Combining Orthogonal Space-Frequency Block Coding and Spatial Multiplexing in MIMO-OFDM System Muhammad Imadur Rahman, Nicola Marchetti, Suvra Sekhar Das, Frank H.P. Fitzek, Ramjee Prasad Center for TeleInFrastruktur (CTiF), Aalborg University, Denmark e-mail: imr|nm|ssd|ff|
[email protected]; ph: +45 9635 8688 Abstract— In the present work, we have combined Orthogonal Space-Frequency Block 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 × 2 MIMO-OFDM system.
I. I NTRODUCTION 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 [1]. 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 [2]. 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 remarkable 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 [1].
In a cellular wireless systems, the Space-Time Block Coded Orthogonal Frequency Division Multiplexing (STBCOFDM) [4] and Space-Frequency Block 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 known STC techniques. One such work 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 2 × 2 SM-OFDM system is now extended to 4 × 2 STC aided SM-OFDM system. In the receiver, the independent STCs are decoded first using prewhitening, followed by maximum likelihood detection. Again, this increases the receiver complexity quite a lot, though the system performance gets much better. In later work, Alamouti’s Space-Time Block 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 Block Code (SFBC) with SM and obtained a linear receiver similar to [8] in this work. 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 work aims to achieve contemporarily the multiplexing gain (via two SM branches) and the diversity gain (via SFBC codes), keeping 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
m11 m1
IFFT
SM branch will be mp,1 m(1) = p (2) mp,2 mp =
CP
SFBC IFFT
CP
2
m
m1
CP rem
FFT
CP rem
FFT
z1 Linear RX
SM m
1 2
IFFT
CP
IFFT
CP
z
z2
SFBC m2 m22
Fig. 1. Scheme
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 SMSFBC-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 T RANSMISSION S CHEME In this section, we will explain the transmission structure of the JDM scheme based on combining SM and Orthogonal Space-Frequency Block 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 Block 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 1 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 mk . The sequences of mk is demultiplexed into m1 , . . . , mP vectors. mp is transmitted via pth spatial channel. For every pth SM branch, we implement a block coding across the sub-carriers, thus SFBC is included in the system. For pth 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 ∆ = 2, we can use well-known Alamouti coding [3] across the sub-carriers. (δ) For pth SM branch, mp is coded into two vectors, mp ; δ = 1, 2. Thus, the output of the SFBC encoder block of the pth
−m∗p,2 m∗p,1
Following this, we define mp,1 mp,3 mp,o = mp,2 mp,4 mp,e =
... ...
mp,N −1 mp,N
−m∗p,N
mp,N −1 mp,N
m∗p,N −1
. . . mp,N −3 . . . mp,N −2
(1) (2)
(3) (4)
(1)
Using these equations, we can write that mp,o = mp,o , (1) (2) (2) mp,e = −m∗p,e , mp,o = mp,e , mp,e = m∗p,o . After SM and SFBC operations, IFFT modulation is performed and Cyclic Prefix (CP) is added before transmission via respective transmit antenna. Transmitted time domain samples, (δ) (δ) (δ) (δ) xp , can be related to mp as, xp = FH {mp }. 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-OSTBCOFDM system in [8]. In this work, we adopt a similar receiver structure for our Spatially-Multiplexed Orthogonal Space-Frequency Block Coded Orthogonal Frequency Division Multiplexing (SM-OSFBC-OFDM) system. We consider P = 2, ∆ = 2 and Q = 2. 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: zk = Hk mk + nk
