Half-Duplex Relaying Strategy Suitable for a Relay with Mobility

Abstract

We propose a new time-division half-duplex estimate-and-forward (EF) relaying strategy suitable for a relay with mobility. We reconfigure EF relaying to guarantee a strong relay-destination link which is required to achieve a high rate using EF relaying. Based on the reconfigured model, we optimize the relaying strategy to attain a high rate irrespective of the relay position with preserving the total transmit bandwidth and energy. The proposed relaying strategy achieves high communication reliability for any relay position, which differs from conventional EF and decode-and-forward (DF) relaying schemes.

1. Introduction

Decode-and-forward (DF) and estimate-and-forward (EF) relaying protocols are two prominent relaying strategies for the three terminal relay channel composed of source, relay and destination nodes [1][2]. The performance of DF relaying is highly dependent on the relay position between the source and the destination [3]. The performance of EF relaying shows less dependency on the relay position under the condition of a strong relay-destination link [3][4][5][6]. In wireless communications, however, a strong relay-destination link is not feasible when the relay is not in close proximity to the destination. Thus, the performance of EF relaying is also highly dependent on the relay position. If the relay has mobility, as in the mobile relay and the nomadic relay systems [7][8], the relay can change its position randomly. Recently, a mobile relay for a LTE-Advanced system was investigated in [9]. A mobile relay equipped with amplify-and-forward (AF) protocol which utilizes minimum power was proposed in [10]. In fact, we need a new relaying strategy with sufficiently high resultant communication reliability, irrespective of the relay position. The new relaying strategy should not require bandwidth expansion and an energy increase for operation.

As a solution, we propose a new time-division half-duplex EF relaying strategy, where half-duplex relaying is preferred in practical cooperative communication systems due to the absence of a self-interference (echo) signal [11], and the time-division relaying strategy can be easily extended to frequency-division relaying. First, we reconfigure EF relaying such that the actual relay-destination channel is included in the newly defined relay unit in order to ensure that the resultant relay-destination link is always strong. Based on the reconfigured model, we manipulate equations associated with the achievable rate of relay channels, and propose a systematic way to optimize the relaying strategy to maximize the achievable rate. The proposed relaying strategy includes quantization at the relay as well as power allocation between the source and the relay. When optimizing the relaying strategy, we consider the actual relay-destination channel condition as well as the modulation order at the source node and the relay node with constraints on the transmit bandwidth and energy. With the same transmit bandwidth and energy, the proposed relaying strategy achieves higher communication reliability than direct communication and conventional EF relaying. The performance of the proposed relaying strategy is much less sensitive to the relay position than conventional EF and DF relaying. These observations show that the proposed relaying strategy is suitable for a relay with mobility.

 

2. System Model

We consider a time-division half-duplex relay channel composed of a source node (S), a relay node (R) and a destination node (D). Channels from S to R, from R to D and from S to D are called SR, RD and SD channels, respectively, each of which has the channel gain hsr, hrd and hsd, respectively.

The relay channel operates in a broadcast (BC) mode during the first time fraction t and in a multiple-access (MAC) mode during the next time fraction 1 − t, where 0 < t < 1, as depicted in Fig. 1. Suppose that S does not transmit a signal (silent) in MAC mode.

Fig. 1.Half-duplex relay channel operating in BC mode and MAC mode.

In BC mode, S transmits a symbol X, which is received as V at R after passing through the SR channel and is received as Z1 at D after the SD channel. In MAC mode, R transmits a symbol W which is received as Z2 at D after the RD channel. Note that W is formed at R by quantizing V as W = Qt(V), where Qt denotes an Lq-bin quantization function. We consider a scalar quantization Qt with low complexity because it does not result in remarkable information loss compared with an optimal vector quantization requiring a great deal of computation [12][13]. No additional channel coding is applied to W to avoid the resultant bandwidth expansion of the RD channel. Then, the relay channel is modeled as

where NR, ND1 and ND2 are zero-mean additive circular symmetric complex white Gaussian noises with the single-sided power spectral density of N0. At D, log-likelihood ratios (LLR's) of bits mapped to X are computed from Z1 in BC mode and from Z2 in MAC mode, which are combined to use in the detection and decoding processes.

