AbstractâIn this paper, we investigate a decode-and-forward. (DF) relaying protocol for a three-node half-duplex single- antenna network, consisting of a single ...
2013 IEEE Wireless Communications and Networking Conference (WCNC): PHY
A Decode-and-Forward Relaying Protocol with Partial CSIT and Optimal Time Allocation Yinjie Su∗† , Lingge Jiang∗ , and Chen He∗
∗
†
Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China Department of Electronic Engineering, Jiangsu University of Science and Technology, Jiangsu, P. R. China Email:{suyinjie, lgjiang, chenhe}@sjtu.edu.cn
Abstract—In this paper, we investigate a decode-and-forward (DF) relaying protocol for a three-node half-duplex singleantenna network, consisting of a single source-destination pair and a relay. The proposed relaying protocol, called DF with time allocation (DF-TA), can switch its transmission mode according to the partial channel state information at the transmitter (CSIT), which is obtained through a one bit feedback from the destination. We derive the diversity multiplexing tradeoff (DMT) of DF-TA in a closed-form, and develop an adaptive time allocation strategy to achieve its optimal DMT. We show that the DF-TA significantly improves the DMT of existing time allocation schemes with or without CSIT in DF relaying channel. Moreover, in contrast to the power control schemes based on CSIT, which are performed with the assumption of long-term power constraint, the DF-TA can be generalized to the practical scenarios where a strict short-term power constraint is imposed on, due to the environmental safety and interference prevention.
I. I NTRODUCTION It is well known that a relay network can act as a multipleinput multiple-output (MIMO) system so as to provide the diversity and/or multiplexing gain. The diversity gain enhances communication reliability, and the multiplexing gain improves spectral efficiency. The diversity-multiplexing tradeoff (DMT) [1] is an elegant formulation for the fundamental tradeoff between reliability and spectral efficiency in the high signalto-noise ratio (SNR) regime, and it has recently been one of the most commonly adopted performance metrics for measuring different cooperative protocols. Specifically, consider a sequence of variable rate codes Cρ operating at SNR ρ with rates R(ρ). Assuming a sufficiently long codeword, the diversity gain d and multiplexing gain r [1, 2] are defined respectively as d = − lim
ρ→∞
log Pout (ρ) log ρ
and
r = lim
ρ→∞
R(ρ) log ρ
(1)
where Pout (ρ) is the outage probability with a given rate R(ρ). The curve d(r) is termed the DMT. A three-node half-duplex single-antenna network, which consists of a single source-destination pair and a relay, is the elemental unit in relay networks. Hence a lot of efforts have gone into improving its achievable DMT. In [3], the orthogonal amplify-and-forward (OAF) and incremental amplify-andforward (IAF) protocols are introduced, and their DMT is determined when the two phases of the protocols ( i.e., the broadcast and cooperative phases ) are of equal duration.
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The nonorthogonal amplify-and-forward (NAF) protocol is presented in [4], where the source and the relay are allowed to transmit simultaneously in the cooperative phase. The work in [5] analyzes the DMT of NAF and shows that it has improved the DMT of OAF. For decode-and-forward (DF) relaying, the fixed and the variable nonorthogonal selection DF (NSDF) protocols are proposed in [6]. In the fixed-NSDF, the duration allocated for relay to listen is fixed, while in the variable-NSDF, to improve the DMT, the time dimension can be optimally allocated according to a given multiplexing gain. Both of them are static protocols [6], where the transmission is not relative to the instantaneous channel state information (CSI). Two wellknown dynamic protocols, i.e., the dynamic DF (DDF) and the enhanced dynamic DF (E-DDF) protocols, are presented in [5] and [7], respectively. In the DDF, the source keeps transmitting during the whole time frame, while the relay can start transmitting as long as it decodes the data packet without error. The duration for relay to listen depends on the instantaneous CSI of the source-relay link. In the E-DDF, the data packet is split into two parts using two separate codebooks, the relay keeps listening until it can decode the first part successfully, and then participates in the cooperation. The DDF and E-DDF can both achieve the cut-set DMT upper bound for multiplexing gains less than 0.5, whereas the E-DDF improves the DMT of DDF for multiplexing gains larger than 0.5. Recently, the impact of imperfect channel state information at the transmitter (CSIT) on the achievable DMT in DF relaying channels are investigated in works [8–13]. In practice, the imperfect CSIT is achieved by quantized CSI feedback from the receiver or imperfect channel estimation at the transmitter through pilots. In [9], various power control schemes based on the quantized CSI feedback in relay channels are investigated with the assumption of long-term power constraint, where average power constraint is taken over both the codewords and channel fading coefficients, and thus the transmitters can use a much higher power level to combat outage. The extended research on two-way channels is given in [13] later. In [12], an adaptive power control strategy with the estimated CSIT was proposed for the orthogonal DF relaying, and then the authors extended the work to the DDF protocol in [8]. It is shown that power control based on the imperfect CSIT significantly improves the achievable diversity gain. These
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power control schemes, however, can not be generalized to the short-term power constraint scenarios, where the transmit power in any time duration should not exceed a certain amount [14], due to the environmental safety and interference prevention. Under the short-term power constraint, it has been known that time allocation with CSIT can improve the DMT in most of the delay-limited DF relaying systems, however, it is still outperformed by DDF. A time allocation scheme with quantized CSIT is proposed in [9], and the authors show that it can approach the performance of DDF as the quality of CSI feedback increases. In this paper, we propose a relaying protocol, called DF with time allocation (DF-TA), and investigate the DMT of the considered relaying channel. The proposed DF-TA protocol can switch its transmission mode according to the partial CSIT, which is obtained through a one bit feedback from the destination. We derive the DMT of DF-TA in a closed-form, and develop an adaptive time-allocation strategy to achieve its optimal performance. We show that the DF-TA can significantly improve the DMT of existing time allocation schemes with or without CSIT in DF relaying channel. Moreover, in contrast to the power control schemes based on CSIT, which are performed with the assumption of long-term power constraint, the DF-TA can be generalized to the practical scenarios where a strict short-term power constraint is often imposed on. The rest of this paper is organized as follows: Section II introduces the system model and describes the proposed protocol. In Section III, we derive the DMT of the protocol in a closed-form, and present the optimal time-allocation strategy. The work is summarized in Section IV.