(5)
where k ∈ [1, . . . , N2 ], Hk is defined as (1) (2) (1) (2) h11,o h11,o h12,o h12,o (2) (1) (2) h(1) 21,o h21,o h22,o h22,o Hk = (2)∗ (1)∗ (2)∗ h11,e −h11,e h12,e −h(1)∗ 12,e (2)∗ (1)∗ (2)∗ (1)∗ h21,e −h21,e h22,e −h22,e
(6)
k
∗ ∗ T and zk = [z1,o z1,e z2,o z2,e ]k , mk = T ∗ ∗ T [m1,o m1,e m2,o m2,e ]k , nk = [n1,o n2,o n1,e n2,e ]k . We denote coherence bandwidth and sub-carrier spacing as Bc and ∆f respectively. We define severely frequencyselective scenario when coherence bandwidth is smaller than a pair of sub-carrier bandwidth, i.e. ∆f < Bc < 2∆f . In this case, we use a tool called ’Companion Matrix’ explained in Appendix I. We can represent (5) as z = Hi | Hj m + n (7)
with " Hi =
(1)
h1,o (2)∗ h1,e
(2)
h1,o (1)∗ −h1,e
#
" & Hj =
(1)
h2,o (2)∗ h2,e
(2)
h2,o (1)∗ −h2,e
#
ei We denote the companion matrices of Hi and Hj as H e j respectively. We define a new matrix H e = [H ei H e j ]T and H with " " # # (1)H (2)T (1)H (2)T h1,e h1,o h2,e h2,o e e Hi = & Hj = (2)H (1)T (2)H (1)T h1,e −h1,o h2,e −h2,o Now, at the beginning of the receiver, we can filter the received signal z like following: " # e H i e = e Hi | Hj m + Hn z0 = Hz (8) ej H Now, (8) can be written as 0 α1 I G12 0 e z = m + Hn (9) 0 G21 α2 I 0 0 (1)H (1) (2)T (2)∗ where α1 = h1,e h1,o + h1,o h1,e , α2 = (1)H (1) (2)T (2)∗ h2,e h2,o + h2,o h2,e and G12 , −G21 , shown in Eq. (10) form an orthogonal pair as defined in Appendix I. Now we define an LS receiver W as 0 1 α2 I −G12 (11) W= 0 0 γ −G21 α1 I
TABLE I OFDM S IMULATION PARAMETERS Parameters System bandwidth, B Carrier frequency, fc User mobility,v OFDM sub-carriers, N Subcarrier spacing, ∆f = B/N CP length, NCP Total samples in OFDM Symbol with CP, Ns = N + NCP Symbol duration, Ts = Tu + TCP OFDM symbols/frame, Nf Frame duration, Tf = Nf Ts Data Symbol mapping Channel coding scheme
Indoor
Indoor 20MHz 5.4 GHz 3 kmph 200 kmph 64 256 312.5 kHz 78.13 kHz 16 100 80 356 4.0 µs
17.8 µs 16
64.0 µs
284.8 µs QPSK 1 -rate convolutional coding 2
B. Theoretical Capacity Analysis
The theoretical outage capacity of SFBC-OFDM, STBCOFDM, 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 0 0 0 where γ = α1 α2 −[G12 (1, 1)G12 (2, 2) − G12 (1, 2)G12 (2, 1)]. following equation: Thus, the estimated symbol vector can be written as N −1 h i ρ 1 X e b = Wz0 = m + WHn m (12) log2 det IQ + Hk H∗k (14) C= N P k=0 In relation to severely frequency-selective scenario, we define moderately frequency-selective scenario when Bc > 2∆f , where ρ is the transmit SNR and Hk is the equivalent effective th and in that case we can easily say that neighboring sub-carriers CTF of k sub-carrier. Equivalent CTF means the CTF at the particular sub-carrier at the receiver, as shown in (5). have identical channel frequency response. The MMSE receiver can be implemented in the same simple The above instantaneous capacity is derived for each channel way. Defining the new constants then we can rewrite (12) as realization and then the Cumulative Distribution Function (CDF) of the instantaneous channel capacity is plotted in 0 1 β2 I −G12 b = 0 (13) Figure 2 for outdoor scenario. For a large number of random m 0 δ −G21 β1 I channels, the outage