For simple analysis, we suppose that all nodes are aligned on a straight line with R located between S and D as shown in Fig. 2. The distance of R from S and from D is d and 1 − d, respectively, with 0 < d < 1. Then, |hsd|2 = 1, |hsr|2 = 1 / dα and |hrd|2 = 1 / (1 − d)α, where α is a channel attenuation factor.

Fig. 2.Relay channel with all nodes aligned on a straight line.

As a reference system, we consider a direct communication system in which the Mo-ary symbol is transmitted from S to D with the energy per symbol ET. The relay system is constrained to utilize the same transmit energy and overall transmission bandwidth as those of a reference system. The energy constraint is expressed by

where ES and ER denote the energy per symbol at S and at R, respectively. To satisfy the bandwidth constraint, the relay system must transmit the same number of symbols as the reference system. For this purpose, alphabet sizes of X and W must be M = and L = , respectively, where X ∈ {x0,…,xM-1} and W ∈ {w0,…,wL−1}. We consider M and L be powers of two. It follows that t = and Lq = 2b(a/log2Mo−1) with positive integers a and b.

 

3. Relaying Strategy

3.1 Conventional EF Relaying

Let us consider a conventional configuration of the time-division half-duplex EF relaying as depicted in Fig. 3, where the relay unit (R) is represented by a dotted box. The achievable rate by this configuration is given by [11][12]

subject to

where Rrd is the achievable rate over the RD channel in MAC mode, and p(x) and p(w) denote the distribution of X and W, respectively. This is obtained from [11][12] by assuming that S is silent in MAC mode. Suppose that V is quantized as W without exploiting the side information Z1, which results in I(V;W | Z1) = I(V;W) . Note that I(V;W) = H(W) − H(W | V) = H(W) because W is a deterministic function of V, i.e., W = Qt(V). Thus, the constraint (4) is simplified as

Note that Rrd ≤ log2(1+|hrd|2). Suppose t = 0.5, d = 0.2, α = 2, Lq ≥ 4 and p(wi) = 1 / L which is identical for all i = 0,…,L - 1. Then, we have 2 ≤ H(W) ≤ and it follows that (1 - d)α ≤ . Since ≥ ER by (2), we obtain ≥ (1 - t)(1 - d)α = -0.1773 dB. This means that ≥ -0.1773 dB is required to satisfy constraint (4). If channel coded bits with the rate Rc = 1/2 are to be transmitted by EF relaying. then ≥ 2.833 dB is required to satisfy (4) because = Rc . In case of direct communication, reliable communication is available at Eb / N0 much lower than 2.833dB by using the rate 1/2 turbo codes [14]. This analysis tells us that conventional EF relaying may result in poorer performance than direct communication with some operating parameters. To avoid this problem, R is placed near D when EF relaying is used. Consequently, a conventional EF relaying strategy is not suitable for a relay with mobility. To resolve this problem, we propose a new EF relaying strategy under a new framework working well for various d values, even at low SNR.

Fig. 3.The models of conventional and reconfigured EF relaying.

3.2 Proposed Relaying Strategy

The proposed relaying strategy operates in the same manner as introduced in Sec. 2. S broadcasts M-ary symbol X ∈ {x0,…,xM−1} in BC mode during the time fraction t, where X is received as V at R and as Z1 at D. At R, V is quantized as L-ary symbol W ∈ {w0,…,wL−1} by W = Qt(V). At D, LLR’s of bits mapped to X are computed from Z1. In MAC mode during 1 − t, R transmits W which is received as Z2 at D. Then, LLR’s of bits mapped to X are computed from Z2 and combined with LLR’s obtained in BC mode. The SR channel can be represented by the transition probability p(wk | xj), j = 0,…,M - 1 and k = 0,…,L - 1 and defined by

where Uk denotes the quantization bin of V mapped to wk. The quantization at R can also be conducted by using the matched filtered signal , by which (6) can be written in another form as

where the bin bounded by is mapped to wk, and ℜ{⋅} and ℑ{⋅} denote the real part and the imaginary part, respectively. The RD channel can be represented by the transition probability f(z2 | wk), k = 0,…,L - 1, defined by

Let bℓ be the ℓ-th bit in the bit stream mapped to X, then the LLR of bℓ is computed in BC mode as

where and denote the set of symbols X whose corresponding ℓ-th bit is 0 and 1, respectively. In MAC mode, the LLR of bℓ is computed as

The LLR’s of each bit bℓ computed in BC mode and MAC mode are combined as L(bℓ) = L(bℓ | z1) + L(bℓ | z2) to be used in the detection and decoding processes.

