Combining Orthogonal Space-Frequency Block Coding and Spatial Multiplexing in MIMO-OFDM System

Transcription

1 Combining Orthogonal Space-Frequency Bloc Coding and Spatial Multiplexing in MIMO-OFDM System Muhammad Imadur Rahman, Nicola Marchetti, Suvra Sehar Das, Fran H.P. Fitze, Ramjee Prasad Center for TeleInFrastrutur CTiF), Aalborg University, Denmar imr nm ssd ff ph: Abstract In the present wor, we have combined Orthogonal Space-Frequency Bloc Coding OSFBC) and Spatial Multiplexing SM) in one transmission scheme for Orthogonal Frequency Division Multiplexing OFDM) systems. In the combined transmission scheme, both spatial diversity and multiplexing benefits are possible to achieve. Simple Alamouti coding as the S-F coding across spatial multiplexing branches and a simplified linear receiver instead of a complex successive interference cancellation receiver are used in our scheme. In the initial analysis, it is found that SM-OSFBC-OFDM system is near to the optimum system capacity for any 4 MIMO-OFDM system. I. INTRODUCTION Multiple antennas can be used in both ends of a Multiple Input Multiple Output MIMO) wireless transmission system to exploit the benefits of the spatial dimension. Two MIMO modes can be exploited, namely Space Diversity SD) and Spatial Multiplexing SM). In SD mode, Space-Time Coding STC) and Maximal Ratio Combining MRC) can be used at the transmitter side and/or receiver side respectively, to exploit the maximum spatial diversity available in the channel. This increases the system reliability. Furthermore, SM is a promising and powerful technique to dramatically increase the system capacity. In rich scattering environment the independent spatial channels can be exploited to send multiple signals at the same time and frequency, resulting in higher spectral efficiency. Most of the available MIMO techniques are effective in frequency flat scenarios. In wideband scenarios, Orthogonal Frequency Division Multiplexing OFDM) can be combined with MIMO systems, for both diversity and multiplexing purposes. In frequency selective environments, amalgamation of SM and OFDM techniques can be a potential source of high spectral efficiency, thus high data rate systems can be realized in wideband scenario. All the algorithms can be implemented on OFDM sub-carrier level, because OFDM converts a wideband frequency selective channel into a number of narrowband sub-carriers. Alamouti s remarable orthogonal transmission structure 3 can be applied in space-time or space-frequency domain in OFDM systems as it is shown in 4 and 5, to obtain higher signal quality. Similarly, SM techniques, such as Vertical - Bell Labs LAyered Space-Time Architecture VBLAST) 6, can also be used in conjunction with OFDM systems to obtain higher spectral efficiency. In a cellular wireless systems, the Space-Time Bloc Coded Orthogonal Frequency Division Multiplexing STBC- OFDM) 4 and Space-Frequency Bloc Coded Orthogonal Frequency Division Multiplexing SFBC-OFDM) 5 can be used to increase the resultant Signal to Noise Ratio SNR) at the receiver, thus, increasing the coverage area in a cellular system. In contrast to this, as SM-OFDM requires high receive SNR for reliable detection, it is evident that users at farther locations from Base Station BS) cannot use SM techniques to enhance the spectral efficiency. Thus, it is required to combine both of these two techniques in one structure so that both the diversity and multiplexing benefits can be achieved at farther locations from transmission source. Recently there are some approaches of incorporating the VBLAST technique with some well nown STC techniques. One such wor is described in 7, where a combination of SD and SM for MIMO-OFDM system is proposed. We call such systems as Joint Diversity and Multiplexing JDM) systems. Arguably, the performance of such a system would be better than SD only and SM only schemes. In 7, the SM-OFDM system uses two independent STC for two sets of transmit antennas. Thus, an original SM-OFDM system is now extended to 4 STC aided SM-OFDM system. In the receiver, the independent STCs are decoded first using prewhitening, followed by maximum