Compressive Channel Estimation for OFDM Cooperation Networks

Transcription

1 Researc Journal of Applied Sciences, Engineering and Tecnology 4(8): , 0 ISSN: Maxwell Scientific Organization, 0 Submitted: October, 0 Accepted: November 5, 0 Publised: April 5, 0 ompressive annel Estimation for OFDM ooperation Networs, Aiua Zang, 3 Guan Gui and Souyi Yang Scool of Information Engineering, Zengzou University, Zengzou, 45000, ina Scool of Electronic and Information Engineering, Zongyuan University of Tecnology, ZengZou, , ina 3 Department of Electrical and ommunication Engineering, Graduate Scool of Engineering, Toou University, Sendai, , Japan Abstract: In tis study, we study compressive cannel estimation for Ortogonal Frequency Division Multiplexing (OFDM) modulated Amplify-and-Forward (AF) relay networs. Based upon te matematical cannel model of PP and sparseness measure function, by using Monte-arlo runs, we sow tat te OFDM cooperation convoluted cannels also exibit sparsity. In tis study, we propose two compressive cannel estimation metods to exploit te inerent sparse structure in multipat fading cannels of OFDM cooperation networs wit Amplify-and-Forward (AF) relays, Simulation results demonstrate tat te proposed compressive cannel estimation metods provide significant improvement in mean square error (MSE) performance compared wit te conventional cannel estimation metods. Key words: Amplify-and-Forward (AF), cooperation networs, ompressive Sensing (S), multipat fading cannel, Ortogonal Frequency Division Multiplexing (OFDM) INTRODUTION ooperative relaying as been researced intensively for wireless networs in recent years due to its capability of enancing te transmission capacity and providing te spatial diversity for single-antenna wireless transceivers by employing te relay nodes as virtual antennas (Laneman and Wornell, 003; Gao et al., 008). Multipleinput multiple-output (MIMO) system is a well-nown tecnique wic can boost te capacity and diversity of wireless communications (Foscini et al., 999). However, it is difficult to equip multiple antennas at mobile terminals because of cost and size limits. In order to recon wit tis problem, relay-based cooperation communication networs ave been proposed recently. It is expected tat relay protocols will be a very promising metod for future ig data-rate radio communication systems. In cooperative communication system, terminals can be usually divided into tree parts: source, relay, and destination, source and destination can be te base station and mobile station, respectively, or vice versa, and te relay receives signal from source and retransmits to destination. Generally, tere are two inds of protocols in cooperation networs: te Amplify-and-Forward (AF) sceme and Decode-and-Forward (DF) sceme. In te AF relaying, te relay amplifies and retransmits its received noisy signal witout decoding it. In te DF relaying, te relay terminals demodulate and modulate again te received signals and ten forward tem to te destination (Laneman et al., 004). ompared wit te DF sceme, te AF sceme is more effective since te cooperative terminals do not need to decode teir received signals. Terefore, we focus our attention on te AF relay sceme in tis study. Many relay studies focused on flat-fading cannels, were single-carrier systems are of interest (Seyfi et al., 0; Gao et al., 008). However, te use of relays in frequency-selective broadband cannels is important as well. It is well nown tat te popular solution against frequency-selective fading is OFDM. So, cooperative OFDM relay networs are increasingly important. Recently, several OFDM cannel estimation metods for modulating cooperation communication ave been proposed (Gao et al., 0; Zang et al., 009; an et al., 007) and tese OFDM cannel estimation metods using AF protocol are based on te assumption tat te wireless cannels between te terminals and te relay nodes ave ric multipat (otter and Rao et al., 00). However, recent cannel measurements ave demonstrate tat te wireless cannels tend to exibit a sparse or cluster-sparse structure (Adaci et al., 009) in delayspread domain. In order to tae advantage of OFDM cooperation cannel sparsity, two novel compressive cannel estimation scemes are proposed in tis study. Simulation results validate te effectiveness of te proposed metods. orresponding Autor: Aiua Zang, Scool of Information Engineering, Zengzou University, Zengzou, 45000, ina 897