Although the proposed relaying strategy and the conventional EF relaying scheme [12] operate in a similar manner, they differ in determining optimal parameters of relaying schemes. In the proposed relaying strategy, the modulation scheme of W and the actual RD channel condition are taken into account to optimize operating parameters. On the other hand, in the conventional EF relaying scheme, the RD channel is assumed error-free. For finding optimal parameters of the relaying strategy, let us reconfigure the time-division half-duplex EF relaying as depicted in Fig. 3, where the new relay unit is represented by a solid box with the label Rnew. Note that Rnew includes the actual RD channel as well as R. The newly defined RD channel is free of additive noise and attenuation so that Rrd → ∞ and the constraint (4) is not needed. Note that W is the output of R in the conventional configuration. Considering that Z2 is the output of Rnew, the optimization problem (3) with constraint (4) in the conventional configuration can be modified as

without a constraint in the new configuration. At low SNR, Z1 and Z2 are almost independent so I(X;Z1,Z2) ≈ I(X;Z1) + I(X;Z2) . In addition, I(X;Z1) and I(X;Z2) are maximized when X is uniformly distributed. Thus, at low SNR, (11) is approximated by

At low SNR, I(X;Z1) is upper-bounded by the capacity of M-ary input additive white Gaussian noise (AWGN) channel, denoted by CM(ES / N0), because X is modulated as an M-ary signal. For given d, ET and N0, p(w) is determined by ES and Qt. Consequently, for given d and ET, (12) can be written by

With p(x) = , we have

where

and

In the second equality of (16), p(xj | wk,z2) = p(xj | wk) is used because X, W and Z2 form a Markov chain in this order as well as in the reverse order, and in the last equality,

is used. A closed form of I(X;Z2) is obtained by plugging (15)-(17) into (14) with the aid of (6)-(8). Then, by using the closed form of I(X;Z2), we can find numerically optimal values of t and ES as well as the optimal quantizer Qt that maximize t(CM(ES / N0) + I(X;Z2)) and we can evaluate the resultant achievable rate REF for given d, ET and N0.

 

4. Numerical Results

Consider BPSK and QPSK modulated direct communication schemes (Mo = 2 and Mo = 4) as reference systems. We suppose that d is known to all nodes, and let α = 2 and N0 = 2. Optimal values of t and ES as well as the optimal quantizer Qt in the proposed relaying strategy for given d and ET are obtained as follows. We first find the candidate values of t satisfying t = with an arbitrary positive integer a, as introduced in Sec. 2, and fix the value of t as one of cadidates. Then, by varying the value of ES, we do the following. For each ES, we find threshold values of Qt that maximize the value of t(CM(ES / N0) + I(X;Z2)) by using the closed form obtained in Sec. 3. The quantization at R is conducted for the matched filtered signal . Each phase component of , i.e., I and Q, is quantized independently based on the set of per-phase thresolds , by which Lq-level quantization is obtained. Then, we find the value of ES and its corresponding which results in the maximum value of t(CM(ES / N0) + I(X;Z2)) for a given t. By repeating the same procedure for all candidate values of t, we find the optimal combination of t, ES and , and evaluate the achievable rate REF. The number of quantization bins Lq is sub-optimally chosen as the value above which the performance is not improved significantly by increasing Lq compared with the resultant growth of complexity. The values of per-phase thresholds are set as symmetric, i.e., θk = , k = 1,…, - 1.

First, consider the case that BPSK-modulated direct communication (Mo = 2) is a reference system. Through a numerical search, we determine t = 0.5 resulting in M = 4, and Lq = L = 16 as optimal values. The set of per-phase thresholds is in the form of {−θ1,0,θ1}. We choose QPSK and 16-QAM as the modulation schemes for X and W, respectively. Let us consider x0 = -a - ja with a = , which is a point in the signal constellation for the QPSK symbol X. The transition probability p(w0 | x0) is obtained by using (7) as

where Q(x) = . All other transition probabilities p(wk | xj) are obtained in a similar manner. Optimal parameters for some d and per-bit SNR, Eb / N0, with t = 0.5 and Lq = 16 are listed in Table 1 as samples.

