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1、精品论文On the frequency offset compensation in physical-layer network coding using OFDM5WANG Zhou, XIE Gang, LI Xu(Electronic Engineering School, Beijing University of Posts and Telecommunications, Beijing100876)Abstract: physical-layer network coding greatly improves the throughput in the two-way rela
2、y system. However, due to the difference between the two frequency offsets coming from two sources10transmitting signals and the fact that the signal at the relay node is overlapped, it is difficult tocompensate the two different frequency offsets together. In the paper, this problem is analysied an
3、d a new method to calculate the compensation frequency offset based on golden section is put forward.Simulation results show that the algorithm has the same performance compared with the mean frequency offset compensation algorithm when the two signals from sources come through the15symmetry channel
4、s, but in other cases that channels are not symmetry, the proposed algorithm will greatly improves the bit-error-rate(BER) performance of demodulated signal at the relay node.Key words: cooperative communication; physical-layer network coding; two-way relay; frequency offset compensation200Introduct
5、ionWith development of the mobile communication technology, the data transmission rate has continuously enhanced, the communication frequency also presents the trend to the high frequency area. The new generation mobile communication technology needs to solve the problem of serious signal attenuatio
6、n causing by using high frequency bands to communicate. The introduction of25wireless relay nodes can expand the signal coverage and improve blind spot and hot spot communication coverage to efficiently solve above problems.Due to the characteristic of half-duplex at the relay node, the spectrum eff
7、iciency of relay system will be lost half. The two-way relay system based on network coding can improve the throughput by 1/4 compared with conventional relay system1. The concept of physical-layer30network coding(PNC) based on two-way relay system has been proposed in 200623. Because ofthe broadcas
8、t characteristics of the wireless channel, PNC is very suitable to be used in the wireless communication system. The two-way relay system using the physical network coding, which can greatly enhance the relay system throughput, and at the same time the transmission bit error rate performance doesnt
9、reduce, causes the upsurge of academic research today. The key35feature of PNC is that two source nodes send messages to the relay node at the same time, and then the overlapped message at the relay node is mapped to the XOR-message of the source nodes messages at physical-layer of the relay node. C
10、ompared with conventional two-way relay, the throughput of PNC improves nearly 1/3.F.Rossetto，M.Zorzi firstly explore OFDM-PNC in 2009 which introduces OFDM to PNC4.40Lu lu etc. implement the first practical PNC two-way relay system based on OFDM in 20125.Practical test shows that OFDM-PNC system im
11、proves the throughput greatly in the high SNR regime. The union of OFDM and PNC two-way relay can further enhance the system transmission rate, but also brings many other problems. In conventional point to point OFDM system, the45Brief author introduction:WANG Zhou(1988-),male,graduate student,mobil
12、e communication technology of next generation and cooperative relay technologyCorrespondance author: LI Xu(1960-),male,professor,wireless communication of next generation and electromagnetic compatibility. E-mail: lixu_- 9 -problem of carrier frequency offset can be solved effectively by accurate ca
13、rrier frequency offset estimation and compensation. However, in the system of OFDM-PNC, there exists different carrier frequency offsets between two source nodes and relay node, and signal at relay node is a overlapped signal from two source nodes, which makes it very difficult to effectively compen
14、sate50two frequency offsets at the same time. In 4, it firstly obtains two different carrier frequency offsets between source nodes and relay node in orthogonal timeslots, and then compensates the carrier frequency offsets using the mean of above two obtained carrier frequency offsets. In this paper
15、, the problem will be studied, then a algorithm calculating the frequency offset compensation will be proposed. The proposed algorithm converts the inter-carrier interference in PNC-OFDM55system and white gaussian noise into two same error pattern, and then minimizes the error pattern.Simulation res
