Subcarrier Pairing based Subcarrier Suppression for ... - IEEE Xplore

2015 IEEE Wireless Communications and Networking Conference (WCNC 2015) - Track 1: PHY and Fundamentals

Subcarrier Pairing based Subcarrier Suppression for OFDM Systems with Decode-and-Forward Network Coding Jian Wang, Wenfeng Ma, Youyun Xu, Cong Wang, Kui Xu College of Communications Engineering, PLA University of Science and Technology Nanjing 210007, China Email: [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract—Subcarrier suppression (SS), a recently proposed technique for orthogonal frequency division multiplexing (OFDM) transmissions that suppresses subcarriers with bad channel condition, has been known as an efficient technique to improve bit error rate (BER) performance. In this paper, we consider a two way relay network (TWRN) applying SS with decode-andforward physical layer network coding (DF-PLNC). According to the asymmetry nature of SS, some subcarriers are suppressed on one side. For these subcarriers, one way relay (OWR) is adopted, which reduces the performance of system since the channel condition of the second hop for OWR is bad. To solve this problem, we propose a modified SS scheme combined with subcarrier pairing (SP), called SP based SS (SPSS) where subcarriers that adopt OWR in opposite directions are paired. As a result, BER performance could be improved. Numerical results show that SPSS outperforms traditional SS schemes without pairing in terms of BER performance. Simulations together with analysis verify the potential benefits for combination of SP and SS.

I. I NTRODUCTION With the increasing demands for high speed wireless applications, future network will be required to provide high reliable data rate services in dynamic environments. Cooperative communication [1] has been considered as a promising technique that could not only provide diversity to combat multipath but also expand the coverage of communication terminals. Among various relay protocols, there are two basic relaying protocols: amplify-and-forward (AF) [2–4] and decode-and-forward (DF) [5, 6]. In AF relaying, relays simply amplify the signal they have received and forward it to the destination. While in DF relaying, relays decode the signal and then transmit it to the destination. In order to cooperate, half-duplex relays have to receive and transmit through orthogonal channels, which reduces spectral efficiency. To deal with this drawback, network coding (NC) [7, 8], which was proposed as a promising technique that can improve throughput by reducing needed time slots in a time division multiplexing (TDM) system, could be applied. One of the most popular applications of NC is two way relay network (TWRN), where two end terminals exchange information through a relay. When two end terminals transmit their packets simultaneously, relay has to deal with additive electromagnetic

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waves. This kind of NC is called physical layer network coding (PLNC). The use of PLNC could reduce the needed time slots to two for a pair of packets exchange. According to the protocol the relay adopts (AF or DF), PLNC is regarded as AFPLNC [9, 10] and DF-PLNC [11, 12] respectively. It is often believed that DF-PLNC is more efficient since procedure of decoding could be considered as a procedure of denoising. While in AF-PLNC protocol, noise level is amplified jointly with useful signal. For higher data rate, relayed transmission is encouraged to be combined with OFDM technique. OFDM is a widely used technique for broadband wireless systems. High speed communication, high spectral efficiency and robustness to multipath fading make OFDM appealing even for the fourth generation of wireless systems. The combination of relayed transmission and OFDM is named OFDM-relay, of which an important technique is subcarrier pairing (SP), which was first proposed in [13], adopting AF protocol. Applying SP, symbols transmitted on some subcarriers to relay are forwarded to destination on other subcarriers, which improve the sum-rate performance. It has been proved that ordered subcarrier pairing could achieve optimal end-to-end capacity [14]. Recently, another promising technique was proposed in OFDM transmissions for DF-PLNC, named subcarriers suppression (SS) [15]. In SS, each subcarrier having a channel gain lower than a specified threshold is suppressed, and saved power are allocated to subcarriers that are not suppressed. As a result, better BER performance could be achieved. According to the asymmetry nature of subcarrier suppression, some subcarriers are only suppressed on one side. For these subcarriers, one way relay (OWR) is adopted, which reduces the performance of system since the channel condition of the second hop for OWR is bad. To solve this problem, we propose a modified SS scheme combined with SP, called subcarrier pairing based subcarrier suppression (SPSS) where subcarriers that adopt OWR in opposite directions are paired. The remainder of this paper is organized as follows. The system model is presented in section II. In section III, we propose a SPSS method, and the BER performance analysis of the proposed method is given in section IV. We provide

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numerical results in section V, and the conclusion is followed in section VI. II. S YSTEM M ODEL We consider a TDMA based TWRN, where two communication nodes, i.e., S1 and S2 , are exchanging information through a relay node R, applying DF-PLNC, as is shown in Fig. 1. Each node exploits the OFDM modulation with K subcarriers, each one modulated through a QPSK scheme. Thus the baseband signal transmitted by node Si , with i = 1, 2, on the k-th subcarrier can be relaxed as √ 2 (ai,I [k] + jai,Q [k]) (1) si [k] = 2 where ai,I [k] and ai,Q [k] are the in phase and quadrature phase components of si [k], and they are assumed values ±1 for equal probability, depending on the bits mapped on the symbol. We assume L-tap i.i.d. Rayleigh fading multipath channel for all the links. As was proven in [16], when L equals the number of subcarriers K 1 , the frequency domain channel can be modeled as circular symmetric complex normal (CN ) random vectors with zero mean and identity covariance matrix CN (0, L1 ). For traditional single carrier transmissions, unified power could be allocated to the single carrier only, while in OFDM transmissions, K subcarriers share the common power. It is assumed that S1 and S2 have the knowledge of channel gains for all subcarriers. Thus power could be allocated unequally to all subcarriers according to the instantaneous channel state information (ICSI) for better system performance. By assuming a pre-compensation of the phases performed at Si , with i = 1, 2, the signal received at the relay R side on the k-th subcarrier can be define as p p rR [k] = P1 [k]|H1 [k]|s1 [k] + P2 [k]|H2 [k]|s2 [k] + nR [k] (2) where Pi [k] and Hi [k] denote the power allocated for the k-th subcarrier at node Si and the subcarrier channel gain between node Si and R, respectively. nR [k] ∼ CN (0, σn2 ) is complex Gaussian noise with zero mean and variance σn2 at R. A possible power allocation scheme is set the amplitude of each subcarrier directly proportional to the reciprocal of the related channel gain2 . As a result, the amplitude of signals of all subcarriers received from Si is same, and this normalization factor can be defined as p Fi = Pi [k]|Hi [k]| (3) Because of power constraint, we have K−1 X