lielihood detection. Again, this increases the receiver complexity quite a lot, though the system performance gets much better. In later wor, Alamouti s Space-Time Bloc Code STBC) is combined with SM for OFDM system in 8, and a linear receiver is designed for such a combination. Following these trends, we have combined Space-Frequency Bloc Code SFBC) with SM and obtained a linear receiver similar to 8 in this wor. One advantage in using SFBC instead of STBC is that, in SFBC, the coding is done across the sub-carriers inside one OFDM symbol duration, while STBC applies the coding across a number of OFDM symbols equal to number of transmit antennas, thus, an inherent processing delay is unavoidable in STBC. Our wor aims to achieve contemporarily the multiplexing gain via two SM branches) and the diversity gain via SFBC codes), eeping the complexity low through the receiver linearity). A possible scenario where such an hybrid scheme would be useful could be the intermediate region of the cell, in fact while close to the BS the SM mode is more advantageous

2 m SM Fig.. Scheme m SFBC SFBC m m rem rem FFT FFT z z Linear RX Simplified System Model for SM-OSFBC-OFDM Transmission and close to the cell edge the SD mode is more suitable, it can be seen that the proposed scheme will give benefits in between. The rest of this paper is organized as follows. The SM- SFBC-OFDM system model is presented in Section II. Capacity analysis, simulations and discussions are provided in Section III. The conclusion is presented in Section IV. II. SM-OSFBC-OFDM TRANSMISSION SCHEME In this section, we will explain the transmission structure of the JDM scheme based on combining SM and Orthogonal Space-Frequency Bloc Code OSFBC). Following this, we propose a linear two-stage receiver, which is an extension of Least-Square LS) receiver in 8, where the linear reception technique is used for Spatially-Multiplexed Orthogonal Space-Time Bloc Coded Orthogonal Frequency Division Multiplexing SM-OSTBC-OFDM) system based on Zero Forcing ZF) criterion. In this part, we investigate the two-stage linear receiver with both ZF and Minimum Mean Square Error MMSE) criterion. A. Joint Diversity and Multiplexing based Transmitter We denote the number of SM branches at the transmitter side and number of receive antennas as P and Q respectively. We have N number of sub-carriers in the system. Figure explains the basic transmitter architecture. At first source bits are Forward Error Correction FEC) coded and bit interleaved. The interleaved bit stream is baseband modulated using an appropriate constellation diagram, such as Binary Phase Shift Keying BPSK), Quadrature Amplitude Modulation QAM) etc. We denote this baseband modulated symbols as m. The sequences of m is demultiplexed into m,..., m P vectors. m p is transmitted via p th spatial channel. For every p th SM branch, we implement a bloc coding across the sub-carriers, thus SFBC is included in the system. For p th SM branch, we have p number of antennas where SFBC can be implemented. When p =, p, then we have P number of transmit antennas at the transmission side. When =, we can use well-nown Alamouti coding 3 across the sub-carriers. For p th SM branch, m p is coded into two vectors, m δ) p ; δ =,. Thus, the output of the SFBC encoder bloc of the p th z SM branch will be m ) p = m p, m p,... m p,n m p,n ) m ) p = m p, m p,... m p,n m p,n ) Following this, we define m p,o = m p, m p,3... m p,n 3 m p,n 3) m p,e = m p, m p,4... m p,n m p,n 4) Using these equations, we can write that m ) p,o = m p,o, m ) p,e = m p,e, m ) p,o = m p,e, m ) p,e = m p,o. After SM and SFBC operations, modulation is performed and Cyclic Prefix ) is added before transmission via respective transmit antenna. Transmitted time domain samples, x δ) p, can be related to m δ) p as, x δ) p = F H {m δ) p }. B. Two-Stage Linear Receiver In 9, a two stage interference cancellation receiver scheme for STBC is presented. This receiver treats one of the branches as the interfering source for the other one. This receiver is used to derive a linear reception technique for SM-OSTBC- OFDM system in 8. In this wor, we adopt a similar