Differential Distributed Space-time Block Code for Two-way Relay. Channel with Physical-layer Network Coding. Kai Zhu and Alister G. Burr. Communications ...
PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
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Differential Distributed Space-time Block Code for Two-way Relay Channel with Physical-layer Network Coding Kai Zhu and Alister G. Burr Communications Research Group, Department of Electronics University of York, YO10 5DD, United Kingdom
Abstract— In this contribution, we present a low-complexity differential cooperation scheme for communications over two-way relay channels. More specifically, a frame of Differential PhaseShift Keying (DPSK) symbols is generated at the source nodes, while differential distributed space-time block coding (DDSTBC) scheme is invoked at each cooperating relay node. Since non-coherent detection can be carried out to recover the transmitted signals at both relay and destination nodes, it is not necessary to incorporate any channel estimation components in our proposed system. A selection relaying protocol based on CRC is utilized at the relay nodes to counteract the negative effects of error propagation. It is shown that full diversity order is still attainable at the destination nodes, even when the source-to-relay link is not protected by powerful channel codes with high computational complexity. 1. INTRODUCTION
New applications of wireless communications in networked devices such as wireless sensor networks, body area networks, and the smart grid will result in networks containing much larger numbers of low powered communication nodes than current wireless networks. Networks of this sort are more likely to form a peer-to-peer or heterogeneous mesh topology, rather than the star topology more common today, and hence require data to be forwarded by relaying from node to node through the network. However, since links in the network may be unreliable due to fading or node failure, diversity provided by cooperation between multiple relay nodes is very desirable to improve network robustness [1]. Distributed space-time block coding (DSTBC) [2] is one of the most popular cooperative MIMO techniques developed for multi-user communication environments. DSTBC is capable of offering similar temporal and spatial diversity gain as conventional MIMO systems employing multiple colocated antennas. However, DSTBC requires accurate estimation of the channel state information (CSI) for reliable detection at the receiver. As a remedy, a differentially encoded non-coherently decodable STBC scheme was proposed in [3]. By taking full advantage of the relationship between two successive transmitted symbols, the information conveyed by differential STBC signals can be recovered without the knowledge of CSI. Hence, compared with its coherently detected counterpart, differential STBC is appealing in saving power and bandwidth otherwise required for training symbols, as well as reducing implementation complexity. The classic unidirectional cooperative communication has been recently extended to bidirectional or two-way relaying [4] with the assistance of physical-layer network coding (PNC) [5]. Unlike other superposition coding techniques, the primary interest of PNC is to directly extract the network coded symbols from superimposed received signals at the relay nodes instead of explicitly detecting the individual symbols separately and independently. Therefore, the spectral efficiency as well as the achievable channel capacity is significantly increased by deploying PNC in the relaying protocol. In this contribution we combine the benefits of differential and distributed STBC with two-way relaying, and propose a differential distributed STBC (DDSTBC) scheme for the physicallayer network coded two-way relay channel using a “decode-and-forward” cooperative protocol. More specifically, our investigation first concentrates on the performance of unidirectional twohop cooperative differential STBC system. Similar to the strategy used in [6], the problem of error propagation induced in the decoding and re-encoding stage can be effectively circumvented by incorporating an appropriately-designed frame-by-frame (or packet-by-packet) based selection relaying protocol [7] at each relay node. Hence, although the antenna array is constructed in a distributed fashion, full diversity order is still achievable at the destination. Subsequently, we extend the selection relaying aided differential DSTBC scheme to two-way relaying scenario and propose a simple method to directly extract the network coded symbols from two superimposed differentially encoded signals without any assistance of CSI.
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 293
r1 h r 1 d2
h r 1 d1
. . .
