Low-Complexity Time-Domain SNR Estimation for OFDM Systems

Transcription

1 Low-Complexity Time-Domain SR Estimation fo OFDM Systems A. jaz, A.B. Awoseyila and B.G. Evans A low-complexity SR estimation algoithm fo OFDM systems in fequency-selective fading channels is poposed. The estimato is based on a conventional peamble having two identical pats. t uses the coelation of the eceived signal samples to estimate signal powe while noise powe is estimated using the diffeence between eceived samples. Simulation esults show that the poposed estimato is obust to the channel s fequency selectivity and its attained accuacy and educed complexity mae it an attactive choice fo cuent wieless OFDM systems. ntoduction: Othogonal fequency division multiplexing OFDM suppots both timedivision and fequency-division multiple access and enables high data ate tansmission in fequency-selective fading channels. Adaptable tansmission paametes such as modulation and coding can play an impotant ole in maing an efficient use of OFDM system esouces. The paametes ae adapted accoding to channel conditions indicated by a nowledge of the signal-to-noise atio SR. SR estimation is also used in soft decoding algoithms and othe applications []. Seveal SR estimatos have been poposed fo the additive white Gaussian noise AWG channel [], [3]. Howeve they cannot be applied in fequency-selective fading channels since the channel coefficients ae vaying acoss the bandwidth. n this pape we focus on peamble-based estimatos fo wieless OFDM systems due to thei impoved pefomance as compaed to non-data-aided techniques. Boumad poposed a method to estimate SR in OFDM systems assuming that the channel fequency esponse vaies slowly [4]. Howeve, its pefomance is significantly degaded in highly fequency selective channels. Ren [4] poposed a method to

2 estimate the noise vaiance by using the least squae LS channel estimates obtained fom two identical OFDM taining symbols while the signal powe is estimated fom thei second ode moment. n [5], Ren used a simila peamble stuctue to estimate noise vaiance using the diffeence between the eceived OFDM subcaies, theeby impoving pefomance. n [6], Zivovic poposed a low complexity estimato, based on peiodically-used subcaies named PS estimato. t estimates signal and noise powe fom active and inactive OFDM subcaies espectively. Howeve, its accuacy deceases as the numbe of used subcaies educes. We popose a time-domain algoithm fo SR estimation in OFDM systems based on conventional peamble stuctue with two identical pats [7], [8]. t has a low computational complexity while maintaining pefomance close to Came-Rao bound CRB. Futhemoe, the poposed algoithm is applicable to CP-based SR estimation. System Model: n an OFDM system, the tansmitted signal samples ae given by: used x X n e n jπn ;,,,..., whee X n is the tansmitted symbol on n th subcaie and is the total numbe of subcaies of which used ae used. Assuming pefect synchonization and sampling pecision, the eceived signal samples of an OFDM symbol, afte the emoval of the cyclic pefix CP, can be epesented as: whee ω ω jω y ;,,,..., ω is the zeo-mean complex AWG, ω ae independent and identically distibuted andom vaiables with L E{ ω } W and y h l x l is the eceived noise-fee signal. h l is l

3 the impulse esponse of the wideband fequency-selective channel whose memoy ode is L- samples. Since we conside SR estimation algoithms fo the pupose of adaptive tansmission, it is assumed that the channel is coheent ove seveal OFDM symbols. The aveage SR is given as: whee S is the aveage signal powe. SR in n th subcaie is given as: E{ y } S ρ avg 3 E{ ω } W H n ρ n 4 W whee H n is the channel fequency esponse on n th subcaie. Poposed Estimato: The poposed method employs a peamble consisting of one OFDM symbol with two identical pats in the time-domain. This stuctue is suitable fo obust timing and fequency synchonisation [7], [8] and also confoms to existing OFDM-based standads such as WiFi and WiMAX. Povided that a CP is used, the eceived noiseless peamble fom a wideband channel will also consist of two identical pats, i.e., y y. Theefoe aveage signal powe can be epesented as follows: S E{ y } E{ y },,,,..., 5 Given an estimate of the noise powe Wˆ, conventional appoaches estimate the signal powe Ŝ, using the second ode moment of the eceived signal as follows: Sˆ Wˆ 6 Rathe than taing this appoach, we popose a computationally-efficient technique based on coelation. The coelation of in-phase and quadatue components of the two pats of eceived peamble can be witten as:

4 } { E R 7 } { E R 8 Since the noise is a zeo-mean pocess and the noise samples ae independent to each othe and to the signal samples, the above equations simplify to: { } y y E R 9 { } y y E R Fom 5, 9 and, it can be obseved that the signal powe can be expessed as: R R S Theefoe, we popose to estimate signal powe fom the samples of eceived peamble as: [ ] ˆ S Based on the conventional appoach, noise powe can be estimated by subtacting the estimated signal powe fom total eceived powe as follows: S W ˆ ˆ 3 Substituting in 3 we get: [ ] ˆ W ω ω ω ω 4 Howeve, the diffeence in noise samples can be obtained by subtacting one half of the eceived peamble fom the othe. Hence noise powe can also be estimated as: [ ] ˆ W 5 Compaing 3 and 5, it can be seen that we now need times less multiplications fo noise powe estimation. Hence, aveage SR can be estimated as: [ ] [ ] ˆ avg ρ 6

5 SR pe subcaie can be estimated using 4, 5 and the sub-channel estimate. Poposed estimato can also be used fo CP-based SR estimation, povided that the channel memoy ode L is nown, wheein: ˆρ avg, CP G G [ ] [ ] Lˆ Lˆ 7 whee G is the CP length in samples. Simulation Results: Compute simulations wee pefomed to veify the pefomance of the poposed estimato in compaison with Ren s estimato [5] and the PS estimato [6] using PSK modulation and a peamble stuctue with identical pats. We assume an OFDM system simila to fixed WiMAX with 56 subcaies, used and G6 samples [7]. Pefomance is evaluated in a channel consisting of L8 independent Rayleigh fading paths with delays of τ,,..., L samples l and an exponential powe delay pofile having aveage powe of e τ l L as used in [7], [8]. Pefomance is evaluated in tems of mean squae eo MSE of the estimated SR nomalized to actual SR i.e. MSE, and also compaed with the CRB []. Fig. and show the MSE pefomance of aveage SR estimation and SR estimation pe subcaie, espectively. The numbe of OFDM symbols in the peamble is indicated within bacets next to the investigated techniques. t can be obseved that the accuacy of the poposed estimato is bette than Ren s and PS estimatos. t has a lowe complexity than Ren s estimato, as shown in the complexity compaison in Table. Although the PS estimato has lowe complexity, oveall pefomance of the poposed estimato in tems of accuacy and complexity maes it a moe obust option. Anothe advantage of the poposed estimato is its applicability to any CP-based OFDM system as shown in 7.

6 Conclusion: n this lette, a low-complexity SR estimation algoithm fo wieless OFDM systems has been pesented. The estimato uses an OFDM taining symbol with identical pats to estimate SR moe efficiently than the existing peamblebased estimatos. ts obust accuacy and educed complexity in fequency-selective channels mae it an attactive choice fo moden wieless OFDM systems. Futhemoe, it can be used fo CP-based SR estimation if the channel delay spead is nown.

7 Refeences. Summes, T. A., and Wilson, S. G.: SR mismatch and online estimation in tubo decoding, EEE Tans. Commun., 998, 46, 4, pp Pauluzzi, D.R., and Beaulieu,.C.: A compaison of the SR estimation techniques fo the AWG channel, EEE Tans. Commun.,, 48,, pp jaz, A., Awoseyila, A. B., and Evans, B.G.: mpoved SR Estimation fo BPSK and PSK signals, Electon. Lett., 9, 45, 6, pp Ren, G., Chang, Y., and Zhang, H.: SR estimation algoithm based on the peamble fo wieless OFDM systems, Science in China Seies F: nfomation Sciences, 8, 5, 7, pp Ren, G., Zhang, H., and Chang, Y.: SR estimation algoithm based on the peamble fo OFDM systems in fequency selective channels, EEE Tans. Commun., 9, 57, 8, pp Zivovic, M., and Matha, R.: Peamble-Based SR Estimation in Fequency Selective Channels fo Wieless OFDM Systems, Poc. EEE 69 th Vehicula Technology Conf., Moelli, M., Kuo, C.-C.J., and Pun, M.-O.: Synchonization techniques fo othogonal fequency division multiple access OFDMA: a tutoial eview, Poc. EEE., 7, 95, 7, pp

8 8. Awoseyila, A.B., Kaspais, C., and Evans, B.G.: mpoved peamble-aided timing estimation fo OFDM systems, EEE Commun. Lett., 8,,, pp Authos affiliations: A. jaz, A.B. Awoseyila and B.G. Evans Cente fo Communications Systems Reseach, Univesity of Suey, Guildfod, GU 7XH, United Kingdom.

9 Figue\Table captions: Fig. MSE of the aveage SR Fig. MSE of SR pe subcaie Table Complexity compaison of estimatos

10 Figue MSE nomalized to tue SR Poposed Ren CRB PS Poposed CRB Tue SR db

11 Figue MSE nomalized to tue SR Poposed Ren CRB PS Poposed CRB Tue SR db

12 Table OFDM Symbols OFDM Symbol Opeation Ren Poposed PS Poposed Additions 8 used - 6- used - 3- Multiplications 6 used 4 used