IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 5, MAY 2015
791
Power Allocation and Performance Comparison of Full Duplex Dual Hop Relaying Protocols Thinh Phu Do and Tuyet Van Thi Le
Abstract—This paper provides two optimal power allocation (OPA) strategies for full duplex (FD) relay networks with amplify and forward (AF) protocol. Two strategies are designed based on statistical channel state information (S-CSI) and instantaneous CSI (I-CSI) to minimize the system outage probability under total source and relay power constraint. For the S-CSI scheme, the OPA factor is found through an exhaustive search while, for the I-CSI scheme, the OPA factor is given in a closed-form expression. To evaluate quickly the system performance with two proposed schemes, we derive the tight closed-form lower and upper bounds on the system outage for S-CSI based OPA scheme and the asymptotic performance for I-CSI based OPA scheme. Furthermore, how much difference in performance between AF and decode and forward (DF) relaying with OPA is also verified through our numerical results. Index Terms—Full duplex, power allocation, relay networks.
I. I NTRODUCTION
D
UAL-HOP relay network with the advantages of high throughput, reliable communication, and broad coverage has been an active research topic. In this network, the relay employing amplify and forward (AF) or decode and forward (DF) protocol operates in half-duplex (HD) or full-duplex (FD) mode. While the HD mode causes loss in spectral efficiency, the FD mode resolves this issue with the price of suffering the loop-interference at the relay. In the literature, a large amount of work has been devoted to FD relaying as a potential candidate for the next generation systems [1]–[4]. The authors in [1] study the feasibility of the full-duplex mode in the presence of loop interference. A transmit antenna gain control scheme for AF protocol to reduce the loop interference was proposed in [2]. In [3], a hybrid scheme that switches opportunistically between HD and FD mode has been proposed for both AF and DF protocol to maximize the end-to-end signal to noise ratio (SNR) at the destination. In [4], block transmission scheme is adopted for FD DF relaying to exploit the available cooperative diversity. Another research line focuses on optimal resource allocation in FD [5]–[10]. In [5], the optimal power allocation (OPA) problem under individual power constraint and total power constraint has been investigated to maximize the capacity of FD relay network with AF protocol without taking into consideration the impact of the direct link. When the direct link is non negligible, transmit power optimization for FD with DF protocol is investigated in [6]. In [7], the authors consider OPA at the secondary source and relay to minimize the outage probability Manuscript received October 14, 2014; revised March 16, 2015; accepted March 16, 2015. Date of publication March 24, 2015; date of current version May 7, 2015. The associate editor coordinating the review of this paper and approving it for publication was T. Riihonen. The authors are with the Department of Electronics and Radio Engineering, Kyung Hee University, Seoul 130-701, Korea (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/LCOMM.2015.2414432
in DF cognitive FD relay systems. The resource allocation problems in the context of MIMO have been addressed in [8]–[10]. Through our survey, the OPA problem for FD with AF relaying when the impact of direct link is non-negligible has not been well addressed. To fulfill this gap, this paper provides two OPA strategies based on statistical channel state information (S-CSI) and instantaneous CSI (I-CSI) to minimize the system outage probability under sum power constraint. In addition, the performance comparison between AF and DF relaying in FD mode with OPA is shown in numerical results. II. S YSTEM AND C HANNEL M ODEL Consider a dual-hop network consisting of a source S, a relay R, and a destination D. The source and destination are singleantenna nodes while the relay is equipped with two-antennas (one for transmitting and one for receiving signals) for FD operation. The channel between two nodes A and B experiences Rayleigh fading and described by hAB ∼ CN (0, ΩAB ) for A, B ∈ {S, R, D} where ∼ stands for ‘distributed as’ and CN (μ, σ 2 ) denotes the circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 . The received signal at the relay and destination at time t are given by ˜ RR (t)xR (t) + nR (t) yR (t) = hSR (t)xS (t) + h (1) (2) yD (t) = hRD (t)xR (t) + hSD (t)xS (t) + nS (t), respectively, where xA (t) is the transmitted signal with power ˜ RR (t) ∼ CN (0, ΩRR ) is the instantaneous PA at node A, h residual interference at the relay after performing interference mitigation,1 and nA (t) ∼ CN (0, σ 2 ) is the additive noise at node A. The signal xR (t) in (1) and (2) is expressed as xR (t) = ˜ RR |2 + σ 2 ) GyR (t − τ ) where G = PR /(PS |hSR |2 + PR |h is the amplification coefficient2 and τ is an amount of delayed symbols due to signal processing operations at the relay. For this system, the instantaneous end-to-end (e2e) signal to interference plus noise ratio (SINR) γe2e is expressed as γR γD γe2e = , (3) γR + γD + 1 αRD 2 2 SR where γR = PRPαSα and γD = PPS RαSD +1 with αAB = |hAB | /σ RR +1 2 2 ˜ RR | /σ . Based on (3), the for A, B ∈ {S, R, D} and αRR = |h outage probability Pout of the system is given by
Pout = Pr {log2 (1 + γe2e ) < R} = Fγe2e (T ),
(4)
1 We model the loop interference channel as a Rayleigh fading channel under the assumption that any line of sight component is effectively reduced by antenna isolation but the scattering multi-path components still remains due to imperfect cancellation. 2 The amplification coefficient changes with the I-CSI. However, this coefficient does not necessarily imply the exact knowledge of the I-CSI since it can be for instance obtained via energy detection techniques.
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IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 5, MAY 2015
where R is the target rate, FX (·) is the cumulative density function (cdf) of the random variable (r.v.) X, and T 2R − 1. In this letter, we design two PA strategies based on statistical CSI (S-CSI) and instantaneous CSI (I-CSI) to minimize Pout under total power budget constraint3 PS + PR = PT where PT denotes the total power. This constraint is widely adopted for cooperative communication and motivated from the perspective of system power usage in delivering a given amount of data from the source to the destination. The details of two PA strategies are presented in the following sections. III. P OWER A LLOCATION ¯ T where In this section, given PS = βPT and PR = βP β¯ = 1 − β with 0 < β < 1, we aim to design the OPA factor depending on the S-CSI (i.e., mean and variance) or I-CSI to minimize the outage probability Pout for AF relaying.4 A. S-CSI Based OPA
IV. P ERFORMANCE A NALYSIS A. S-CSI Based OPA For notational convenience, we define λ1 βPT1ΩSR , λ2 1 1 1 ¯ T ΩRR , λ3 βP ¯ T ΩRD , and λ4 βPT ΩSD . The outage probaβP bility of the AF relaying is given by λ2 λ4 e−(λ1 +λ3 )T λ3 (λ2 + λ1 T ) × {(1 + λ4 + λ3 T )I1 (q) + λ3 I2 (q)} (9) 2 +λ1 T λ4 2 and where q = λ1λT2 +λ , + T, λ T + λ T, λ 1 1 3 T λ 1 3 ∞ k −(dt+ ct ) t e Ik (a, b, c, d) dt (10) (t + a)(t + b)2 Pout∗ = Fγe2e (T ) = 1 −
0
The OPA factor β † is determined by exhaustive searching as †
β = arg min Pout (β).
(5)
0
