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Optimal Power Control over Fading Cognitive Radio Channels by Exploiting Primary User CSI

Rui Zhang

arXiv:0804.1617v2cs.ITmath.IT

TL;DR

In spectrum-sharing cognitive radio, interference-temperature control is practical, but its optimality for the secondary-primary performance tradeoff has not been carefully addressed. The paper optimizes secondary-user power under a constraint on primary ergodic-capacity loss, reporting improved ergodic capacities for both users over AIPC.

  • Problem

    Interference-temperature control is practical for protecting primary transmission, but its optimality for the achievable secondary-primary performance tradeoff had not been carefully addressed.

    Source: §I · pp. 1–2

  • Method

    The paper optimizes secondary-user power across fading states under a primary capacity loss constraint that caps the primary user's ergodic-capacity loss.

    Source: §I · p. 3, §II · p. 5

  • Results

    The proposed policy improves the achievable ergodic capacities of both primary and secondary users over AIPC.

    Source: §I · p. 3

  • Takeaways & Limitations

    The primary capacity loss constraint is more directly related to primary transmission than the average interference power constraint.

    Source: §I · p. 3

Abstract

from arXiv · show

This paper is concerned with spectrum sharing cognitive radio networks, where a secondary user (SU) or cognitive radio link communicates simultaneously over the same frequency band with an existing primary user (PU) link. It is assumed that the SU transmitter has the perfect channel state information (CSI) on the fading channels from SU transmitter to both PU and SU receivers (as usually assumed in the literature), as well as the fading channel from PU transmitter to PU receiver (a new assumption). With the additional PU CSI, we study the optimal power control for the SU over different fading states to maximize the SU ergodic capacity subject to a new proposed constraint to protect the PU transmission, which limits the maximum ergodic capacity loss of the PU resulted from the SU transmission. It is shown that the proposed SU power-control policy is superior over the conventional policy under the constraint on the maximum tolerable interference power/interperferecne temperature at the PU receiver, in terms of the achievable ergodic capacities of both PU and SU.

I. INTRODUCTION

In spectrum-sharing cognitive radio networks, secondary users transmit alongside primary users, but interference-temperature power control leaves its optimal performance tradeoff insufficiently addressed. This paper uses additional primary-user channel information and a primary-capacity-loss constraint to optimize secondary-user power, reporting improved ergodic capacities for both links over the average-interference-power constraint.

I. INTRODUCTION

  • Spectrum sharing permits secondary and primary users to transmit simultaneously when the resulting primary performance loss remains acceptable.This differs from opportunistic spectrum access, in which secondary users transmit only when primary transmission is detected to be off.Source: §I · pp. 1–2
  • Although interference temperature is a practical way to protect primary transmission, its optimality for the achievable secondary-primary performance tradeoff had not been carefully addressed.Source: §I · p. 2
  • The model considers one single-antenna primary link and one single-antenna secondary link, with the secondary transmitter knowing the fading CSI for all three links.The additional CSI is for the primary transmitter-to-primary receiver channel.Source: §I · p. 2
  • With primary-channel CSI, the secondary user can transmit at higher power during deep fading when the resulting primary performance loss is negligible.Obtaining primary-channel CSI is described as challenging; suggested routes include eavesdropping on primary feedback or using a cooperative secondary node.Source: §I · p. 3
  • The proposed primary capacity loss constraint (PCLC) limits the primary user's ergodic capacity loss from secondary transmission to a prescribed threshold.The paper states that PCLC is more directly related to primary-user transmission than the average interference power constraint (AIPC).Source: §I · p. 3
  • The authors study optimal secondary-user power control under PCLC and report improved ergodic capacities for both primary and secondary users over AIPC.Source: §I · p. 3

II. SYSTEM MODEL

The system model has primary and secondary links sharing a narrow band under block fading. Each transmitter adapts power under its own constraints, while the SU uses available channel information to protect the PU.

II. SYSTEM MODEL

  • The PU and SU transmit simultaneously over a narrow band under block fading, with coherent communication and a joint fading state across the channels.The receivers have independent unit-variance CSCG noise, and both links use optimal Gaussian codebooks.Source: §II · p. 4
  • The channel power gains e_i, g_i, f_i, and o_i are independent continuous random variables, and the SU transmitter knows g_i, f_i, and its equivalent channel gain h_i.The SU power policy is based on this available channel information.Source: §II · pp. 4–5
  • The PU may adapt q_i to f_i subject to average power Q, but is assumed oblivious to SU transmission and treats its interference as additional Gaussian noise.The PU power policy maps f_i to q_i, and the SU transmit power at state i is denoted p_i.Source: §II · pp. 4–5
  • The PU reaches Cmax only when the SU is off during PU transmission, while the unconstrained SU maximum uses water-filling.The PU condition is equivalent to OSA with perfect spectrum sensing; the SU water level is set so E[p_i] = P.Source: §II · p. 5
  • The SU adapts transmit power using available CSI to maximize its average rate while protecting the PU, subject to average power P.The SU receiver treats PU interference as additional Gaussian noise.Source: §II · p. 5
  • The model excludes PU power reactions to SU interference; such coupled SU–PU adaptations would complicate the design even for deterministic channels.The paper leaves this feedback phenomenon for future work.Source: §II · p. 5

III. SU POWER CONTROL UNDER AIPC

The AIPC policy maximizes the SU’s ergodic capacity while keeping average interference at the PU receiver below a threshold. Its PU capacity-loss bound holds regardless of the fading-gain distributions.