receiver structure for our Spatially-Multiplexed Orthogonal Space-Frequency Bloc Coded Orthogonal Frequency Division Multiplexing SM-OSFBC-OFDM) system. We consider P =, = and Q =. We assume perfect time and frequency synchronization is achieved in the system. Thus, we can represent the system in frequency domain notations. We can write the equivalent system model as the following: where,..., N, H is defined as H = z = H m + n 5) h ),o h ),o h ),o h ),o h ),o h ),o h ),o h ),o,e h ),e,e h ),e,e h ),e,e h ),e and z = z,o z,e z,o z,e T, m = m,o m,e,o,e T, n = n,o n,o n,e n,e T. We denote coherence bandwidth and sub-carrier spacing as B c and f respectively. We define severely frequencyselective scenario when coherence bandwidth is smaller than a pair of sub-carrier bandwidth, i.e. f < B c < f. In this case, we use a tool called Companion Matrix explained in Appendix I. We can represent 5) as with H i = 6) z = H i H j m + n 7) h ),o h ),o,e h ),e h ),o h ),o & H j =,e h ),e

3 We denote the companion matrices of H i and H j as H i and H j respectively. We define a new matrix H = H i Hj T with h )H,e h )T,o h )H,e h )T,o H i =,e h )T,o & H j =,e h )T,o Now, at the beginning of the receiver, we can filter the received signal z lie following: z = Hz Hi = Hi H j m + Hn 8) H j Now, 8) can be written as z α = I G m + G α I Hn 9) ) where α = h )H,e h ),o + h)t,o h),e, α = ) h )H,e h ),o + h)t,o h),e and G, G, shown in Eq. ) form an orthogonal pair as defined in Appendix I. Now we define an LS receiver W as W = α I G ) γ α I G where γ = α α G, )G, ) G, )G, ). Thus, the estimated symbol vector can be written as m = Wz = m + W Hn ) In relation to severely frequency-selective scenario, we define moderately frequency-selective scenario when B c > f, and in that case we can easily say that neighboring sub-carriers have identical channel frequency response. The MMSE receiver can be implemented in the same simple way. Defining the new constants then we can rewrite ) as m = β I G 3) δ β I G where β = α + σ n, β = α + σ n, with σ n noise variance on one receive antenna, and δ = β β G, )G, ) G, )G, ). III. ANALYSIS, SIMULATIONS AND DISCUSSIONS A. System Parameters We have used two simulation scenarios as explained in Figure I. For all our analysis and simulations, we have confined ourselves to the case of dual transmit and receive antenna MIMO system with antennas per spatial multiplexing branches i.e. Q =, P = and = ). We assume that perfect time and frequency synchronization is established. We also assume that perfect channel estimation values for each sub-carrier for both the spatial channels are available at the receiver. We use exponential channel model to generate corresponding Channel Impulse Response CIR) and Channel Transfer Function CTF) of the channel. In our exponential model, power delay profile of the channel is exponentially distributed with decay between the first and last impulse as -4dB. TABLE I OFDM SIMULATION PARAMETERS Parameters Indoor Indoor System bandwidth, B MHz Carrier frequency, f c 5.4 GHz User mobility,v 3 mph mph OFDM sub-carriers, N Subcarrier spacing, f = B/N 3.5 Hz 78.3 Hz length, N 6 Total samples in OFDM Symbol with, N s = N + N Symbol duration, T s = T u + T 4. µs 7.8 µs OFDM symbols/frame, N f 6 Frame duration, T f = N f T s 64. µs 84.8 µs Data Symbol mapping QPSK Channel coding scheme -rate convolutional coding B. Theoretical Capacity Analysis The theoretical outage capacity of SFBC-OFDM, STBC- OFDM, SM-OFDM and SM-SFBC-OFDM systems are evaluated in this section via a semi-analytical Monte-Carlo simulation approach. This is done primarily for indoor environment. First, the indoor channel is simulated using the exponential model mentioned above. Then the instantaneous channel capacity is obtained using the simulated CTF based on the following equation: C = N N = log det I Q + ρ ) P H H 4) where ρ is the transmit SNR and H is the equivalent effective CTF of th sub-carrier. Equivalent CTF means the CTF at the particular sub-carrier at the receiver, as shown in 5). The above instantaneous capacity is derived for each channel realization and then the Cumulative Distribution Function CDF) of