16、ults show that the proposed algorithm greatly improves the BER performance of the relay node under the asymmetric channel compared with the method which compensates the frequency offsets using the mean of carrier frequency offsets.The rest of this paper is organized as follows. System model of PNC-O
17、FDM is introduced in60section 1. A new carrier frequency offset compensation algorithm is proposed in section 2. Then in section 3 the process of proposed algorithm is given. In the next section simulation results are depicted. At the last conclusion follows in section 5.1System model1.1 Introductio
18、n of PNC65Petar Popovski etc. and ShengLi Zhang etc. firstly proposed the idea of PNC separately in2006. The system model is as follow:S1 R S2time slot1 time slot2Fig.1. PNC system modelIn the time slot one, two source nodes send messages to relay node at the same time. Relay70node demodulates the s
19、uperposed signal through proper mapping in physical-layer resulting to bit-lever XOR superposition between source nodes messages at relay node. That is to say the result of demodulation is the result of XOR operation of the source nodes messages in the ideal situation. In the time slot two, relay no
20、de broadcasts the XOR message to two source nodes. After receiving the message, each source node gets the message from the other node by executing XOR75operation between itself message and the receiving XOR message. As a result, the purpose of exchanging the messages of two sources through two time
21、slots is achieved.1.2 System model of OFDM-PNCThe modulation of OFDM is used at the two source nodes. The relay node firstly processes the superposed signal by FFT, then gets the XOR message through maximum likelihood detection80toward the result of FFT. The receiving signal at the relay node is as
22、follow:cj 2p fct + x (t)e j 2p f ty(t) = x1(t)e 2+ n(t)e- j p2fct(1)c cx1 (t ) , x2 (t ) denote the base band signals of source node one and two.f , f are the carrierfrequencies of signals sending from source nodes.fc is defined as the frequency of relay nodesoscillator.n(t) is additive white Gaussi
23、an noise. Soy(t) denotes the signal before operating85frequency offset compensation.The expression in Eq. (1) can be rewrite as:y(t ) = x1 (t )e- j 2pDfc tc+ x2 (t)e- j 2pDf t+ n (t )(2) c c c c c cDf = f - f , Df = f - f denote carrier frequency offsets between source nodes and relaynode respective
24、ly, which are supposed to be obtained by the method of classical frequency offset90estimation in the orthogonal timeslots. Our goal is to find a proper Dfto compensate thereceiving signal y(t) , which could improve the BER performance of XOR message at the relay node. The time domain signal after co
25、nsidering frequency offset compensation can be expressedas:y (t ) = x (t )e- j 2pDfc t + x (t )e- j 2pDfc t + n (t )e j 2pDft1212= x (t )e j 2p ( Df - Dfc )t + x (t )e j 2p ( Df - Dfc )t + n (t )(3)95100105Different from conventional communication, the relay node in PNC need to deal with superposed
26、signal from two source nodes in timeslot one, leading to the requirement of perfect synchronization. In the OFDM system, signal with time delay in time domain equals to signal with phase rotation in frequency domain. As a result, without considering the phase rotations in symbols, OFDM symbols from
27、source nodes at the relay node are aligned when the symbol offsetin the time domain is within the cyclic prefix of the OFDM system6. It will ease the requirementof synchronization using OFDM in PNC, which is the main motivation to combine the two technologies together.2 A new method to the frequency
28、 offset compensation2.1 Problem formulationGiven that signals with different power go through flat flading channels, the signal in time domain at the relay node can be rewritten as:j 2p ( Df - Dfc )t j 2p ( Df - Dfc )ty(t ) = h1E1 x1 (t )e+ h2E2 x2 (t )e+ n (t )(4)E1 , E2denote transmitting power of
29、 source nodes signals,h1 , h2 is the channel gains from source110nodes to relay node.The relay node then samples the time domain signal and processes the discrete signal by FFT. The signal in frequency domain at the relay node can be expresses as follow7:R = H (1) S (1) + H ( 2) S ( 2) + CFO(1) (Df
