Improved Frequency-offset Estimation Research for MIMO Systems

Transcription

1 Sensos & ansduces Vol. 74 Issue 7 July 4 pp Sensos & ansduces 4 by IFSA Publishing S. L. Impoved Feuency-offset Estimation Reseach fo MIMO Systems Wang Min Xiao Bin School of Electical and Infomation Engineeing Southwest Petoleum Univesity Cheng Du China School of Compute Science Southwest Petoleum Univesity Cheng Du China el.: wangmin866@63.com Received: 7 Febuay 4 /Accepted: 3 June 4 /Published: 3 July 4 Abstact: ML feuency-offset estimation is hadly be widely used in pactical communication systems because of the computational complexity. hee is loss of SR by using low complexity feuency offset estimation based on coelation elative. A novel feuency-offset estimato based on best-weighted coelations is poposed in the pape. By using peiodic taining seuences the algoithm calculates the coelations of eceived signals and weights the esults popely to estimate the feuency-offset. heoy and simulation show that the method with less complexity makes the mean suae eo estimato asymptotically optimal pefomance and can effectively ovecome the SR loss. Copyight 4 IFSA Publishing S. L. Keywods: Multiple input multiple output Feuency synchonization Feuency-offset estimation.. Intoduction MIMO is a techniue to incease channel capacity with adding moe antennas and has vey high spectum utilization. It is one of the most competitive technologies in futue mobile communications. But the pesence of caie feuency offset unavoidable in MIMO systems. he pesence of feuency offset can seveely educe the pefomance of signal detection system. heefoe accuate detection of feuency offset and effective compensation has a vey impotant pactical significance. ML feuency-offset estimation is hadly be widely used in pactical communication systems because of the computational complexity. he low complexity feuency offset estimation method based on coelation [ ] is widely used in the MIMO system now. But this method consideed only the two adjacent sub-seuences the coelation between the eceived signal algoithms elative asymptotic CRLB (Came-Rao Lowe Bound) is a non-optimal feuency offset estimation method. In most cuent pactical systems feuency offset estimation typically elies on tansmitting a known taining seuence which may be petended appended o embedded in the data packet. Although this appoach wastes bandwidth eliable and computationally simple estimates can be obtained. heefoe this appoach has eceived enewed attention in the last few yeas [3 6]. If taining is to be used it is impotant to optimize the esouces allocated fo taining: the tadeoff is clealy between impoved channel estimation and impoved ate; the impact on the bit eo ate (BER) is moe subtle since BER depends both upon the uality of the channel estimate as well as the nominal signal-to-noise atio (SR). Optimal taining fo multiple-input multiple-output (MIMO) feuencyselective channel estimation has been ecently addessed by many authos e.g. [8 ]. he designs 5

2 Sensos & ansduces Vol. 74 Issue 7 July 4 pp in [8 ] wee deived fo othogonal feuencydivision multiplexing (OFDM) systems. he wok in [] focused on zeo-padded single-caie and cyclic-pefixed multicaie block tansmissions. aining symbols wee inseted in each block in ode to tack channel vaiations. By decoupling channel estimation fom data detection and using linea minimum mean-suae eo optimal taining designs wee deived. In [9] optimum finite-alphabet constant amplitude taining seuences wee poposed fo single-caie systems. aining designs maximizing the mutual infomation capacity o cutoff ate wee studied in [ 3 5]. A novel feuency-offset estimato based on bestweighted coelations is poposed in the pape. By using peiodic taining seuences the algoithm calculates the coelations of eceived signals and weights the esults popely to estimate the feuency-offset. heoy and simulation show that the method with less complexity makes the mean suae eo estimato asymptotically optimal pefomance and can effectively ovecome the SR loss. he pape is oganized as follows. In Section feuency offset estimation model ae povided. In Section 3 CRB is povided. Section 4 pesents offset estimation based on coelation. he impoved feuency offset estimation is povided in Section 5. And in Section 6 pesents the analysis of the impoved algoithm pefomance. Compute simulation esults ae given in Section 7. Finally some conclusions ae dawn in Section 8.. Feuency Offset Estimation Model Assume that the nomalized caie feuency offset is the same between all tansmit antenna and eceive antenna and expessed as ν.aking into account the multipath channel chaacteistics a cyclic pefix of L wee added to the font of the taining seuence and though channel on the o. eceive antenna discading the cyclic pefix he o. k eceived seuence can be expessed as euation (). t L ( k) j π( k+ t) ν ( k) = p l p + p= l= y () t e h x ( t l) n () t () t= k= B whee hp l can expess as the o. p path channel multiplex gain of subchannel fom the o. p tansmitting antennas to the o. eceiving antennas. xp ()( t t = ) can be expessed as the o. t taining symbol in the o. k subseuence taking palace on the o. p tansmitte antennas. x p( ) xp( ) xp( L+ ) can be expessed as the Cyclic pefix. ( k n ) () t epesents the Gaussian white noise. whee whee j k y( k) e π ν = DXh + n( k) () ( k) ( k) ( k) ( ) () () ( ) = y k y y y jπν j π ( ) ν { } D = diag e e h = h h h t hp = hp hp h pl = t X X X X ( k) ( k) ( k) ( ) () () ( ) == n k n n n y( k ) can expess the eceived vecto of the o. k subseuence coesponding to the o. Received antenna. n ( k ) epesents the oise vecto which is the Cicula white Gaussian noise and the Powe spectal density is. X ( p = ) can epesented as X p p t xp() xp( ) xp( L+ ) xp() xp() xp( L ) + = xp( L) xp( L) xp() xp( L) xp( L) xp() xp( ) xp( ) xp( L) L (3) 3. Came-Rao Bounds he motivation behind the use of the CRB to design taining seuences stems fom the fact that the CRB is a lowe bound on the mean suae eo of any unbiased estimato and the fact that the maximum-likelihood (ML) estimato (asymptotically) achieves the CRB. In this case ω = and Γ ( ω) = I.he eceived signal becomes x = IM A h+ ω (4) he channel vecto h is identifiable if and only if A has full column ank: ank{ A} = M tl hus a necessay but not sufficient condition fo channel identifiability is ML t. he CRB fo h is a lowe bound on the covaiance of any unbiased estimate ĥ of h i. e. [3]. 5