and mean capacity can be determined where β1 = α1 + σn , β2 = α2 + σn , with σn noise from these figures. In our case, we have simulated 5,000 0 0 0 variance on one receive antenna, and δ = β1 β2 − random channels and obtained the CDFs. We have compared the system capacity of diversity only [G12 (1, 1)G12 (2, 2) − G12 (1, 2)G12 (2, 1)]. schemes, multiplexing only schemes and hybrid diversityIII. A NALYSIS , S IMULATIONS AND D ISCUSSIONS multiplexing schemes. For diversity only schemes, 2×1 SFBC A. System Parameters and STBC are presented. For multiplexing schemes, 2 × 2 and We have used two simulation scenarios as explained in 4 × 2 multiplexing schemes are used. Obviously our scheme Figure I. For all our analysis and simulations, we have becomes 4 × 2 hybrid scheme. confined ourselves to the case of dual transmit and receive We define ’10% outage capacity’ as the system capacity antenna MIMO system with 2 antennas per spatial multiplex- in bits/second/Hz (bps/Hz) above which the system capacity ing branches (i.e. Q = 2, P = 2 and ∆ = 2). We assume remains at least 90% of the connection time. According to that perfect time and frequency synchronization is established. Figure 2, diversity only schemes (i.e. STBC and SFBC) have We also assume that perfect channel estimation values for similar outage capacity characteristics, approximately at 1.6 each sub-carrier for both the spatial channels are available bps/Hz. In contrast to this, 2 × 2 spatial multiplexing only at the receiver. We use exponential channel model to generate scheme has 10% outage capacity of 4.2 bps/Hz, compared to corresponding Channel Impulse Response (CIR) and Channel our 4 × 2 hybrid schemes at 6.2 bps/Hz. The maximum outage Transfer Function (CTF) of the channel. In our exponential capacity of any 4 × 2 ’open loop’ MIMO schemes can be 6.9 model, power delay profile of the channel is exponentially bps/Hz. The last outage capacity value is an upper bound for distributed with decay between the first and last impulse as any 4 × 2 ’open loop’ MIMO scheme. This is achievable with best available source, channel and S-F coding. In our case, -40dB.
" G12 =
(1)H
(1)
(2)T
(2)∗
h1,e h2,o + h1,o h2,e (2)H (1) (1)T (2)∗ h1,e h2,o − h1,o h2,e
(1)H
(2)
(2)T
(1)∗
h1,e h2,o − h1,o h2,e (2)H (2) (1)T (1)∗ h1,e h2,o + h1,o h2,e
"
# ; G21 = k
(1)
(2)T
(1)H
(2)
(2)T
(1)∗
h2,e h1,o − h2,o h1,e (2)H (2) (1)T (1)∗ h2,e h1,o + h2,o h1,e (10)
0
10
ZF−BLAST MMSE−BLAST ML SM−OSFBC, ZF−Lin SM−OSFBC, MMSE−Lin
−1
FEP
10
−2
10
2
CDF of the correponding capacity of at 10 dB SNR
4
6
8
1
10 12 SNR, dB
14
16
18
20
Fig. 4. FER performance of diversity only and hybrid schemes in outdoor scenario
0.9
0.8
4x2 SM−SFBC−OFDM
2x1 SFBC−OFDM 1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0 0.9065 0.907 0.9075 0.908 0.9085 0.909 b/s/Hz
0 1.8208
0.7
0.6
0.5
Probability that quantity < abscissa
Probability that quantity < abscissa
(2)∗
Modulation:QPSK, Coded FER, Outdoor
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. In terms of mean capacity, we see that the schemes obtain 1.9374, 1.7482, 8.1031, 7.5242 and 5.5859 bps/Hz respectively. These values are obtained by finding the mean value of simulation data that are used in Figure 2. Thus the hybrid scheme gains 1.9383 bps/Hz of mean capacity compared to 2 × 2 spatial multiplexing only schemes. This is achieved by introducing 2 more antennas and by incorporating SFBC across each spatial multiplexing branch.