III. SU POWER CONTROL UNDER AIPC

  • AIPC constrains average interference power at the PU receiver below a predefined threshold while the SU maximizes its ergodic capacity under its own transmit-power constraint.The optimization is stated as convex.Source: §III · p. 6
  • The optimal AIPC policy is a modified water-filling rule whose water level varies with the SU-to-PU channel gain g_i.When g_i = 0, the policy reduces to standard water-filling with a constant water level; as g_i grows without bound, SU power becomes zero.Source: §III · p. 6
  • AIPC power control does not require PU-channel CSI, but can miss SU transmission opportunities when the PU is off and can expose an active PU to strong SU interference.The paper attributes these drawbacks to not jointly exploiting all CSI available at the SU transmitter.Source: §III · p. 7
  • The PU ergodic capacity loss under AIPC is at most log(1+Γ), regardless of the distributions of f_i, h_i, and g_i.The bound applies under the given AIPC threshold Γ.Source: §III · p. 7

IV. SU POWER CONTROL UNDER PCLC

The PCLC policy uses the PU’s capacity loss to constrain SU power while maximizing SU ergodic capacity. Its optimal rule uses the available channel information and is obtained through a zero-duality-gap formulation under continuous fading-gain distributions.

IV. SU POWER CONTROL UNDER PCLC

  • The proposed PCLC policy uses h_i, g_i, and f_i q_i; the required PU-side quantity is received signal power f_i q_i rather than exact PU-channel CSI f_i.The paper notes that f_i q_i may be easier for the SU to obtain in some cases.Source: §IV · pp. 7, 9
  • The PCLC directly constrains the PU’s ergodic capacity loss to a maximum tolerable value while the SU maximizes its ergodic capacity under its transmit-power constraint.The paper states that this optimization is non-convex, but the time-sharing condition holds for continuous fading-gain distributions, yielding zero duality gap.Source: §IV · p. 8
  • Compared with the AIPC rule, the PCLC power policy adds a multiplication factor before the ν(2)g_i term and is described as a self-biased water-filling solution.The factor is further expressed using f_i q_i and the SU power.Source: §IV · pp. 8–9
  • Under PCLC, SU power is positive only when g_i and/or f_i q_i are sufficiently small; when either is zero, the condition matches standard water-filling over h_i.The paper relates these low-interference cases to negligible PU capacity loss.Source: §IV · p. 9

V. NUMERICAL EXAMPLES

The simulations compare the proposed PCLC-based SU policy with the conventional AIPC-based policy under CP and WF primary-user power control. They report substantial SU capacity gains, particularly with WF, and show different SU-capacity behavior at maximum PU capacity for the two PU policies.

V. NUMERICAL EXAMPLES

  • In simulations, the channels are assumed independent CSCG random variables; P = Q = 10 corresponds to an equivalent average signal-to-noise ratio of 10 dB for both PU.The channel distributions are CN(0, 1), CN(0, 1), CN(0, 0.5), and CN(0, 0.01), respectively.Source: §V · p. 9
  • The simulations compare PCLC and AIPC policies across achievable PU and SU ergodic-capacity pairs, using CP and WF for PU power control.They also include AIPC lower-bound and auxiliary-MAC upper-bound cases; the MAC assumes collocated PU and SU receivers for joint processing.Source: §V · p. 10
  • At a 5% PU capacity loss, the proposed policy’s SU capacity gain over the AIPC policy is around 28% with CP and 50% with WF.Across both cases, gains are more significant with WF than with CP.Source: §V · pp. 10–11
  • With the proposed policy, SU capacity falls to zero at maximum PU capacity under CP, but remains nonzero under WF.The paper attributes WF’s greater gains to variable PU transmit powers based on PU CSI, which the proposed SU policy exploits.Source: §V · p. 11

VI. CONCLUDING REMARKS

The paper proposes protecting the PU by limiting its maximum ergodic-capacity loss from SU transmission, using PU CSI to make the constraint more directly tied to PU performance. Simulations show substantial capacity gains for both users over the conventional policy, while the conclusions identify scope boundaries and extensions.

VI. CONCLUDING REMARKS

  • The proposed policy limits the maximum permissible PU ergodic-capacity loss caused by SU transmission and exploits PU CSI, unlike conventional interference-power or interference-temperature constraints.The paper characterizes the new constraint as more directly related to PU transmission.Source: §VI · p. 11
  • Simulations show that the proposed policy can provide substantial capacity gains for both PU and SU over the conventional policy.Source: §VI · p. 11
  • The analysis considers ergodic capacity; the paper notes that outage capacity may be more appropriate for SU channels.The work also identifies imperfect or quantized PU CSI as an extension.Source: §VI · p. 11
  • The proposed scheme applies to general parallel Gaussian channels with sufficiently many subchannels, including broadband channels decomposable into narrow-band channels by multicarrier modulation and demodulation.Source: §VI · p. 11

PU-Tx

The supplied figure captions identify a system-model diagram, a root illustration, and achievable-rate figures for CP and WF primary-user power control.

PU-Tx

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