2 Res. J. Appl. Sci. Eng. Tecnol., 4(8): , 0 Fig.: A typical sparse multipat cooperation networ adopting OFDM modulation SYSTEM MODEL Relay transmission model: onsider a tree-node OFDM cooperation networ wit two terminals S, D and one relay node R is sown in Fig.. We assume tat all te terminals are equipped wit only one antenna and wor in te alf-duplex mode, terefore, tey cannot receive and transmit simultaneously. In a relay networs, data transmission is usually divided into two pases. Te source broadcasts its own information and te relay forwards its received signal to te destination. Due to te limited transmit power and te multipat fading cannel, we assume tat tere is no direct pat between S and D as sown in Fig.. Terefore, frequency-selective multipat cannels will generate multiple delayed and attenuated copies of te transmitted waveform. Source and relay are assumed to ave average power constraints in P S and P R respectively. Assume tat te cannel impulse response between S and R is (t), wic is constant witin one transmission period and represented by L, l, l l 0 () t ( ) were,l is te complex-valued pat and it satisfies L l 0, l E[ ], () and J,l denotes te symbol-spaced time delay of te lt pat, and L is te lengt of te cannel between S and R. Due to te same cannel property as Eq. (), cannel vector between R and D is given by te follows: L, l, l l 0 () t ( ) () were,l and J,l denote te complex-valued pat and te lt pat symbol-spaced time delay, respectively. L is te lengt of te cannel between R and D: Transmitted signal at te source: Suppose tat eac OFDM bloc contains N information symbols and denote te frequency domain training vector from S as x [ x, x,..., x ]. Te corresponding time-domain signal 0 N vector can be obtained from te normalized inverse discrete Fourier transformation (IDFT) as: H x F x [ x, x,..., 0 xn ] were F is te discrete Fourier transformation (DFT) matrix wit te (m,n) -t entity given by F / N exp( jmn/ N),( m, n 0,,..., N). In order to avoid te Inter-bloc Interference (IBI), S inserts te cyclic prefix (P) of lengt L p in te front of eac OFDM bloc before te transmission, and L p sould satisfy tat L p max(l -,L -). After performing DFT and inserting P, te transmitted signal vector can be written as: S x,... x, x..., x NLp, N 0, N (3) (4) Te received signals at te relay node and te destination: In te AF relay transmission, te received signal at te relay is amplified by a relay factor ". Over a doubly selective cannel between te source S and te relay R, after removing P, te received signal at te relay node can be represented as (Adaci et al., 009) y = H x+n (5) were H is an N N circulated cannel matrix wit [ T 0 (N-L )] T as its first column, n is te complex additive Gaussian wite noise (AWGN) wit zero mean and covariance matrix E[n n H ] = F ni N. Te received signal at te destination D, wic is from relay R, can be written as: y = "H y +n = "H H x+n (6) were n = "H n +n is te composite noise wit zero mean and covariance matrix E{nn H } = " F n H +l N. Te amplified positive coefficient " is given by: 898

3 Res. J. Appl. Sci. Eng. Tecnol., 4(8): , 0 P R L L P l 0, l l 0, l (7) According to te matrix teory, matrices H and H can be de-composited as H = F H 7 F and H = F H 7 F (Gray, 006), respectively. F is te discrete Fourier transformation (DFT) matrix. Tus, system model (6) can be rewritten as: y = F H "7 7 Fx + n (8) We define te convolution cannel vector = " ( * ) wit te lengt of (L + L -). After left-multiplying by F, Eq. (8) can be rewritten as: y XW n X n (9) were X = diag (Fx) denotes te training signal matrix, X = diag (Fx)W, W is a matrix taing te first (L +L -) columns of NF and n Fn Fn is a realization of a complex Gaussian random vector. OMPRESSIVE HANNEL ESTIMATION Overview of compressive sensing: ompressed Sensing (S) teory as recently gained a fast-growing interest in applied matematics and signal processing communities. And it as been applied in various areas, suc as imaging, radar, speec recognition, data acquisition, etc. In communications, an immediate application of S is in wireless sparse multipat cannel estimation (Gui et al., 