the instantaneous channel capacity is plotted in Figure for outdoor scenario. For a large number of random channels, the outage and mean capacity can be determined from these figures. In our case, we have simulated 5, random channels and obtained the CDFs. We have compared the system capacity of diversity only schemes, multiplexing only schemes and hybrid diversitymultiplexing schemes. For diversity only schemes, SFBC and STBC are presented. For multiplexing schemes, and 4 multiplexing schemes are used. Obviously our scheme becomes 4 hybrid scheme. We define % outage capacity as the system capacity in bits/second/hz bps/hz) above which the system capacity remains at least 9% of the connection time. According to Figure, diversity only schemes i.e. STBC and SFBC) have similar outage capacity characteristics, approximately at.6 bps/hz. In contrast to this, spatial multiplexing only scheme has % outage capacity of 4. bps/hz, compared to our 4 hybrid schemes at 6. bps/hz. The maximum outage capacity of any 4 open loop MIMO schemes can be 6.9 bps/hz. The last outage capacity value is an upper bound for any 4 open loop MIMO scheme. This is achievable with best available source, channel and S-F coding. In our case,

4 G = h )H,e h ),o + h)t,o h),e h )H,e h ),o h)t,o h),e,e h ),o h)t,o h),e,e h ),o + h)t,o h),e ; G = h )H,e h ),o + h)t,o h),e h )H,e h ),o h)t,o h),e,e h ),o h)t,o h),e,e h ),o + h)t,o h),e ) even though we have simple convolutional code as the FEC code and simple Alamouti scheme as the S-F code, it can be seen that the capacity performance is very close to the optimum boundary. Modulation:QPSK, Coded FER, Outdoor ZF BLAST MMSE BLAST ML SM OSFBC, ZF Lin SM OSFBC, MMSE Lin In terms of mean capacity, we see that the schemes obtain.9374,.748, 8.3, 7.54 and bps/hz respectively. These values are obtained by finding the mean value of simulation data that are used in Figure. Thus the hybrid scheme gains.9383 bps/hz of mean capacity compared to spatial multiplexing only schemes. This is achieved by introducing more antennas and by incorporating SFBC across each spatial multiplexing branch. FEP.9.8 CDF of the correponding capacity of at db SNR SNR, db Fig. 4. FER performance of diversity only and hybrid schemes in outdoor scenario x SFBC OFDM 4x SM SFBC OFDM Probability that quantity < abscissa x Alamouti SFBC x Alamouti STBC 4x SM OFDM 4x SM SFBC OFDM x SM OFDM Probability that quantity < abscissa Capacity in bps/hz.. Fig.. CDF of theoretical capacity of corresponding MIMO-OFDM systems Modulation:QPSK, Coded FER, Indoor ZF BLAST MMSE BLAST ML OSFBC SM OSFBC, ZF Lin SM OSFBC, MMSE Lin Fig b/s/hz b/s/hz CDF of spectral efficiency of corresponding MIMO-OFDM systems FEP SNR, db Fig. 3. FER performance of diversity only and hybrid schemes in indoor scenario C. FER Analysis Figures 3 and 4 show the Frame Error Rate FER) performance of the JDM schemes in indoor and outdoor scenario respectively. In indoor scenario, a frame consists of N L f M P R c = 64 6 = 48 source bits, while in outdoor scenario, it is 56 6 = 89 source bits in one frame. All the schemes use Quadrature Phase Shift Keying QPSK) as the baseband modulation scheme. As a reference, performance of optimum ML receiver for SM scheme is plotted along with the other schemes. For various transmit antenna configurations, the total transmit power was ept constant, thus, the SNR at the x-axis reflects total SNR of the systems. We note that Spa-

5 tial Multiplexed Orthogonal Frequency Division Multiplexing SM-OFDM) performs worse in terms of FER compared to SFBC-OFDM system. In SM-OFDM system, we get a higher rate, but we lose in diversity. Considering this, we can see that 4 SM-OSFBC-OFDM performs better than SFBC-OFDM system in terms of FER. In this case, not only the diversity gain is achieved, but also spatial multiplexing is realized. This clearly shows the benefits obtained by adding spatial dimensions at the transmitter and using SFBC in the SM branches. For instance, SM-OSFBC MMSE-Lin achieves a gain of db, compared to MMSE-BLAST at an FER of 3 in indoor scenario as seen in Figure 3. Similar trend is also noted in outdoor scenario. Including more