A novel design of physical layer network coding in strong asymmetric two-way relay channels
© Wei et al.; licensee Springer. 2013
Received: 13 December 2012
Accepted: 28 May 2013
Published: 17 June 2013
The quality of two-way links is always asymmetric in practical two-way relay channels (TWRC) and therefore, the capacity of TWRC will be limited by the weaker link. An asymmetric modulation scheme, with physical layer network coding, was presented in order to improve the transmission reliability in TWRC. This makes full use of the stronger link to improve the overall transmission rate and also ensures the reliability of the weaker link. The simulation results show that the proposed asymmetric modulation scheme in the case of strongly asymmetric channels, compared to the symmetric transmission, enhances the system capacity significantly and also guarantees the system reliability.
KeywordsNetwork coding Asymmetric modulation Two-way relay channel Subset constellation
Network coding (NC) was originally proposed to improve the performance of multicast throughput in wired networks by Ahlswede et al. in 2000 . Recently, the broadcast nature of wireless channels has attracted a lot of research activities on the application of NC in wireless networks.
The two-way relay channel (TWRC) is a typical scenario in wireless communications. Physical layer network coding (PLNC) was proposed to improve the throughput of TWRC , which maps the superimposition of the signals received simultaneously to a digital bit stream. PLNC improves the system performance by making use of the interference, instead of avoiding it. PLNC can further be classed into two categories - PNCF (PNC over finite field) and PNCI (PNC over infinite field) - according to whether the network coding field adopted is finite or infinite . The capacity of TWRC with PLNC is higher than the traditional communication strategies [4, 5]. The design of modulation suited for TWRC with PLNC can be BPSK or QPSK , and an unconventional 5-ary modulation which is optimized according to the channel condition . In addition, PLNC can be combined with channel code to improve bit error rate (BER) performance of the system .
The research works reported above are all based on the same assumption that the transmission rate of two end nodes is symmetric. In practical TWRC, however, the quality of two-way links is always asymmetric. Therefore, the capacity of TWRC will be limited by the weaker link. Thus, in the symmetric rate transmission of TWRC, in order to ensure the reliability of the weaker link, the stronger link has to transmit and receive with low-order modulation as same as the weaker link. For this reason, the stronger link does not take advantage of its good channel conditions to improve the overall transmission rate, which lowers the validity.
Asymmetric modulation is a method to realize the asymmetric rate transmission. The power matching ratio of the two end nodes in TWRC is corresponding to the performance of symbol error rate in the multiple access phase [9, 10]. In the broadcast phase of TWRC, under the same BER constraint, the weaker link can decode at lower signal noise ratio (SNR) compared to the stronger link by exploiting a priori bit information in each transmit symbol .
This paper investigates the asymmetric rate transmission both in the multiple access phase and broadcast phase of the two-phase TWRC by designing an asymmetric modulation scheme with PLNC. The simulation results show that the proposed scheme not only improves the transmission validity by increasing the system capacity but also guarantees the transmission reliability.
The rest of this paper is organized as follows. Section 2 introduces the system model. Section 3 presents the new scheme of asymmetric modulation with PLNC. Section 4 analyzes the performance of the asymmetric modulation scheme. Simulation experiments and performance comparisons between the symmetric transmission mode and the proposed scheme will be discussed in Section 5. Finally, Section 6 concludes this paper.
2. System model
Multiple access phase (MAC). First, n 1 and n 2 modulate B 1 and B 2 respectively to X 1 and X 2. Second, n 1 and n 2 transmit X 1 and X 2 to the relay node n R simultaneously. Then n R demodulates the superimposition of the signal Y R to B R = B 1⊕B 2.
Broadcast phase (BRC). The relay node n R modulates B R to X R and broadcasts it to n 1 and n 2, simultaneously. Then n 1 demodulates Y 1 to B R and get the bit information of n 2 by using exclusive or (XOR) operation B 2 = B 1⊕B R. Similarly, n 2demodulates Y 2 to B R and get the bit information of n 1 by using XOR operationB 1 = B 2⊕B R.
So, n1 and n2 can finish the information exchange only by two phases. The importance of the information exchange is the design of modulation and demodulation at the relay node nR. In multiple access phase, nR is supposed to realize the demodulation of YR → BR = B1⊕B2. In broadcast phase, nR has to realize the modulation of BR → XR. The performance of the system depends on the design at nR, which is a key point in this paper.