0; Bajwa et al., 008). In tis study, we consider te linear model as (9). According to te S, if an unnown signal vector satisfies sparse or approximate sparse, ten a designed measurement matrix X can accurately capture most of its dominant information. Hence, tese inds of unnown signal can be reconstructed from observation signal y However; te sparsest solution is always a Nondeterministic Polynomial-time ard (NP-ard) problem. In order to solve tis problem, several metods ave been proposed. Donoo (Donoo, 006) presented a necessary and sufficient condition (RIP) on te sensing matrix. andès and Tao (and, 008; andes and Tao, 005) introduced te Restricted Isometry onstants (RI) of te matrix. Suppose tat X be a n p complex-valued measurement matrix, wic as unit R -norm columns. Te X satisfies te RIP of order S wit parameter * s,(0,), wic can satisfy te following inequality: ( S ) X ( s) () said to satisfy RIP of order S, and accurate cannel estimator wit ig probability can be obtained by using S metods. Altoug it is quite difficult to judge weter a given matrix satisfies tis condition, it as been demonstrate tat many matrices satisfy te RI wit ig property and few measurements. In particular, it as been sown tat wit exponentially ig probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy te RI wit number of measurements nearly linear in te sparsity level. Sparse cannel estimation: Because te cannel impulse responses is sparse, its convolution from and ave been verified to be sparse or approximate sparse (Gui et al., 0). Numerous practical algoritms exist for te cooperation convoluted cannel. Generally, tese algoritms can be classified into two inds. Te first ind is greedy algoritms suc as Ortogonal Matcing Pursuit (Omp) and ompressive Sampling Matcing Pursuit (osamp), wic selects eac dominant coefficient in cannel by iteration. Te second ind is convex relation metods suc as Lasso. In tis study, we also consider te LS cannel estimator for comparison. Te LS estimator is written as te follows. X Ty T Suup 0 oters () were suup() denotes te nonzero taps supporting te cannel vector,x T is te submatrix constructed from te columns of X, and T denotes te selected subcolumns corresponding to te nonzero index set of te cannel vector. Te MSE of LS estimator is given by (Bajwa et al., 008): n T T MSE Tr X X () By utilizing S recovery algoritms for compressive cannel estimation, we propose S-Lasso, S- osamp. Te two metods for cooperation convoluted cannel estimate are described as follows: S-Lasso estimator Lasso : Given te received signal y, te unitary DFT matrix F and W, training X signal matrix parameter logn 0) cannel estimator Lasso given by: = diag (Fx)W te regularized Te S-Lasso (Gui et al., Lasso arg min y X (3) were 55 denotes te R -norm wic is given by If () is satisfied, te training sequence is. i S-oSaMP estimator osamp : Given y,f and W and training signal matrix X = diag (Fx)W te 899

4 Res. J. Appl. Sci. Eng. Tecnol., 4(8): , 0 maximum number of dominant cannel coefficients is assumed as S. Te S-oSaMP metod (Gui et al., 0) can be described as follows: Set T 0 = Ø, r 0 = y,t is nonzero coefficient index, and r is te residual estimation error. Set te initialize iteration index =. Select a column index n of X wic is most correlated wit te residual: n r, X and T T n n (4) Here we use LS metod to calculate a cannel estimator as T Ls = argmin5y- X 5, and select T maximum dominant taps Ls. Were T LS denotes te positions of te selected dominant taps in tis substep. Update te dominant taps by T TLsT annel estimation, arg min y X T (5) Find te dominant cannel coefficients, and replace te left taps T/T by zero: = [] S (6) Update te estimation residual: r y X T (7) Increment te iteration counter. Repeat (3)-(6) until stopping criterion olds and ten set osamp =. SIMULATION RESULTS In tis study, we adopt 000 independent Monte- arlo runs for average. Te lengt of training sequence is N = 56. All of te nonzero taps of sparse cannel vectors and are generated by Gaussian distribution and subject to 5 5 = 5 5 =. Te lengt of te two cannels is L = L = 3, and te positions of nonzero cannel taps are randomly generated. We set transmit power equal to AF relay power, tat is P s = P R = P. Te Signal to Noise Ratio (SNR) is defined as S as log P/F