Virtual MIMO Space Division Multiplexing for MC-CDMA Koichi Adachi † , Fumiyuki Adachi ‡ , and Masao Nakagawa † † Graduate School of Science and Technology, Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan {kouichi, nakagawa}@nkgw.ics.keio.ac.jp ‡ Graduate School of Engineering, Tohoku University 6-6-05 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8579 Japan adachi@ecei.tohoku.ac.jp Abstract—To increase the data rate without signal bandwidth expansion, a combination of MC system with multiple-input multiple-output (MIMO)-space division multiplexing (SDM) is attractive. MIMO-SDM transmission performance is governed by min {N t , N r }, where N t and N r are the numbers of transmit and receive antennas, respectively. For downlink transmission, many receive antennas cannot be equipped at a mobile station due to space limitation. Therefore, the achievable data rate is limited by the number of receive antennas. In this paper, we propose a virtual MIMO-SDM for multi-carrier-code division multiple access (MC-CDMA) that can use the signals received via different propagation paths as virtual receive antennas. The equivalent number of receive antennas can be increased by a factor of the number of distinct paths of the channel. We confirm, by computer simulation, the effectiveness of virtual MIMO-SDM in a frequency-selective fading channel. Keywords-component; MIMO; MC-CDMA; Phase rotation I. INTRODUCTION Because of the rapid growth of multimedia services, very high speed data transmission is required for the future wireless communication systems [1]. For high speed data transmissions, the wireless channel consists of a number of propagation paths [2] and the channel becomes a severe frequency-selective fading channel. Multi-carrier (MC) system, such as orthogonal frequency division multiplexing (OFDM) and multi-carrier- code division multiple access (MC-CDMA), is robust against the frequency selective fading. To increase the data rate without signal bandwidth expansion, multiple-output (MIMO)- space division multiplexing (SDM) is attractive [3][4]. MIMO- SDM transmission performance is governed by min{N t , N r }, where N t and N r are the numbers of transmit and receive antennas, respectively [5]. For downlink transmission, many receive antennas cannot be equipped at a mobile station due to space limitation. Therefore, the achievable data rate is limited by the number of receive antennas. In this paper, we propose a virtual MIMO-SDM for MC- CDMA that can use the signals received via different propagation paths as virtual receive antennas. By removing the phase rotation associated with time delay of each path, the signals received via different propagation paths can be separated through the despreading process without inter-path interference (IPI) to form an N t -by- ) ( L N r ⋅ MIMO channel, where L denotes the number of propagation paths. Various MIMO signal detection schemes can be applied to virtual MIMO-SDM. They are maximum likelihood detection (MLD) [6], minimum mean square error (MMSE) detection [7], vertical-Bell laboratory’s layered space-time (V-BLAST) detection [8], sphere decoding [9], and QR-decomposition based M-algorithm [10][11]. The rest of the paper is organized as follows. Sect. II gives the received signal representation for virtual MIMO- SDM for MC-CDMA. Virtual MIMO-SDM signal detection is described in Sect. III. Computer simulation results are presented in Sect. IV. Section V concludes the paper. II. RECEIVED SIGNAL REPRESENTATION The transmission system model using N t transmit antennas and N r receive antennas is illustrated in Fig. 1. In this paper, the discrete-time signal representation is used. The binary data sequence to be transmitted is serial-to-parallel (S/P) converted to N t streams, each stream being data-modulated. The n t -th data-modulated symbol stream ( ) 1 ( ~ 0 − = t t N n ) is transmitted from the n t -th transmit antenna using multicode MC-CDMA. In multicode MC-CDMA with N c sub-carriers and code multiplexing order U, the u-th ( ) 1 ( ~ 0 − = U u ) data symbol sequence ⎣ ⎦ )} 1 ( ~ 0 ); ( { , − = SF N n n d c u n t is spread by the spreading code )} 1 ( ~ 0 ); ( { − = SF q q c u , where ⎣ ⎦ x is the largest integer smaller than or equal to x and SF is the spreading factor. After spreading, the chip sequence is mapped onto equally spaced SF sub-carriers as shown in Fig. 2. The k-th subcarrier component ) (k S t n can be expressed as () () ∑ − = ⋅ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ = 1 0 , 2 U u u u n c c c n q c n d T SF E n q SF N k S t t , (1) where E c is the signal energy per sample of fast Fourier transform (FFT) and T c is the FFT sample duration. The same spreading code is reused for all the transmit antennas. The time-domain MC-CDMA signal to be transmitted from the n t -th transmit antenna is generated by N c -point inverse FFT (IFFT) as () () ∑ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π = 1 0 2 exp c t t N k c n n k N t j k S t s . (2) After inserting an N g -sample cyclic prefix (CP) into the guard interval (GI) to avoid inter-block interference (IBI), MC- CDMA signal is transmitted. 978-1-4244-2515-0/09/$25.00 ©2009 IEEE