Comparison of Full-Duplex and Half-Duplex Modes with a Fixed Amplify-and-Forward Relay

Transcription

1 Comparison of Full-Duplex and Half-Duplex Modes with a Fixed Amplify-and-Forward Relay Taneli Riihonen, Stefan Werner, and Risto Wichman Helsinki University of Technology, Finland IEEE WCNC, Budapest, Hungary April 6, 9

2 Outline Introduction

3 Introduction to relaying modes S R D channel channel S R D one channel for end-to-end transmission Half-Duplex (HD) Pre-log / in capacity Mobile relays and cooperative communication Also with a single antenna Full-Duplex (FD) Loop interference Fixed infrastructure-based relays Separate rx and tx antennas Loop cancellation algorithms How to select the optimal mode?

4 Amplify-and-forward full-duplex relay link h LI h SR h RD S R D Fig.. Two-hop relay link with potential loop interference. The signal model: r[i] = h SRx[i] + h LIt[i] + n R[i] t[i] = βr[i τ] = β (h LIβ) j (h SRx[i jτ] + n R[i jτ]) y[i] = h RDt[i] + n D[i] j= Amplification by β = ( h SR + h LI + σ R) / due to transmit power normalization E x { t[i] } =, where E x { t[i] } = β j= ( h LI β ) j ( ) h SR + σ R = β h SR + σ R h LI β

5 End-to-end SINR Parametrization in terms of channel SNRs: Instantaneous: γsr = h SR /σ R, γ RD = h RD /σ D, γ LI = h LI /σ R Mean: γsr = E h { h SR }/σ R, γ RD = E h { h RD }/σ D, γ LI = E h { h LI }/σ R The received power in the destination E x { y[i] } = h SR β h RD } {{ } useful signal The instantaneous end-to-end SINR: γ = ( ( h SR +σ R ) h LI h SR h RD /β h LI + σ R ( ) + h SR + σ R β h RD h LI β } {{ h LI β } loop interference + β h RD σ R + σ D }{{} noise γ ) SR γ RD = h RD + σ D γ SR + (γ RD + )( γ LI + ) β

6 Average capacities () Infrastructure-based relay link The source and the relay are fixed and the destination is mobile SR and LI channels are modeled as static (AWGN) RD channel is modeled with Rayleigh fading Calculation of the average capacities ( C = E h {log ( + γ)}) In the full-duplex mode: C FD = e γ RD E ( γ RD ) e γ SR + γ LI + ( ) γ RD ( γ LI +) E γsr + γ LI + γ RD ( γ LI +) log e () In the half-duplex mode ( γli = and pre-log factor /): C HD = γ e ( ) γ SR + ( ) RD E γ e RD E γsr + γ RD γ RD log e ()

7 Average capacities () 6 γrd [db]. γrd [db]. γ SR [db] (a) Full-duplex, γ LI = 6dB. γ SR [db] (b) Half-duplex Fig.. Contour plots for the average capacity [bit/s/hz] with the transmission modes. The shaded region illustrates the SNR area where capacity with the half-duplex mode is higher than that with the full-duplex mode. There is a clear trade-off between the modes How large is the capacity gain due to proper mode selection? In which SNR region one mode if preferred over the other?

8 Mode selection Analytical rules for selecting the best mode Proposition : If γsr > γ LI, then C FD > C HD for all γ RD Full-duplex is the best at high SNR Corollary : If γli < db, then C FD > C HD for all γ SR and γ RD The loop interference may be embedded in the receiver noise Proposition : If γsr < γ LI, then C FD < C HD for all γ RD Half-duplex is the best at low SNR When γli γ SR γ LI, the choice depends on γ RD The mid-snr range

9 Capacity ratio of the modes γrd [db] γsr [db] γrd [db] γsr [db] Fig.. Contour plot for the capacity ratio CFD/ CHD when γli = db. The shaded region illustrates the SNR area where capacity with the half-duplex mode is higher than that with the full-duplex mode. Fig.. Contour plot for the capacity ratio CFD/ CHD when γsr/ γli = 6dB. The shaded region illustrates the SNR area where capacity with the half-duplex mode is higher than that with the full-duplex mode. When γ LI = db: C FD < C HD, if γ SR < db (Proposition ) C FD > C HD, if γ SR >.7dB (Proposition )

10 Break-even loop interference power () The capacity trade-off C FD C HD when γ LI C FD when γ LI For which γli = Γ LI the capacities are equal ( C FD = C HD)? Numerically solving γ LI from [ ( ) E γ RD γ SR + e γ RD E ( γsr + γ RD ) ] γ SR / γ RD = e γ LI + E ( γsr + γ LI + γ RD( γ LI + ) ) C FD > C HD when γ LI < Γ LI

11 6 7 Break-even loop interference power () γrd [db] γsr [db] γrd [db] γsr [db] 7 Fig.. Contour plot for the maximum γli [db] for which CFD CHD. Fig. 6. Contour plot for the minimum γsr/ γli [db] for which CFD CHD. C FD > C HD when γ LI < Γ LI The power of the loop interference in FD can be quite high, because the effect of having pre-log factor / in HD is severe

12 SNR gain of the FD mode The minimum SNRs needed to achieve capacity of bit/s/hz: Half-duplex Full-duplex, varying γli Full-duplex, varying γsr/ γli γrd [db] γ LI =,,, 6, 9dB γ SR/ γ LI =, 9, 6, db γ SR [db] Fig. 7. Contour plot illustrating the SNR value pairs ( γsr, γrd) that result in average capacity C = bit/s/hz. Depending on the loop interference power, the FD mode achieves the same capacity as the HD mode with up to db smaller SNRs

13 Numerical examples In a system where γ SR and γ RD are db: Capacity with the HD mode is..7bit/s/hz Capacity with the FD mode is..bit/s/hz if γli = 6dB When γli = db or γ SR/ γ LI = 6dB, the FD mode achieves % 67% or % % higher capacity than the HD mode The FD mode has approximately the same capacity as the HD mode if the loop interference power is as high as 6..7dB relatively to the relay input noise power if the desired signal power in the relay input is as low as..db relatively to the loop interference power The full-duplex mode is preferable in this example system, if the loop interference power can be suppressed below the calculated limits

14 The choice between full-duplex and half-duplex relaying modes represents a fundamental capacity trade-off The loop interference can be suppressed to a tolerable level in fixed infrastructure-based relays It may be better to allow some SINR degradation with the full-duplex mode than to allocate two channels for eliminating the loop interference with the half-duplex mode Derivation of closed-form end-to-end capacities Evaluation of the capacity improvement due to the full-duplex mode Solving for the SNR ranges in which one mode outperforms the other The full-duplex mode can be superior with practical SNR values

15 Thank you! Questions? Discussion?