Table 1.Optimal parameters of the proposed relaying strategy and resultant REF for some d and Eb / N0 with t = 0.5, Lq = 16, α = 2 and N0 = 2, where the reference system is BPSK-modulated direct communication. In numerical search, increments of ES and θ1 are 0.001.

Next, consider the case that QPSK-modulated direct communication (Mo = 4) is a reference system. We determine t = 0.5 resulting in M = 16, and Lq = L = 256 as optimal values. The set of per-phase thresholds is in the form of {−θ7,…,−θ1,0,θ1,…,θ7}. We choose 16-QAM and 256-QAM as the modulation schemes for X and W, respectively. Transition probabilities p(wk | xj), j = 0,…,15, k = 0,…,255, are obtained in a similar manner to the case of BPSK-modulated reference system as introduced above. Optimal parameters for some d and per-bit SNR, Eb / N0, with t = 0.5 and Lq = 256 are listed in Table 2 as samples.

Table 2.Optimal parameters of the proposed relaying strategy and resultant REF for some d and Eb / N0 with t = 0.5, Lq = 256, α = 2 and N0 = 2, where the reference system is QPSK-modulated direct communication. In numerical search, increments of ES and θk are 0.001.

The achievable rates evaluated by (13) with optimally chosen parameters for d = 0.95 are plotted in Fig. 4 for the cases that the reference system is BPSK and QPSK modulated direct communications. The capacity of the reference system (direct link) and the upper bound on the achievable rate of relay channel are also plotted. For fair comparison, the same transmit bandwidth and energy are considered for all schemes. The upper bound on the achievable rate of relay channel corresponds to the capacity of 1 × 2 SIMO (single-input multiple-output) AWGN channel under the assumption that the RD channel is perfect and S remains silent in MAC mode. It is observed from Fig. 4 that the achievable rate of the proposed scheme approaches the upper bound of the relay channel at low SNR especially when the reference system is BPSK-modulated direct communication. Achievable rates of the proposed relaying strategy for various relay positions are plotted in Fig. 5 and Fig. 6. Achievable rates of the conventional EF relaying are also plotted for various relay positions in Fig. 7 and Fig. 8. It is observed that the achievable rate of the proposed relaying strategy is insensitive to the relay position. On the other hand, the conventional EF relaying scheme shows high dependency on the relay position in terms of the achievable rate, and may not provide a reliable communication link when d is small, i.e., R is far from D. It is also observed that the proposed relaying strategy results in a higher rate than the conventional EF relaying scheme when d is not close to 1.

Fig. 4.Achievable rate of the proposed relaying strategy, the direct link capacity and the upper bound on the achievable rate of a relay channel, where the relay position d = 0.95.

Fig. 5.Achievable rates of the proposed relaying strategy for different relay positions d, where the reference system is BPSK-modulated direct communication.

Fig. 6.Achievable rates of the proposed relaying strategy for different relay positions d, where the reference system is QPSK-modulated direct communication.

Fig. 7.Achievable rates of the conventional EF relaying strategy for different relay positions d in case that the reference system is BPSK-modulated direct communication, where the achievable rate of the proposed relaying scheme for d = 0.9 is also plotted.

Fig. 8.Achievable rates of the conventional EF relaying strategy for different relay positions d in case that the reference system is QPSK-modulated direct communication, where the achievable rate of the proposed relaying scheme for d = 0.9 is also plotted.

