periods.

APPENDIX C COMPUTING D

  • The appendix computes a finite D satisfying condition (2), using frame-length and queue-related terms in its derivation.Source: Appendix C · p. 14
  • Each frame duration is the sum of primary idle and busy periods; the idle period is geometric with parameter λpu and mean 1/λpu.Source: Appendix C · p. 14
  • For the busy-period calculation, the proof uses a preemptive-LIFO representation, with interruptions N binomial conditional on service duration X.The packet stay durations Bi are i.i.d. with the busy-period distribution and independent of N; X is geometric with parameter φnc.Source: Appendix C · p. 14
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