3 Sensos & ansduces Vol. 74 Issue 7 July 4 pp { ˆ ˆ } E ( hh)( hh) CRB( h) (5) Since ω is an AWG vecto the CRB fo h is eadily obtained as CRB( h) = σ I M ( A A) no CFO (6) 4. Offset Estimation Based on Coelation Based on offset estimation model conside the eceiving two consecutive vecto seuences on the o. eceived antennas so jπkν y() k = e DXh+ n() k j π( k+ ) ν y ( k+ ) = e DXh + n ( k+ ) (7) Coelation pocessing on the o eceived antenna as follows: jπν y() k y( k+ ) = e Xh = = j π( k+ ) ν + e n() k DXh = jπkν = = + e ( DXh) n ( k+ ) + n ( k) n ( k+ ) (8) he feuency offset estimation based on coelation can be obtained by using the statistical aveage eplace the time aveage B ˆ ν = ag y( k) y( k + ) (9) π K= = Compaed to ML feuency estimation an explicit expession is given by the above fomula Impoved feuency estimation algoithm to avoid the ML complex seach poblems and geatly educe the computational complexity. 5. Impoved Feuency Offset Estimation Algoithm Define abbeviations and aconyms the fist time they ae used in the text even afte they have been defined in the abstact. Abbeviations such as IEEE IFSA ac dc ms etc. do not have to be defined. Do not use abbeviations in the title o heads unless they ae unavoidable. Although the feuency offset estimation based on coelation can educe the complexity of the algoithm but this method consides only the two adjacent sub-seuences the coelation between the eceived signal algoithms elative asymptotic CRLB (Came-Rao Lowe Bound) is a non-optimal feuency offset estimation method. Coelation popety of the oveall eceived signal to be consideed based taining mechanism.weighted to be consideed to impove the pefomance of feuency offset estimation algoithm. Accoding to euation () of the feuency offset estimation model coelation function of the eceived signal on the o. eceived antenna is as follows: R m y k y k m m M Bm ( ) = ( ) ( + ) = B ( m) k= () Feuency offset estimato is consideed in euation (8) fo the entie MIMO communication system In which ˆ ν = ag( ϕ) () π = ϕ ϕ ϕ ϕ ϕ = ϕ() ϕ() ϕ( M ) α α α α = α = α() α() α( M ) whee α can be expessed as the weighted vecto that is paametes to be detemined. he aim is to find an optimal weight vecto so that euation () shows the feuency estimation is unbiased and minimum mean suae eo. At high SR euation () can be expessed as jπmν Xh R( m) = e + γ ( m) () In which Bm γ ( m) = ( ) ( ) ( )( ) Xh n k + m + n k Xh Xh ( B m) k = n ( k) = e D n ( k) and n ( k ) is the euivalent jπkν complex Gaussian andom vecto. Omitted the highe ode tems of noise in the high SR euation () can be expessed as ν α γ γ 4 M Xh jπν ˆ = ag e ( ) ( ) ( ) m + m + m π = m= (3) Accoding to the liteatue [] When η is small enough ag( + η) can be appoximated as η I he imaginay pat of η that η I. Euation (3) can be appoximated as 5

