Risk Sensitive Filter for Quasi-Static Fading Channel Estimation of OFDM System under Parameter Uncertainty

Transcription

1 Advances in Wieless and Mobile Communications. ISSN Volume 0, Numbe (207), pp Reseach India Publications Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM System unde Paamete Uncetainty K. Rajenda Pasad Asst. Pof, Dept. of ECE, K L Univesity, India M. Sinivasan Post doc, Dept. of SRT, Lulea Univesity of Tech., Sweden T. Satya Savithi Pofesso & HoD, Dept. of ECE, JNTU-Hydeabad, India Abstact In this pape, is-sensitive filte (RSF) appoach has been poposed to estimate quasi static time vaying channel (QSTV) fo othogonal fequency division multiplex (OFDM) system. The novelty of the poposed appoach is QSTV channel estimation poblem is fomulated with moe uncetainty in paamete and obustness of the poposed estimato has been exploed. In time vaying FIR filte, estimation of time vaying coefficients unde uncetain conditions and it is citical tas in the pocess of etieving oiginal signal at eceive end. In liteatue, Kalman filte(kf) based fading channel estimation appoach fo OFDM has been studied and it has limitations that leads to inaccuate estimation when thee is high level of uncetainty in initial conditions and bias in system model and/o noise covaiance. In this pape pilot based channel estimation is adopted with linea intepolation appoach and the pefomance has evaluated in tems of bit eo ate (BER) and mean squae eo (MSE) and compaed esults with the Kalman filte pefomance. The esults poved that poposed estimato is outpefoming when compaed with Kalman. Keywods: Pilot based Channel Estimation, Quasi Static Time vaying Channel, Kalman Filte,Ris Sensitive Filte, Uncetainty.

2 28 K. Rajenda Pasad, M. Sinivasan & T. Satya Savithi INTRODUCTION In ecent yeas, due to huge demand of highe data ates the moden wieless technologies has adopted to meet the equiement fo diffeent applications especially in digital video boadcasting (DVB). Othogonal Fequency Division Multiplexing (OFDM) is emeged as an effective technique fo alleviating fequency-selective channel effects in wieless communication systems. In this technique, a wideband fequency-selective channel is conveted to a numbe of paallel naow-band flat fading sub-channels helps to mitigate the effect of inte-symbol intefeence (ISI) [2]. To attain the bette system pefomance channel estimation needs to be moe accuate. But Channel estimation becomes a challenging tas when the mobility of the eceives is high []. Seveal schemes and algoithms ae poposed based on pilot aided, semi blind and blind estimation [5-7]. Among that Pilot based schemes has been poved as most efficient and accuate. Fo fast-vaying channels, non-negligible fluctuations of the channel gains ae expected between consecutive OFDM symbols. In ode to ensue an adequate tacing accuacy, it is suggested to place pilot subcaies in each OFDM symbol [6]. In this pape, we conside the comb pilot patten aangement shown in Fig. 2, which has been shown to satisfy diffeent citeia of optimality such as mean squae eo on the channel estimate and capacity [7]. In the poposed wo, the taditional scenaio to estimate the channel by using the initial estimates eithe in iteative o decision diected eceives which consist of initial estimates by least squaes (LS) ove the pilot subcaies and then bac otating the eceived signal accoding to the nowledge of the pilot symbols. Then, the LS estimates ae intepolated/smoothed ove the entie fequency-time gid. In this pape, we poposed a RSF which is a vaiant of Kalman gives bette pefomance fo channel estimation [22] unde paamete uncetainty in OFDM. Seveal advanced algoithms ae poposed based on the Kalman Filte (KF) and post Kalman filteing methods [8-7], on the basis of nown channel statistics, the Kalman estimato is optimal in the sense that the eo covaiance is minimized. But no eseache consideed the uncetainty in the channel model. Howeve, in pactical systems, channel statistics ae not completely nown. When the Kalman estimato is not the dual of the channel, the pefomance of the Kalman estimato may suffe significant degadation. KF equie a linea ecusive state-space epesentation of the channel. Howeve, the exact Clae model does not admit such a epesentation. An appoximation often used in the liteatue consists of appoaching the fading pocess as auto-egessive [3]. Hence, a widely used channel appoximation is based on a fist-ode Auto-Regessive model (AR), as ecommended by [3, 0], combined with a Coelation- Matching (CM) citeion to fix the AR coefficient. A obust channel estimation algoithm is poposed to estimate the channel unde paamete uncetainty in the channel model. The poposed RSF based estimation algoithm is moe appopiate fo channel estimation [22] whee thee is significant uncetainty in the statistics of noise and channel fading. Since the RSF has an obseve stuctue simila to that of the Kalman algoithm [8-2], the implementation complexity is simila to