We plot the simulated bit error rate (BER) performances of the proposed relaying, conventional EF relaying and DF relaying strategies in Fig. 9 - Fig. 12. In simulations, 16200-bit irregular low-density parity check (LDPC) codes [15][16] with 50 iterations of message passing decoding are used. For simulations associated with BPSK-modulated reference system, we use rate 1/3 irregular LDPC codes whose degree distribution polynomials are defined by λ(x) = 0.4x + 0.2x2 + 0.4x11 and ρ(x) = x4. For simulations associated with QPSK-modulated reference system, we use rate 1/5 irregular LDPC codes whose degree distribution polynomials are defined by λ(x) = 0.5333x + 0.1111x2 + 0.3556x11 and ρ(x) = 0.2x2 + 0.8x3. Degree distribution polynomials of irregular LDPC codes are chosen to show sufficiently good BER performances over a direct link. In conventional EF relaying [12], no data loss over the RD channel is assumed, i.e., z2 = wk. Since there is, in fact, signal attenuation and additive noise over the RD channel, we first demodulate z2 as , k = 0,…,L - 1, and compute L(bℓ | z2) by modifying (10) as

for MAC mode simulations of conventional EF relaying, where is the demodulated symbol of z2. When optimizing the conventional EF relaying scheme given by (3) and (4), a L-ary input AWGN channel capacity is used as Rrd. In DF relaying, V is decoded, re-encoded and mapped to M-ary symbols W at R, where the same channel codes are used at S and R, and the transmit power is allocated between S and R to achieve the maximum rate [1][3].

Fig. 9.BER performances of the proposed relaying and conventional EF relaying strategies, where the reference system is BPSK-modulated direct communication and the code rate is 1/3.

Fig. 10.BER performances of the proposed relaying and conventional EF relaying strategies, where the reference system is QPSK-modulated direct communication and the code rate is 1/5.

Fig. 11.BER performances of the proposed relaying and DF relaying strategies, where the reference system is BPSK-modulated direct communication and the code rate is 1/3.

Fig. 12.BER performances of the proposed relaying and DF relaying strategies, where the reference system is QPSK-modulated direct communication and the code rate is 1/5.

It is observed that the proposed relaying strategy achieves a BER performance gain over the reference system for all d values with satisfying bandwidth and energy constraints. The proposed relaying scheme shows good BER performances, irrespective of d, which is different from conventional EF relaying [12]. The performance of conventional EF relaying gets poorer as d decreases. It is also observed that DF relaying shows poorer BER performance than the proposed scheme for large and small d values, where the performance of DF relaying is highly dependent on d.

In Fig. 13 and Fig. 14, we plot the minimum values of Eb / N0 required by the proposed relaying, conventional EF relaying and DF relaying strategies to achieve the target rate with various relay positions, where minimum Eb / N0 required by direct communication is also plotted for comparison. For cases whose reference systems are BPSK and QPSK-modulated direct communications, the target rates are set as 1/3 and 1/5, respectively. Although the minimum Eb / N0 is achieved by an infinite-length optimal coding scheme, this performance index provides enough insight on the BER performances of coded relaying schemes under comparison. The minimum Eb / N0 requirement of the proposed relaying strategy is insensitive to the relay position, which differs from conventional EF relaying and DF relaying schemes. In case of conventional EF relaying, a higher value of minimum Eb / N0 is required as d gets smaller. For great or small d, the proposed relaying strategy requires lower minimum Eb / N0 than DF relaying.

Fig. 13.Minimum values of Eb / N0 required by the proposed relaying, conventional EF relaying and DF relaying strategies to achieve the rate 1/3 with various relay positions, where the reference system is BPSK-modulated direct communication.

Fig. 14.Minimum values of Eb / N0 required by the proposed relaying, conventional EF relaying and DF relaying strategies to achieve the rate 1/5 with various relay positions, where the reference system is QPSK-modulated direct communication.

Through various analyses, it is observed that the performance of the proposed relaying strategy is insensitive to the relay position. Consequently, the proposed relaying strategy is suitable for the relay system with mobility in which a relay position varies randomly.

 

5. Conclusion

We proposed a new time-division half-duplex EF relaying strategy resulting in reliable communication for all relay positions. We reconfigured EF relaying such that the channel between the relay and the destination is perfect, which is the basic requirement for EF relaying to achieve a high rate. From the reconfigured model, we manipulated equations associated with an achievable rate and found a systematic way to optimize an EF relaying strategy to maximize the achievable rate. The proposed EF relaying strategy enables reliable communication for all relay positions without bandwidth expansion and energy increase for transmission. Consequently, the proposed relaying scheme is suitable for a relay system with mobility.