30、) + CFO(1) (Df ) + n(5)k k k k k k k(1)CFOk (Df ) =h1 E1N -1 Smsinp (m - k - N (Dfc - Df )Ts )e jp (1-1/ N )(p ( m -k - N DfcTs )Nm=0m k sinp (m - k - N (Dfc - Df )Ts ) / N (6)kCFO( 2) (Df ) = h2E N -1m2 Sc ssinp (m - k - N (Df - Df )T )e jp (1-1/ N )(p ( m-k - N DfcTs )Nm=0m k sinp (m - k - N (Dfc-
31、 Df )Ts ) / N (7)115H (1) = h1E1 sin(p N (Dfc - Df )Ts ) e- jp ( N -1)( Dfc - Df )Tsk N sin(p (Dfc - Df )Ts )(8)H ( 2) = h2E sin(p N (Df - Df )T ) 2 c s e- jp ( N -1)( Dfc - Df )Ts(9)c sk N sin(p (Df - Df )T )In eq. (5)(9),Rk denotes the superposed signal of source nodes in the kth subcarrier.kS (1)
32、 ,S( 2)kare the normalized base-band signal of source nodes in kth subcarrier. CFO(1)(Df ) , CFO( 2)(Df )represent the interference brought by two carrier frequency offsets,kkccDf , Df . Assuming thatDfc120Dfc , h1 , h2 can be got by classical methods of frequency offset estimation and channel estim
33、ation,so the interference caused by frequency offsets is just the function ofDf . N is the number ofsubcarriers in the OFDM system. Tsis the sampling interval of signal in the time domain.n denotes discrete additive white Gaussian noise.1252.2 Problem analysisAs showed from above equations,H (1) , H
34、 ( 2 ) , CFO (1) (Df ) , CFO( 2 ) (Df )change togetherk k k kwith Df , which influences the performance of the maximum likelihood detection at the relay node.A method to calculatingDf is proposed here. Numerical simulations show that the proposed130algorithm improves the BER performance at the relay
35、 node in the situation of asymmetric channel.Due to the effection of both inference and noise, we assume that the error pattern of receivedk ksignal are E (1) , E ( 2 ) . Rewrite (5) as follower:(1) (1) (1) ( 2) ( 2) ( 2)Rk = H kDefine(1) ( 2 )(Sk- Ek) + H k(Sk- Ek )(10)Ek = Ek= Ek , it is because t
36、hat the error of each link can bring a error of the135XOR-operation of two source nodes, so that it can reduce BER at the relay node if the two error patterns are the same. And following equation can be got together with eq.(5):CFO(1) (Df ) + CFO(1) (Df ) + nE = k k kkk H (1) + H ( 2)(11)Without los
37、s of generality, signal in the first subcarrier is taken as the study term, Namely,supposek = 0 . Minimize the expectation of the square of error pattern as follow, can we obtainthe compensating frequency offsetDf .(1)(1) 22minEkc cDf Df ,Df = minDf Df ,Df CFOk(Df ) + CFOk(1)( 2)(Df ) + n(12)c c c c
38、H k + H k140AssumingDf Df , It may expect that theDf fitting eq.(12) must be in the range ofc cDf , Df . And it can be proved using symbolic computation by Maxima that eq.(12) is a convexfunction ofDf . So Dfc ccan be derived by numerical algorithm. And a golden sectionalgorithm8 solving the problem
39、 will be introduced in the next section. Numerical simulation showthat compared withDf = (Df+ Df ) 2 , the BER performance of the relay node of145PNC-OFDM system greatly improves when the SNRs of the two receiving signals at relay node are different.3Algorithmc cThe process of calculatingDf can be s
40、ummed up in following steps:cc(1) Assume the carrier frequency offsets between source nodes and relay node as150Df , Df (Df Df ). Define error margin as e . Define golden section ratio asGOLDEN = 2.0 (1.0 + 51 2 ) .(2) CalculateToF = (Df - Df ) * GOLDEN ; compute the two probe points2ccToF1 = ToF2 *
41、 GOLDENF1 = Dfc + ToF1 ;2F2 = Dfc + ToF2. Calculate the value ofEk at the probe points,ERR(Df )= Ekdef, so ERR1 = EER(F1 ) ;ERR2 = EER(F 2) .155(3) IfToF1 e , goto step(6); otherwise, execute step(4) continually.(4)ToF2 = ToF1 ;ToF1 = GOLDEN *ToF2 ;(5) IfEER1 EER2 , thenFend = F2 ;F2 = F1 ;ERR2 = ER
42、R1 ;F1 = First + ToF1 ;ERR1 = EER(F1 ) ;otherwise step(3).First = F1 ;F1 = F2 ;ERR1 = ERR2 ;F2 = First + ToF2 ;ERR2 = ERR(F2 ) . Go back to160(6) IfERR1 ERR2 ,Df = F1 ; otherwise2Df = F2 .After deriving frequency offset compensationDf , receiving signal in time domain is165processed as eq.(3). Then
43、final XOR message can be got through FFT and maximum likelihood detection. As one of the probe points after shrinking search rang is the same with one of the probe points in previous rang, a half amount of the calculation can be saved. Because it is intricate to compute ERR(Df ) , that is very necessary to use the numerical algorithm with a small amount ofcalculation.c c4Numerical simulationSimulations to the proposed algorithm above are provided in this section. The parameters used in simulations are as follow: adopt OFDM modulation; the number of subcarriers is 64;170symbol rate is