3 Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM 29 that of the Kalman algoithm. Fo this eason, the Kalman algoithm will be used as the benchma fo pefomance compaison. Fig : Bloc Diagam of OFDM System SYSTEM MODEL A. OFDM System Model Fig. shows the bloc diagam of a typical OFDM system based on pilot-aided channel estimation [2-4]. The IFFT bloc tansfoms the fequency-domain data on the -th subcaie ( X ) to time-domain samples x n by, 0,...,, N /2 j2 n / N xn X e n N N N/2 whee N is the numbe of sub-caies. In ode to deal with inte-symbol intefeence (ISI), a cyclic pefix of Ng samples is inseted at the beginning of evey symbol. () In geneal, impulse esponse of the multipath fading channel is given by z( t, ) h ( t) x( ) whee the gain and delay of the path is denoted by h () t and, espectively. The eceived signal, is being coupted by the multipath fading channel and contaminated by the additive white Gaussian noise v(), taes the fom of z( t, ) h ( t) x( ) v( ) whee x() is continuous-time epesentation of the tansmitted discete-time samples x n. (2) (3)

4 30 K. Rajenda Pasad, M. Sinivasan & T. Satya Savithi Afte conveting the eceived continuous-time signal bac to a discete-time signal, zn, the eceive then emoves the cyclic pefix and tansfoms zn to the fequency domain and epesented as Z n nn m e K 2, m0 j m/ K Assume that duation of cyclic pefix is long enough, so that thee is no inte-symbol intefeence. Futhemoe, assume channel is almost stationay within one symbol peiod, i.e. h () t h often can be called as quasi static time vaying channel. The fequency-domain channel esponse at subcaie is given by H he j2 TN s whee T s is the sample inteval. Let V denote the fequency domain countepat of v(), and we have the fequency domain eceived baseband data Z X H V, Z as In the system model, assume that M pilot subcaies ae unifomly inseted into N total subcaies with pilot subcaie spacing D N / M, whee D is an intege [4]. Usually, guad bands ae eseved at both ends of the allocated spectum in ode to facilitate filte design. Among the Nu+tansmission subcaies, we have M p pilot subcaies fo channel estimation, whee Nu and M p ae even numbes and N / M D as shown in u p (4) (5) (6) Fig 2: Aangement of data and pilot subcaies Fig. 2. [4] The pilot subcaies ae extacted afte the FFT bloc and channel estimation is pefomed based on these pilot subcaies. The eceived data ae then equalized by the channel estimate fo the -th subcaie, H ˆ i.e.

5 Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM 3 Xˆ Z N / 2,...,0,... N / 2. (7) Hˆ TIME VARYING CHANNEL MODEL A. Tapped delay line channel Model A multiplicative channel model with an additive Gaussian white noise (AGWN) model is used sometimes it also efes as Gauss-Maov pocess epesented [,22] above as equation (2) i.e. y( t, ) h ( t) x( ) The function yt (, ) in the above equation is just same as Finite Impulse Response (FIR) filte which has time-vaying coefficients. In eal wold scenaio thee ae many factos, as distubance, affect the medium, which leads to model the system with additive noise and esult the system model become (3).i.e. z( t, ) h ( t) x( ) v( ) To design effective communication, it is necessay to have good nowledge about these coefficients. Thee ae too many paametes to estimate in (9). As obsevation samples ae coupted with noise, weights of samples will apidly change fom one to othes. The weighted taped channel is modeled as Gauss-Maov model. The Gauss-Maov model will be used to fix the coelation between successive values of given taped weight in time. In channel estimation, the state vecto is given as whee h n Ah n u n 0 hn hn. A is a p pmatix hn. hn p (8) (9) (0)

6 32 K. Rajenda Pasad, M. Sinivasan & T. Satya Savithi and un is AWGN, with zeo mean and vaiance Q. Standad assumption made that tap weights ae joined Gaussian and uncoelated with each othe. Measuement/obsevation model is witten by eaanging (0) 2... z n x n x n x n x n p and it can be expessed as h n w n () T z n x n h n w n whee w[n] is Gaussian white noise with vaiance sequence, act as input to the channel. R 2 and ( ) (2) xn is nown B. Tapped delay line channel Model with uncetainty In a cicumstance, when thee is uncetainty in the channel state vecto, () may be witten as h n Ah n A un whee A is a constant which aises due to channel phase otation duing coding and it is consideed as a paamete modeling uncetainty in matix A. This model is simila to case of andom wal pocess descibed in [22] and in state-space domain the model (3) CHANNEL ESTIMATION A. Kalman based channel estimation The Kalman filte is a mathematical method used to use obseved values containing noise and othe distubances and poduce values close to tue value and calculate value [, 8-7]. The basic opeation done by the KF is to geneate estimates of the tue and calculated values, fist by pedicting a value, then calculating the uncetainty of the above value and finding an weighted aveage of both the pedicted and the measued values [8]. Most weight is given to the value with least uncetainty. The esult obtained the method gives estimates moe closely to tue values. It is a ecusive pedictive filte based on the use of state space techniques and ecusive algoithms. It demands the desciption of the dynamical poblem in a state-space fom which includes a system model and an obsevation model which is consideed only fo linea systems. Kalman filte is a ecusive minimum mean squae eo (MMSE) estimato and it povides optimal estimation solution fo linea and unbiased pocess with additive white noise. Thee is enough liteatue on KF, fo example [].