Pi [k] = K

(4)

k=0

1 Notice that it is not practical to set L = K in OFDM systems, however, due to the difficulty in dealing with the correlated frequency domain channel statistics for general case (L y|y) fx (x > y|y) i−λx e if x > y e−λy = 0 otherwise

fM (x|x > y, y) =

(18)

The joint PDF of ordered norm of x1 , x2 , · · · , xK can be given as fxˆ1 ,··· ,ˆxK (x1 , · · · , x ˆK ) = N !e−λ(ˆx1 +···+ˆxK )

(19)

where N ! denotes the factorial of N and x ˆ1 ≤ · · · ≤ x ˆK correspond to ordered x1 , · · · , xK . We could get the PDF of y by integral as

fy (y) = (K − M )

K M

(1 − e−λy )K−M −1 e−λ(M +1)y

(20) Thus, for one of the M best channels, its PDF could be given as

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0

10

x

fxi (x|x > y, y)fy (y)dy K = (K − M ) e−λx · M Z x K−M −1 −λM y (1 − e−λy ) e dy 0 K = (K − M ) e−λx · M K −M −1 i (−1) K−M −1 X i 1 − e−λ(i+M )x i+M i=0 0

−1

BER

10

(21)

−2

10

−3

10

−4

10

The theorem has been proved. Applying (16) to (15), we could get the BER for BC stage Z ∞ PeBC (M, k1 ) = PeBC (M, k1 |x)fM (x)dx 0 K −M −1 i K−M (−1) X−1 i K = (K − M ) M i + M i=0 √ ρ K i+M √ − · 2λ(i + M + 1) 2M − k1 2λ 2λ+ρ √ p ρ K λ (i + M + 1) 2λ(i + M + 1) + ρ + 2M − k1 2 (22) For POWR, PeP OW R (M, k1 ) could be given as ! PeP OW R (M, k1 ) = PeP OW R,M A (M ) 1 − PeBC (M, k1 ) ! + 1 − PeP OW R,M A (M ) PeBC (M, k1 ) (23) where PeP OW R,M A (M ) denotes the BER of POWR in MA stage. It is related to FM,i and can be given as Z √ (24) PeP OW R,M A (M ) = fFM,1 Q( ρx)dx FM,1

Applying (13)(14)(23) to (12), we could obtain the expression of BER. V. S IMULATION R ESULTS In this section, numerical simulations are carried out, and simulation results are presented to validate our proposed subcarrier pairing based subcarrier suppression scheme. All nodes transmission powers are set to K, and QPSK modulation is adopted. We first consider L = K = 64, that is, 64taps i.i.d. channels subject to CN (0, L1 ). As we can see in Fig. 3, the simulated curve overlaps with the analytical one, which verifies our analysis. As comparison, the ISS and JSS schemes proposed in [15] are also depicted in this figure. Since ISS and JSS are implemented by setting a channel threshold, under which the subcarrier would be suppressed, M for ISS and JSS denotes the average number of active subcarriers3 . 3 It is fair to compare the schemes with the same value of M , since under this condition, they have the same transmission rate, and throughput is inversely correlated to BER.

2

simulated ISS M=60 L=64(L=16) simulated ISS M=55 L=64(L=16) simulated JSS M=60 L=64(L=16) simulated JSS M=55 L=64(L=16) simulated SPSS M=60 L=64 analytical SPSS M=60 L=64 simulated SPSS M=60 L=16 simulated SPSS M=55 L=64 analytical SPSS M=55 L=64 simulated SPSS M=55 L=16

4

6

8

10 ρ (dB)

12

14

16

18

Fig. 3. Simulated (ISS, JSS, SPSS) and analytical(SPSS) BER performance. L = 16, 64, M = 55, 60

0

10

−1

10

BER

fM (x) =

Z

−2

10

−3

10

−4

10

64

ISS ρ=5dB ISS ρ=10dB ISS ρ=15dB JSS ρ=5dB JSS ρ=10dB JSS ρ=15dB SPSS ρ=5dB SPSS ρ=10dB SPSS ρ=15dB

62

60

58

56

54

52

50

M

Fig. 4. Simulated (ISS, JSS, SPSS) BER performance. L = 16, ρ = 5, 10, 15dB

Results show that SPSS scheme outperforms ISS and JSS in terms of BER for both M = 55 and M = 60. Fig. 3 also shows the BER performance of more practical situation, i.e., L = 16