h s 1r1
t1 h s 1rN
h s 2r1
t2 h s 2rN
h r N d2
rN
h r N d1
MAC Phase BC Phase
Figure 1: The schematic of a classic multi-relay aided two-way cooperative communication system. 2. SYSTEM MODEL
The symmetric structure of a classic multi-relay aided two-way cooperative communication network is depicted by Fig. 1, where two ordinary time-division half-duplex wireless terminals (t1 , t2 ) simultaneously exchange information with the assistance of N number of parallel cooperating relay nodes (r1 , r2 , . . . , rN ). Note that each terminal node acts as a source node (s) as well as a destination node (d). Furthermore, each terminal and relay node as seen in Fig. 1 is equipped with a single antenna for the consideration of balancing the trade-off between the implementation complexity and system robustness. A transmission session consists of two stages: the multiple access (MAC) phase as well as the broadcast (BC) phase. In the MAC phase, a frame of uniformly-distributed information bits xsi are encoded using Differential M-ary Phase-Shift Keying (DPSK) modulation and transmitted by the two source nodes simultaneously. If the DPSK symbols are denoted as vsi , the received signal at the jth relay node, which is basically a noisy version of the superposition of two differentially-encoded and channel-corrupted M-PSK signals, is formulated by: yrj =
2 X ¢ ¡ hsi rj vsi + nrj ,
(1)
i=1
where j ∈ {1, 2, . . . , N } and hsi rj is the quasi-static Rayleigh fading coefficient of the transmission link between the ith source node and the jth relay node, which is constant for all symbols within a frame. And nrj is the complex-valued Additive White Gaussian Noise (AWGN) introduced at the 2 = N /2. jth relay node having a zero mean and a variance σI2 = σQ 0 Next, PNC is employed to decode this superimposed signal yrj and extract the network coded (r ) (exclusive or-ed) symbols urj without the knowledge of CSI. Assuming the notation xˆsi j represents the information sequences estimated by the jth relay node, the network coded symbols are defined as: j) j) urj = x ˆ(r ˆ(r (2) s1 ⊕ x s2 , where ⊕ indicates an element-by-element modulo-two addition performed in the Galois Field GF(2m ), which can be simplified to the exclusive or arithmetic when m = 1. The principle of acquiring the network coded symbols using differential PNC will be elaborated further in the next section. In order to enhance the error-resilience against potential error propagation, after obtaining the network coded symbol frame, an error-detecting process is carried out to calculate its Cyclic Redundancy Check (CRC) value. Owing to the linearity of the CRC encoders1 , each relay node is capable of distinguishing whether one specific frame of network coded symbols is generated correctly by comparing its CRC with the ‘modulo-two sum’ of two CRCs corresponding to the information streams at two source nodes. More specifically, if two uncoded information sequences pass the same CRC check using identical CRC generator polynomial, their modulo-two sum will also pass. On the other hand, when one is in error, or both are in error but in different positions, the check will fail. Depending on the results of CRC checks, each cooperating node can decide whether to become active during next transmission period or just keep silent. 1 The
generator polynomial used here is Γ = [x8 + x7 + x4 + x3 + x + 1], which corresponds to the 9-bit string {110011011}.
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During the BC phase, only correctly estimated network coded symbols are re-encoded into differential DSTBC symbols wrj and broadcasted to the destination nodes. Although each cooperating relay node only constitutes one row of the differential STBC code matrix, a frame of virtual differential STBC codewords is received at the destination nodes. The received signal at the ith destination node can be expressed as: yd i =
N X ¡ ¢ hrj di wrj + ndi ,
(3)
j=1
where i ∈ {1, 2} and hrj di denotes the complex-valued quasi-static Rayleigh fading coefficient of the channel between the jth relay node and the ith destination node, while ndi is the AWGN induced 2 = N /2. Note that the at the ith destination node with a zero mean and a variance σI2 = σQ 0 transmit power of each source, relay node is normalized to unity; therefore, the overall power of P 2 = 1. differential DSTBC codewords is N |w | rj j=1 At the destination node, a conventional differential STBC decoder followed by a M-PSK demapper are deployed to recover the network coded symbols u ˆrj . Eventually, each destination node is capable of retrieving the information bits transmitted from corresponding source node by applying the exclusive or between the estimated network coded symbols and their local information as follows: x ˆs1 = u ˆrj ⊕ xs2 . (4) Similarly, for the information bits transmitted from s2 , we have: x ˆs2 = u ˆrj ⊕ xs1 ,
(5)
where j ∈ {1, 2, . . . , N }. 3. PRINCIPLE OF DIFFERENTIAL PNC MAPPING
In this section, we will introduce the principle of differential PNC mapping, which is employed at each receiving relay node to extract the network coded symbols from the superimposed signal yrj . For ease of analysis, we assume that a 2-level differential PSK modulation scheme, namely differential BPSK, is used at the source nodes to modulate the information bits. Furthermore, we consider N = 2 relay nodes located in the middle of the direct line-of-sight path between t1 and t2 in the following discussion. If ‘+1’ is chosen as the reference symbol for the DBPSK modulators at both source nodes, the mapping rule of this novel differential PNC can be generalized in Table 1. Similar to the conventional DPSK demodulation, the differential PNC mapping is designed to successively process the received signal by taking advantage of the relationship between two adjacent Diff. PSK Decoder Diff. PSK Encoder
Quasi Static Rayleigh Fading
Diff. DSTBC Encoder Quas i Static Rayleigh Fading
Relay node 1
Diff. PSK Decoder
Source node
CRC
CRC
Diff. DSTBC Encoder
Diff. STBC Decoder
PSK & PNC Demapper
Destination node
Relay node 2
Figure 2: The schematic of the proposed DPSK-DDSTBC scheme for one-way relaying case.
yr j
ur j
|yr j |
f (| y r j | )
D
Figure 3: The schematic of the novel differential PNC mapper used at the relay nodes.