7 Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM 33 The implementation of KF fo channel estimation poblem given in above subsection is given in detail as follow steps [9-]. Filte initialization hˆ n n h and P n n Ch (4) Pio state estimation hˆ ˆ n n Ah n n (5) Pio estimate eo covaiance T P n n AP n n A Q (6) Kalman Filte gain Posteio state estimate T K n P n n V n V n P n n V n ( R (7) ˆ ˆ T h n n h n n K n x n V n h ˆ n n (8) Posteio estimate eo covaiance T P n n I K n V n P n n (9) B. Poposed Ris Sensitive Filte appoch A RSF which is ecusively update a posteioi state and estimate eo covaiance as given in [2,22] is used hee fo fading channel estimation. Implementation of fading channel estimation using RSF is follows: Fo linea system, the posteioi state estimate ĥ of h at th time is obtained by the is sensitive appoach such that m0 h ˆ ag min E[exp { (, ˆ l h ), } m hm l hm x n ] (20) Hee, θ is a tuning paamete, nown as is facto o is paamete, the function l( h, h ˆ) is defined as T, ˆ ˆ ˆ l h h h h h h 2 (2)

8 34 K. Rajenda Pasad, M. Sinivasan & T. Satya Savithi,, x n x x n (Notation T denotes tanspose) (22) This is stictly filteing poblems. Fo moe details eades can efe [,9-2]. As [26], the posteioi state estimation is given as T ˆ hˆ n n Ah n n P n n V n R T xnv n Ahˆ n n (23) Posteioi estimation eo covaiance is given as T P[ n n] A P n n I A Q V n R V n (24) T SIMULATION RESULTS The simulation paametes ae as follows. The FFT size, N, is 64. The data symbol X is based on QPSK. The channel h n is the Rayleigh fading channel which has two paths. The initial values of the fo the KF ae as follows: 0 h [0 0]T, 0 P 00 I, 0 S0 I, 0 q [0 0]T, and 0 a. The compaison facto, MSE, is obtained afte 00 independent tials. The linea intepolato is used as we consideed slow fading channel. In contast, the poposed RSF algoithm wos well in paamete uncetainty conditions and usual pefomance and close to KF in absence of paamete uncetainty [22]. Although this pape focuses mainly on channel estimation unde paamete uncetainty. we compaed pefomance in the aspect of mean squae eo (MSE) LS, KF and RSF unde uncetainty with 0.5 and the symbol eo ate (SER) shown in Fig.3 and Fig.4 espectively. Fig.3 MSE vs SNR fo LS, KF and RSF

9 Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM 35 Fig.4 BER vs SNR fo LS, KF and RSF REFERENCES [] Steven M.Key, Fundamental of Statistical Signal Pocessing: Estimation Theoy, pages: , Pentice Hall, NJ 993. [2] Ahmad R. S. Bahai, Buton R. Saltzbeg, Mustafa Egen, Multicaie Digital Communications: theoy and application of OFDM, Spinge, Second Edition, 2004 [3] Kaeem E. Baddou, Noman C. Beaulieu, Autoegessive Model fo Fading Channel Simulation, IEEE Global Telecommunication Confeence, vol.2 pp:87-92, 200 [4] Pei-Yun Tsai, Tzi-Da Chiueh Adaptive Raised-Cosine Channel Intepolation fo Pilot-Aided OFDM Systems IEEE tansactions on wieless communications, vol. 8, no. 2, febuay [5] Ye (Geoffey) Li, Pilot-Symbol-Aided Channel Estimation fo OFDM in Wieless Systems IEEE tansactions on vehicula technology, vol. 49, no. 4, July 2000 [6] SinemColei, Mustafa Egen, Anuj Pui, and Ahmad Bahai, Channel Estimation Techniques Based on Pilot Aangement in OFDM Systems, IEEE Tans. on Boadcasting, Vol.48, No.3, Sept [7] Tao Cui and Chintha Tellambua, Joint Fequency Offset and Channel Estimation fo OFDM Systems Using Pilot Symbols and Vitual Caies IEEE tansactions on wieless communications, vol. 6, no. 4, apil 2007 [8] Ki-Young Han, Sang-Woo Lee, Jun-Seo Lim, and Koeng-Mo Sung, Channel Estimation fo OFDM with Fast Fading Channels by Modified

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11 Ris Sensitive Filte fo Quasi-Static Fading Channel Estimation of OFDM 37 [22] K.Rajenda Pasad, M.Sinivasan, T.Satya Savithi Robust Fading Channel Estimation unde Paamete and Pocess Noise Uncetainty with Ris Sensitive Filte and Its compaison with CRLB WSEAS tansactions on communications, Volume 3, 204