n). Wen te number of nonzero taps in cooperation cannels i,( i =,) is canged, te simulation results are sown in Fig. and 3. annel estimators are evaluated by average Mean Square Error (MSE) wic is defined by: averagemse( ) M( L L ), (8) Average MSE 0 B (LS) - B (S-Lasso) B (S-oSaMP) - B (LS:nown position) SNR (db) Fig. : MSE perfomance as a function of SNR (number of nonzero taps of and are ) Average MSE B (LS) B (S-Lasso) B (S-oSaMP) B (LS:nown position) SNR (db) Fig. 3: MSE perfomance as a function of SNR (number of nonzero taps of and are 4) were and denote cannel vector and its estimator, respectively. M is te number of Monte arlo runs and ((L + L -) is te overall lengt of cannel vector. In Fig., te number of nonzero taps of i,(i =, ) is set to, te cooperation convoluted cannel also as sparsity. Figure sows tat performance of te proposed S estimator metods outperforms LS estimator and it is close to te ideal LS estimator by using nown position of te cannel. In addition, under low SNR (less tan db), te proposed S-Lasso estimator acieves even better performance tan te LS estimator (nown position). In Fig. 3, te number of nonzero taps of i,(i =, ), is set to be 4. From te simulation results in Fig. and 3, it can be seen tat te proposed estimators can exploit te cannel sparseness. And if cannels are dense rater tan sparse, all of te proposed estimators will ave te same performance as LS estimator. ONLUSION In tis study, we introduce OFDM cannel estimations for te AF cooperative cannel. Distinct from te conventional linear cannel estimation metods, we 900

5 Res. J. Appl. Sci. Eng. Tecnol., 4(8): , 0 proposed compressive cannel estimation metods for te OFDM cooperation networs under AF protocol. Sparseness of OFDM cooperation convoluted cannel was demonstrated by a measure function. Te proposed metods ave exploited te sparsity in OFDM cooperation cannel. Simulation results ave confirmed te performance superiority of te proposed metod to te conventional linear LS metod. AKNOWLEDGMENT Tis study is funded by te National Natural Science Foundation of ina (No. 6775). REFERENES Adaci, F., H. Tomeba and K. Taeda, 009. Introduction of Frequency-Domain Signal Processing to Broadband Single-arrier Transmissions in a Wireless annel. IEIE Trans. ommun., E9- B(9): Bajwa, U.W., J. Haupt, G. Raz and R. Nowa, 008. ompressed cannel sensing. ISS 08, pp: 9-. and, E.J., 008. Te Restricted Isometry Property and Its Implications for ompressed Sensing, ompte Rendus de l Academie des Sciences. Paris, Serie I(346): andes, E. and T. Tao, 005. Decoding by Linear Programming. IEEE Trans. Inf. Teory, 5(): an, A.M., H.T. Kung and V. Taro, 007. Design of an OFDM cooperative space-time diversity system. IEEE Trans. Veicular Tecnol., 56(4): otter, S.F. and B.D. Rao, 00. Sparse cannel estimation via matcing pursuit wit application to equalization. IEEE Trans. ommun., 50(3): Donoo, D.L., 006. ompressed sensing. IEEE Trans. Inf. Teory, 5(4): Foscini, G.J., G.D. Golden, R.A. Valenzuela and P.W. Wolniansy, 999. Simplified processing for ig spectral efficiency wireless communication employing multi-element arrays. IEEE J. Selected Areas ommun., 7(): Gao, F., T. ui, A. Nallanatan and S. Member, 008. On cannel estimation and optimal training design for amplify and forward relay networs. IEEE Trans. Wireless ommun., 7(5): Gao, F., B. Jiang, X.Gao and X.D. Zang, 0. annel estimation for ofdm modulated amplify-and-forward relay networs. IEEE Trans. ommun., 59(7): Gray, R.M., 006. Toeplitz and circulant matrices: A review. Foundations Trends ommun. Inf. Teory, 3(): Gui, G., Z. en, Q.W. Meng, Q. Wan and F. Adaci, 0.compressed cannel estimation for sparse multipat twoway-relay networs. Int. J. Pys. Sci., 6(): Laneman, J.N. and G.W. Wornell, 003. Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networs. IEEE Trans. Inf. Teory, 49(): Laneman, J.N.D., N.. Tse and G.W. Wornell, 004. ooperative diversity in wireless networs: efficient protocols and outage beavior. IEEE Trans. Inf. Teory, 50(): Seyfi, M., S. Muaidat and J. Liang, 0. apacity of selection cooperation wit cannel estimation errors. 0 5t Biennial Symp. ommun., 3: Zang, Z., W. Zang and S. Member, 009. ooperative OFDM cannel estimation in te presence of frequency offsets. IEEE Trans. Veicular Tecnol., 58(7):