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Fig. 1. Two modes of the DF-TA. In mode 1, each data packet is transmitted over its dedicated frame. In mode 2, the current data packet is transmitted over a fraction of the current frame ( i.e., duration t ), the remainder duration ( i.e., duration 1 − t ) is utilized for improving the transmission quality of the next data packet.
where i, j ∈ {S, R, D}, F ∈ {1, 2}. The superscript F = 1 ( F = 2 ) denotes that the channel coefficient is for the current frame ( the next frame ). The duration of each frame is normalized as 1, and the duration of broadcast phase in the DF-TA is denoted as t ( 12 ≤ t ≤ 1). Note that we only consider the case when t ≥ 12 , and the reason follows [6], i.e., if t < 12 and r > 12 , the relay is always in outage. With t, two events can be defined as: M1 = {t log(1 + ρ∥h1SD ∥2 ) < R′ } M2 =
{t log(1 + ρ∥h1SD ∥2 )
′
≥R}
(3) (4) ′
II. S YSTEM MODEL AND P ROTOCOL DESCRIPTION Consider a three-node relay network consisting of a single source-destination pair and a DF relay, each node with a single antenna. A half duplex constraint is imposed on the relay, i.e., it can not transmit and listen simultaneously. Throughout this paper, a frequency non-selective, quasi-static, Rayleigh fading environment is assumed, where all the channel coefficients are constant within a frame, but change independently from one frame to another. Let hij be the channel coefficient of the link between a transmitting node i and a receiving node j. hij is a complex Gaussian random variable with zero mean and equal variance 0.5 on both real and imaginary parts. The white Gaussian noise at the receiving node j denoted by nj , is assumed to be independent and identically distributed (i.i.d.) with zero mean and unit variance. The short-term power constraint is assumed. All the nodes transmit with the same power, denoted by ρ. We adopt the following input-output relation for the channel: √ yj = ρ hij xi + nj (2) where yj represents the normalized signal received at node j, and xi represents the normalized signal transmitted by node i. In order to describe the protocol clearly, we denote the source, the destination, and the DF relay as S, D, and R, respectively. The channel coefficients are denoted as hF ij ,
where ∥ ⋅ ∥ denotes the modulus of a complex scalar, R is the transmission rate. The two events reflect the channel state of the source-destination link. Specifically, if M2 occurs, the link can support a successful transmission for the data packet within t, and if M1 occurs, this transmission can not be supported. As a result, we can use a one bit feedback to denote the CSI of the source-destination link. Before S starts its transmission, D measures its incoming channels and evaluates whether M1 or M2 occurs. Then, the transmitters can obtain the CSI through a one bit feedback broadcasted by D. According to the partial CSIT, the DF-TA can work in the following two different modes ( see Fig.1 ): 1) If M1 occurs, the system works in mode 1: In this mode, the system transmits each data packet over its dedicated frame. Specifically, the transmission for each data packet is divided into two phases, i.e., the broadcast phase and the cooperative phase. t and 1 − t are the durations of the broadcast and cooperative phases, respectively. S keeps transmitting during the whole frame, while R listens in the broadcast phase ( i.e., duration t ). If R decodes the data packet without error, it will transmit the data packet in the cooperative phase ( i.e., duration 1 − t ), otherwise R remains silent. 2) If M2 occurs, the system works in mode 2: Firstly, the current data packet is transmitted directly from S to D over a fixed duration within the current frame ( i.e.,
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duration t ). Then, S starts its transmission for the next data packet and keeps it till the end of the next frame. On the other hand, R listens for the next data packet over the remaining portion of the current frame ( i.e., duration 1−t ). If R decodes the data without error, it will transmit it during the next frame, otherwise R remains silent.
3
2.5
0.5
0
(6) (7)
O∣M2 =
We use the symbol ≐ to denote exponential equality, i.e., the expression log f (ρ) lim =b (8) ρ→∞ log ρ ⋅
⋅
can be denoted as f (ρ) ≐ ρb , and ≥, ≤ are similarly defined [15]. With (1), the system outage probability can be calculated in the following theorem. Theorem 1: Giving the transmission rate R′ ≐ r log ρ, a fixed time duration t ( 12 ≤ t ≤ 1), the outage probability of DF-TA is given by P (O) ≐ ρ−d(r) , where, √ for 12 ≤ t ≤ 17−3 , 2 r r ∈ [0, 1] (9) d(r) = 2(1 − )+ + (1 − r) t ⋆ (a)+ denotes max(0, a). for
√ 17−3 2
