Spatial ivision Multipleing of Space Time Block Codes for Single Carrier Block Transmission aiming Wang*, Wei ong, Xiqi Gao and Xiaohu Yu epartment of Radio Engineering, Southeast University, Nanjing 0096, China Email: hmwang@seu.edu.cn, weihong@seu.edu.cn Abstract: This paper presents a new Spatial ivision Multipleing (SM) based scheme combined with Space Time Block Coding (STBC) for Cyclic Prefi based Single Carrier Block Transmission (CP-SCBT). CP-SCBT technique converts the linear convolution of the frequency selective fading channel to the circular convolution. The optimum detection scheme based on the Minimum Mean Square Errors (MMSE) criterion can be easily solved with FFT/IFFT after simple pre-processing in the receiver. The Bit Error Ratio (BER) performances over different channels are assessed by simulations.. Introduction Since its introduction of by Alamouti in [], space-time block code has attracted considerable attention because of many attractive features. The Alamouti STBC scheme in [] assumes a flat-fading channel. The STBC is used in symbol level. Recently, several schemes have been proposed to etend the Alamouti STBC to frequency selective fading channels. The STBC is encoded in block level such as FE-STBC and TR-STBC [3]. S. Rouquette-Leveil proposed a Spatial ivision Multipleing based scheme combined with STBC [6]. But this scheme only can be used in flat-fading channels. Block transmissions (e.g., [][4][5]) such as cyclic prefi based single carrier block transmission (CP-SCBT) and orthogonal frequency division multipleing (OFM) are very effective techniques to combat frequency selective channels. ue to the use of FFT/IFFT operations the receiver compleity is kept significantly below the compleity of conventional single carrier system with time domain equalizers. We propose a new SM of STBC scheme for CP-SCBT which can be used in frequency selective fading channels. The notation adopted in this paper conforms to the following convention. Vectors are column vectors and are denoted in lower case bold:. Matrices are upper cases bold: A. I N denotes the identity matri of size N N. ei denotes the i-th unit vector. A k,m denoted the (k, m)-th entry of a matri A. () *, () T, () denotes conjugate, transpose, and ermitian transpose, respectively. diag { a } stands for a diagonal matri with the vector a on its diagonal. denotes Knonecker product.. Space-Time Joint Transmit for CP-SCBT Fig. shows the space-time joint transmitter of the proposed spatial division multipleing of space time block codes for CP-SCBT. We assume that the number of transmit antennas is N=4, and the number of receive antennas is M. The transmit antennas are split into two groups. Two streams can be transmitted simultaneously, and each stream is transmitted over two antennas and two data blocks according to the block-level Alamouti coding. 0-7803-9068-7/05/$0.00 005 IEEE
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The ST encoder takes four consecutive blocks of length N as input, and it generates the following output N 4 ST block-coded matri: (0) (0) (0) (0) (0) () () (3) s s s3 s 4 space () () () () *() *(0) *(3) *() s s s3 s4 P P P P time, () N ( ) k where P is a permutation matri that is drawn from a set of permutation matrices { P N }, with N ( k ) denoting the dimensionality N N. Each P N performs a reverse cyclic shift (that depends on k) when applied to a N vector a= [ a(0) a() a( ) ] T ( k ). Specifically, the p-th entry of P a is p (( N p k ) mod N) ( k ) P N a = + a. N k = 0 N (0) () () (3),,,, (0) (), () (3) (0) () *() P *(0) P () *(3) P (3) *() P Fig.. SM of STBC for CP-SCBT 3. MMSE Space-Time Joint etection for 4 TX Antennas We assume that the receiver achieved the perfect synchronization and perfect channel estimation. After removing the CP, the received signal vector in m-th antenna in j-th data block can be epressed as: 4 ( j) ( j) ( j) ( j) rm = m, nsn + zm, m=,,, M; n=,,...,4; j = 0, n=. () The different received signals can be concatenated vertically, T(0) T(0) T() T() r = r rm r rm. (3) If the matri C is a circulant matri, pre- and post-multiplying C by P yields [7]: T * PC P = C, (4) CC= CC. (5) (0) () We assume that the channels are fied over two consecutive blocks, i.e., =. Using (4) and (5), we get mn, mn, mn,