3. Asymmetric rate transmission
The design of the modulation and demodulation for n1, n2, and nR will be presented in this section to realize the asymmetric rate transmission both in the multiple access phase and broadcast phase. For simplicity and without loss of generality, we assume (respectively denote the variances of h1 and h2) which means that the stronger link C1 (the channel between n1 and nR) has better quality than the weaker link C2 (the channel between n2 and nR).
3.1 Design of asymmetric modulation
The asymmetric modulation is proposed by utilizing the asymmetric channel quality to make n1 and n2 transmit and receive at different rates. For simplicity and clarity, QPSK and 16QAM will be as examples to be depicted for the design of the asymmetric modulation, which are respectively 2 bit/symbol and 4 bit/symbol.
3.1.1 MAC phase
3.1.2 BRC phase
In the BRC phase, nR first modulates B R to X R . Then nR broadcasts XR to n1 and n2. The constellation of XR is shown in Figure 3, which is same as the constellation of X2 in the MAC phase.
As illustrated in Figure 5, the constellation used to demodulate signals by n2 is QPSK, which is a subset of 16QAM constellation. In this way, the distance of the adjacent points is increased, so the BER performance is improved and the transmission reliability is guaranteed.
By using this scheme, in BRC phase, the signal modulated by high-order modulation (16QAM) is transmitted through the stronger link C1 to improve the transmission rate, while the signal modulated by low-order modulation (QPSK, which is the subset of 16QAM constellation) is transmitted through the weaker link C2 to ensure the transmission reliability.
3.2 Symmetric modulation for comparison
In order to show up the advantages of the proposed asymmetric modulation scheme, we use the symmetric modulation QPSK-QPSK as examples for a simple comparison.
4. Performance analysis
In this section, we will analyze the performance of the proposed asymmetric modulation and compare it to that of the symmetric modulation. As we known, C1 is better than C2. Without loss of generality, we assume μ> 1. For simplicity, we assume that the noises at the three nodes have the same variance, .
4.1 BER analysis
4.1.1 MAC phase
Where γR is SNR of the signals received at nR.
4.1.2 BRC phase
where γ1 and γ2 denote SNR of the signals received at n1 and n2, respectively.
4.3 Capacity analysis
The input X are equally probable symbols, and the probability p(x i ) can be obtained according to the corresponding modulation constellation. Substituting p(x i ) and Equation 7 into Equation 8, we can obtain the capacity of the equivalent virtual channel CV.
5. Simulation results
In this section, simulation results are presented to demonstrate the performance of our proposed scheme and to verify the accuracy of our analytical analysis in Section 4. In the simulation, all the numerical results are calculated with averaging over 10,000,000 packets, and the number of bits contained by each packet is equal to the bits contained by each symbol in the corresponding constellation. For simplicity and without loss of generality, we consider two scenarios of μ = 4 and μ = 8. The SNR of the stronger link C1 is 6 and 9 dB higher than that of the weaker linkC2.
5.1 BER performance
Here, the simulation results are presented to demonstrate the BER performance of the asymmetric modulation at n1 and n2.
Here, the simulation results are presented to demonstrate the capacity of the asymmetric modulation at the end nodes n1 and n2. The sum of capacity is also illustrated here.
In this paper, an asymmetric modulation scheme with PLNC in TWRC is proposed, which aims to improve both the validity and reliability in two-way relay transmissions. The proposed asymmetric modulation scheme realized the asymmetric rate transmission both in MAC phase and BRC phase of TWRC. In MAC phase, the BER performance at the relay is improved. In BRC phase, the capacity is boosted by making full use of the stronger link, and the BER performance is guaranteed by exploiting a priori bit information to demodulate for the weaker link. We derived the approximated BER expressions for the scheme proposed, which were also demonstrated by simulation experiments. Through the comparisons of the symmetric modulation scheme, it is found that by using the proposed asymmetric modulation scheme, the total capacity is improved significantly under the asymmetric level of the two-way links.
In addition, as well-known channel coding possesses the correcting ability and can improve the BER performance further, combining channel coding, network coding, and modulation for asymmetric transmissions in TWRC will be our future researches.
This work was supported by the National Natural Science Foundation of China under No. 61271240.
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