4 Sensos & ansduces Vol. 74 Issue 7 July 4 pp ˆ ν = ν + P w (4) π whee P = Xh α Xh α Xh α P = w w w w w γi () γi () γi () γi () = γi ( M) γi ( M) P is the nom of P vecto. Visible offset estimato ˆ ν is unbiased. If and only if vecto C P = thee is a C d d d Minimum Mean Suae Eo of Feuency offset estimato ˆ ν. MSE = (5) {} ˆ ν ( π ) dc d he noise covaiance matix of vecto w is epesented by C. C=diag[C C C n ] Covaiance matix of w is epesented by C. When M B/ C is the invetible matix [7]. ( M ) B i j C M = ij (6) M B+ ( Bi)( B i+ ) i= j Into () available by using the optimal weight the feuency offset estimato ˆ ν is followed as M C M ϕ ˆ ν = ag π (7) = Xh Euation (7) is given the optimal weight vecto. aking into account the actual communication system the eceive antenna is usually eual to the aveage eceived SR when M is Used the same value M (7) can be futhe expessed as ˆ ν = ag MC M ϕ π = (8) Mean suae eo of the feuency offset estimato ˆ ν if followed as MSE 3 {} ˆ ν = 4 π ( ) = M BM B M M Xh (9) Fom the above euation the pefomance of the algoithm can be impoved by inceasing M. 6. Algoithm Pefomance Analysis Euation (8) show that the impoved feuency offset estimato has nothing to do with the channel gain. hus in pactical communication systems the optimal weight vecto can be calculated in advance and stoed avoiding the eal-time computation at the eceiving end thus educing the MIMO system eceive eal-time computational buden And an impoved algoithm to find only pieces of angle calculation the calculation is a simple algoithm is mainly elated to opeations so that the impoved algoithm has low complexity and good eal-time. Design paametes M is a vey impotant facto in the impoved algoithm. By (8) and (9) complexity and pefomance of the impoved algoithm is diectly affected by the choice of diffeent coelation length. he computational complexity of impoved algoithm shown in able Maked as BWE (Best Weighted Estimation Based on Coelation). In ode to compae able also shows the computational complexity of the coelation estimation method the computational complexity of the BWE and CBE. able shows that the computational complexity of the impoved algoithm is the same as the Estimation method based on coelation. Fig. shows the effect of the computational complexity and MSE pefomance by using diffeent design paametes. he computational complexity of the lowest when M =. (8) can be simplified as B ˆ ν = ag y( k) y( k + ) () π = k= By compaison to euation (9) the impoved algoithm is the same as the Estimation method based on coelation. able. he computational complexity of the BWE and CBE. Algoithm BWE CBE Real Poducts M ( B M ) B 6 M M (5B 4 + 5) + 3 Real Additions M ( B M ) B B M (6B 4 + B) 53

5 Sensos & ansduces Vol. 74 Issue 7 July 4 pp Conclusions Fig.. Selection of design paametes. If the design paametes of M selected maximum value B / MSE has the Optimal pefomance. he synchonization issue of MIMO systems is studied in this pape in the condition that all the timedelay and feuency-offset fom diffeent tansmitting and eceiving antenna pais ae the same. he pimay eseach concentates mainly on the feuency synchonization. A novel feuency-offset estimato based on bestweighted coelations is poposed. It is futhe poved that the poposed algoithm can asymptotically attain the low bound of MSE with the optimum paamete selected and can be consideed as an asymptotically optimal feuency-offset estimato in MIMO systems. heoy and simulation show that the method with less complexity makes the mean suae eo estimato asymptotically optimal pefomance and can effectively ovecome the SR loss. MSE 3 {} ˆ ν = π BB ( ) = Xh () Can be seen fom the above euation the mean suae eo of the Feuency offset estimato is the same as the asymptotic CRLB of coelation algoithm. hus the MSE pefomance of the algoithm asymptotic to the CRLB of Feuency offset estimation. Ovecome the shotcomings of existing SR loss about the coelation estimation method. hee is an efficient compomise between the computational complexity with the pefomance of estimatos in impoved algoithm M=B/ is the optimal value In the actual communication system the total length of taining seuence is usually fixed (P=B). heefoe thee is necessay to select the appopiate seuence length o seuence numbe B to impove the pefomance of feuency offset estimation when optimal = min =L Pefomance is the best and it can accuate estimates. Fig.. MSE pefomance compaison of vaious algoithms. Acknowledgements he authos would like to thank the anonymous eviewes fo thei citical comments which impoved the pesentation of this pape. 7. Simulation Results he peiodic taining seuence of =8 B=8 is used. he pefomance of vaious algoithms is compaed in Fig.. he figue shows that the M is lage and the pefomance is bette in the impoved algoithm. When M = the poposed optimal weight offset estimation is educed to the estimation method based on coelation (CBE). he MSE is the wost at the same time. With the incease of the maximum coelation length M BWE algoithm pefomance is also constantly impoving. When M = B/ the pefomance of MSE is the best. his is consistent with the theoetical analysis esults. the method with less complexity makes the mean suae eo estimato asymptotically optimal pefomance. Refeences []. Zhuo Lu Jiandong Li Linjing Zhao and Liang Chen Design of the peiodic taining seuence fo joint channel and feuency estimation in MIMO feuency-selective channels Cicuits Systems and Signal Pocessing Vol. 48 Issue 3 7. []. S. M. Kay Fundamentals of Statistical Signal Pocessing: Estimation heoy Englewood Cliffs Pentice-all ew Jesey 993. [3]. M. Moelli and U. Mengali Caie-feuency estimation fo tansmission ove selective channels IEEE ansactions on Communications Vol. 48 pp [4]. P.. Moose A techniue fo othogonal feuency division multiplexing feuency offset coection IEEE ansactions on Communications Vol pp

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