antennas for transmitter SFBC offers immense benefit. But, of course, it is clear that outdoor channel is more frequency selective, thus all the systems require more SNR compared to indoor scenario for any FER reference point. D. Spectral Efficiency Analysis It is expected that the achievable spectral efficiency of the system appears to be as close as possible to the upper bound. In our case, the upper bound is shown in Figure as 4 SM-OFDM system capacity. We have simulated the spectral efficiency in the following way. For every frame realizations, we simulate the channel CTF, and we run the simulations for times with different AWGN contents. Then we find out the FER that can be used according to following equation to find our instantaneous spectral efficiency, E s = B r B = N b F ER)/T f B 5) where E s is the spectral efficiency, B r is the data rate, N b is the number of source bits. For Outdoor parameters, we have obtained the spectral efficiency curves for SFBC-OFDM and SM-SFBC-OFDM as it can be seen in Figure 5. The % outage capacity is seen to be.9 bps/hz and.8 bps/hz respectively. It has to be noted that the theoretical capacity as shown in Figure ) is the upper bound achievable if one uses the best channel coding, the best space-frequency coding and optimum receiver in terms of error rate performances. Here we show Figure 5) that the spectral efficiency achievable with SM-SFBC is nearly one-quarter of the theoretical capacity optimum.8 bps/hz against 8.3 bps/hz), therefore by using better channel coding e.g. Turbo-codes or LDPC) or a space-frequency coding optimized for the combination with SM i.e. Alamouti is optimized for each SM barnch separately, what we need is a spatial code optimum for both the SM branches together), it should be possible to further increase the spectral efficiency. system. Our scheme is compared via simulations with OSFBC and VBLAST based SM techniques. It can be interesting to study this hybrid MIMO schemes for multi-user scenario. Future wors that will extend the present single-user lin-level analysis to a multi-user system, will provide more insights about the achievable advantages of the proposed hybrid scheme when multiuser diversity is present in the system. REFERENCES A.J. Paulraj, R. Nabar & D. Gore, Introduction to Space-Time Wireless Communications, st ed. Cambridge University Press, September 3. M. I. Rahman et al., Multi-antenna Techniques in Multi-user OFDM Systems, Aalborg University, Denmar, JADE project Deliverable, D3., September 4. 3 S. M. Alamouti, A Simple Transmit Diversity Technique for Wireless Communications, IEEE JSAC, vol. 6, no. 8, October K.F. Lee, & D.B. Williams, A Space-time Coded Transmitter Diversity Technique for Frequency Selective Fading Channels, in IEEE Sensor Array and Multichannel Signal Processing Worshop, Cambridge, USA, March, pp , A Space-Frequency Transmitter Diversity Technique for OFDM Systems, in IEEE GLOBECOM, vol. 3, November-December, pp P.W. Wolniansy et al., V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel, in Proc. IEEE-URSI International Symposium on Signals, Systems and Electronics, Pisa, Italy, May Y. Li et al., MIMO-OFDM for Wireless Communications: Signal Detection with Enhanced Channel Estimation, IEEE Trans. Comm., vol. 5, no. 9, September. 8 X. Zhuang et al., Transmit Diversity and Spatial Multiplexing in Four- Transmit-Antenna OFDM, in Proc. of ICC, vol. 4, May 3, pp A. Stamoulis, Z. Liu & G.B. Giannais, Space-Time Bloc-Coded OFDMA With Linear Precoding for Multirate Services, IEEE Trans. on Signal Processing, vol. 5, no., pp. 9 9, January. APPENDIX I COMPANION MATRIX Let us define a matrix H as h h H = h h We can define another pair matrix H as h T H = h T h T h T 6) 7) The matrix pair H and H is an orthogonal pair. h ij, i, j, is a column vector of size m, thus H and H are matrices of sizes m and m respectively. IV. CONCLUSION A combination of OSFBC and SM in one transmission scheme for OFDM systems has been presented, such that both spatial diversity and multiplexing benefits are possible to achieve. It is found that SM-OSFBC-OFDM system is near to the optimum system capacity for any 4 MIMO-OFDM