(0) (0) r,,,3,4 z (0) (0) () r M M, M, M,3 M,4 = *() (0) z M + () *() Pr,,,4,3 PzM (3) *() *() PrM M, M, M,4 M,3 PzM r z. (6) Using vector and matri notation we obtain r = + z. (7) Assuming that the transmit signal vector is zero mean and statistically independent and independent with noise vector z, and the vector z is the zero mean comple additive white Gaussian noise with the variance of z is σ, we get the optimum detection of transmitted data blocks according to the MMSE criterion: z where W σ I +. z 4N Since ( = = ) ( σ ) z 4 N ˆ = I + r = W r mn,, m,,, M, n,,...,4 are circulant matrices, using the relation of unitary matrices, we can get the result of W : or more compactly where W3,3 0,3,3 0 3,3 W W,3 W,3 W = W, W3,3 W,3W,3 W,3W,3 I4 W,3 W,3 W, 0 U 0 W,3 W W,3, U, (9) ( 4) W W = U I U, (0) W, 0N W,3 W,3 0N W, W,3 W,3 W = W,3 W W,3 3,3 0N W,3 W 0 W,3 N 3,3. Since is still a circulant matri, the inverse of U has a fast solution using FFT/IFFT [7]: U * * U = Q diag { N Q( Ue) } Q= Q Λ Q Λ * where Q is the normalized FT matri, Q is the normalized IFT matri. We found that the diagonal elements of are all real values, so Λ only need the real division. We rewrite (8) into Λ Our proposed detector is shown in Fig.. * ( ) W (8) () ˆ = Q Λ Q I4 U r. ()
r r y y y y3 r M U Λ Fig.. MMSE ST Joint etector for MIMO (TX antennas: N=4, RX antennas: M) Item Parameter Item Parameter Carrier frequency.45gz Channel estimation A root-of-unity sequence of length 3, LS method Bandwidth.8Mz Modulation 6QAM Channel environment COST 07 Turbo code (, 3), information bits: 7677, code rate: /, iteration number: 6, Log-MAP TX and RX antennas N=M=4 Inner interleaver interleaver size: 7677, S-random interleaver with S=6 Cyclic prefi length 6 Outer interleaver matri interleaver, interleaver size: 3070 Table. Simulation parameters 4. Simulation Results In this section, we demonstrate the performance of the proposed scheme in mobile multipath fading channels. Table shows the simulation parameters. The BER versus SNR @ per RX results of the proposed MIMO system are presented in Fig. 3. BER Performance of SM of STBC for CP-SCBT over Frequency Selective Channel 0 0 0-0 - 0-3 BER 0-4 0-5 0-6 0-7 Rayleigh (COST 07, 5km/h) Rayleigh (COST 07, 0km/h) 3 4 5 6 7 8 9 0 SNR @ Per RX Fig. 3. BER performance of the proposed MIMO system
5. Conclusion Combining SM of STBC and CP-SCBT, we propose a new SM of STBC scheme for CP-SCBT which can be used in frequency selective fading channels. We also present a low compleity MMSE ST joint detection. Considering CP and pilots inserted in time slots, the spectrum efficiency is about 3 bps/z in our simulation eample. Acknowledgement The authors are grateful to the support from the National igh Tech Research Plan of China (863 Plan) under grant 00AA303. References [] M. Alamouti, A simple transmitter diversity scheme for wireless communications, IEEE J. Select. Areas Commun., vol. 6, pp. 45 458, Oct. 998. [] Z.. Wang and G. B. Giannakis, Wireless multicarrier communications: where Fourier meets Shannon, IEEE Singnal Processing Magazine, pp. 9 48, May 000. [3] E. Lindskog and A. Paulraj, A transmit diversity scheme for channels with intersymbol interference, IEEE ICC 000. vol., pp. 307-3, 000. [4] N. Al-hahir, M. Uysal and C.N. Georghiades, Three space-time block-coding schemes for frequency-selective fading channels with application to EGE, IEEE VTS 54th, Vol. 3, pp. 834-838, 00. [5]. Sari, G Karam, and I. Jeanclaude, Frequency-domain equalization of mobile radio and terrestrial broadcast channels, IEEE GLOBECOM, pp. -5, 994. [6] S. Rouquette-Leveil, K. Gosse, X. Zhuang, and F.W. Vook, Spatial division multipleing of space-time block codes., ICCT-003.Vol., pp. 343-347, Apr. 003. [7] R. M. Gray, Toeplitz and Circulant Matrices: A review, downloadable, URL: http://www-isl.stanford.edu/~gray/toeplitz.pdf.