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 295 Table 1: An example of PNC mapping using two differential BPSK symbols. The reference symbols for vs1 and vs2 are assumed to be [+1, +1].
Time T Time T +1 Time T Time T +1 Time T Time T +1 Time T Time T +1
Info. Bit xs1 xs2 0 0 0 0 0 1 1 0 1 1
Diff. Symbol vs1 v s2 +1 +1 +1 +1 +1 −1 −1 +1 −1 −1
Superimposed Symbol at Relay m +2 +2 0 0 −2
PNC Codeword 0 0 1 1 0
New Diff. Symbol f(m) +1 +1 −1 −1 +1
0 0 0 1 1
1 0 1 0 1
+1 +1 +1 −1 −1
−1 −1 +1 −1 +1
0 0 +2 −2 0
1 0 1 1 0
−1 +1 −1 −1 +1
1 0 0 1 1
0 0 1 0 1
−1 −1 −1 +1 +1
+1 +1 −1 +1 −1
0 0 −2 +2 0
1 0 1 1 0
−1 +1 −1 −1 +1
1 0 0 1 1
1 0 1 0 1
−1 −1 −1 +1 +1
−1 −1 +1 −1 +1
−2 −2 0 0 +2
0 0 1 1 0
+1 +1 −1 −1 +1
symbols. Hence, accurate estimation of CSI is unnecessary. When the received signal at each relay node is the superposition of two differential BPSK modulated symbol sequences, the schematic of the differential PNC mapper is illustrated in Fig. 3. As shown in Fig. 3, the amplitude of the received signal yrj is first acquired by calculating its absolute value. Subsequently, the resultant output is fed into a function f (m), which is defined as: f (m) =
m2 − 1, 2
m > 0.
(6)
Finally, a classic differential decoder is invoked to produce the network coded symbols. 4. PERFORMANCE EVALUATION
The Bit Error Ratio (BER) performance of the proposed DPSK-DDSTBC scheme with a straightforward CRC-based selection relaying strategy for the one-way relaying case is evaluated and quantified using Monte-Carlo simulation shown in Fig. 4. It is assumed that the quasi-static Rayleigh fading channel model is invoked in the simulation. Furthermore, the frame length used at both source and relay nodes is defined as Ns = Nr = 50, 100, 300 DPSK/DDSTBC symbols with BPSK modulation. As illustrated in Fig. 4, the BER of the DDSTBC with selection relaying (DDSTBC-SR) shares the same slope with the conventional non-cooperative differential STBC scheme having two colocated transmit antennas and a single receive antenna, which is chosen as the benchmark. This indicates our proposed DDSTBC scheme achieves second order diversity. By contrast, although the cooperation stage is assisted by multiple relay nodes, the DDSTBC scheme without selection relaying strategy (DDSTBC-NO-SR) is only capable of providing a diversity order of one due to the lack of an efficient countermeasure to alleviate the detrimental effect of error propagation, which degrades the system BER performance by more than 5 dBs at BER = 10−3 . It is also worth noticing the effects of different frame length shown in Fig. 4. When the frame length increases from 50 to 300, the BER performance has a slight degradation. This is caused by
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SISO (Tx = 1, Rx = 1) Non-cooperative Differential STBC (Tx = 2, Rx = 1) DDSTBC-NO-SR DDSTBC-SR (Frame length = 50) DDSTBC-SR (Frame length = 100) DDSTBC-SR (Frame length = 300)
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10 0
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Figure 4: BER versus Eb /N0 performance of the proposed novel DPSK-DDSTBC scheme with selection relaying strategy.
the fact that it becomes difficult to ensure the whole frame is decoded correctly when the frame length is relatively long. Therefore, as mentioned before, the number of valid differential STBC codewords constructed by two relay nodes will decline in such circumstances. 5. CONCLUSION
A novel relay selection assisted differential distributed space-time block coding (DDSTBC) scheme for two-way cooperative communications was proposed and investigated in this paper. We have shown that, with the assistance of CRC-based selection relaying protocol, the proposed virtual differential STBC system was capable of approaching full transmit diversity order. On the other hand, the complexity of such system is lower than conventional MIMO system, since the distributed antenna array is constructed by a group of single antenna aided cooperating nodes. The signal detection is performed non-coherently at the relay and destination nodes so that the system complexity can be further reduced. Hence, our proposed scheme is practical and easy to implement. ACKNOWLEDGMENT
The financial support of the EPSRC UK and British Telecom (BT) is gratefully acknowledged. REFERENCES
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