(1)H
h2,e h1,o + h2,o h1,e (2)H (1) (1)T (2)∗ h2,e h1,o − h2,o h1,e
0.4
0.3 2x1 Alamouti−SFBC 2x1 Alamouti−STBC 4x2 SM−OFDM 4x2 SM−SFBC−OFDM 2x2 SM−OFDM
0.2
0.1
0
0
2
4
6 8 Capacity in bps/Hz
10
12
14
Fig. 2. CDF of theoretical capacity of corresponding MIMO-OFDM systems Modulation:QPSK, Coded FER, Indoor 0
10
ZF−BLAST MMSE−BLAST ML OSFBC SM−OSFBC, ZF−Lin SM−OSFBC, MMSE−Lin
1.821
1.8212 b/s/Hz
1.8214
1.8216
Fig. 5. CDF of spectral efficiency of corresponding MIMO-OFDM systems
C. FER Analysis −1
FEP
10
−2
10
0
2
4
6
8
10 SNR, dB
12
14
16
18
20
Fig. 3. FER performance of diversity only and hybrid schemes in indoor scenario
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 ∗ Lf ∗ M ∗ P ∗ Rc = 64 ∗ 16 ∗ 2 ∗ 2 ∗ 0.5 = 2048 source bits, while in outdoor scenario, it is 256∗16∗2∗2∗0.5 = 8192 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 2 × 2 SM scheme is plotted along with the other schemes. For various transmit antenna configurations, the total transmit power was kept constant, thus, the SNR at the x-axis reflects total SNR of the systems. We note that 2 × 2 Spa-
# k
tial Multiplexed Orthogonal Frequency Division Multiplexing (SM-OFDM) performs worse in terms of FER compared to 2 × 1 SFBC-OFDM system. In SM-OFDM system, we get a higher rate, but we lose in diversity. Considering this, we can see that 4 × 2 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 2dB, compared to MMSE-BLAST at an FER of 10−3 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 2 as 4 × 2 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 1000 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, Nb (1 − F ER)/Tf Br = (15) B B where Es is the spectral efficiency, Br is the data rate, Nb 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 10% outage capacity is seen to be 0.9 bps/Hz and 1.8 bps/Hz respectively. It has to be noted that the theoretical capacity (as shown in Figure 2) 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 (1.8212 bps/Hz against 8.1031 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. Es =
IV. C ONCLUSION 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 × 2 MIMO-OFDM
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 works that will extend the present single-user link-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. R EFERENCES [1] A.J. Paulraj, R. Nabar & D. Gore, Introduction to Space-Time Wireless Communications, 1st ed. Cambridge University Press, September 2003. [2] M. I. Rahman et al., “Multi-antenna Techniques in Multi-user OFDM Systems,” Aalborg University, Denmark, JADE project Deliverable, D3.2[1], September 2004. [3] S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications,” IEEE JSAC, vol. 16, no. 8, October 1998. [4] 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 Workshop, Cambridge, USA, March 2000, pp. 149–152. [5] ——, “A Space-Frequency Transmitter Diversity Technique for OFDM Systems,” in IEEE GLOBECOM, vol. 3, November-December 2000, pp. 1473–1477. [6] P.W. Wolniansky 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 1998. [7] Y. Li et al., “MIMO-OFDM for Wireless Communications: Signal Detection with Enhanced Channel Estimation,” IEEE Trans. Comm., vol. 50, no. 9, September 2002. [8] X. Zhuang et al., “Transmit Diversity and Spatial Multiplexing in FourTransmit-Antenna OFDM,” in Proc. of ICC, vol. 4, May 2003, pp. 2316 – 2320. [9] A. Stamoulis, Z. Liu & G.B. Giannakis, “Space-Time Block-Coded OFDMA With Linear Precoding for Multirate Services,” IEEE Trans. on Signal Processing, vol. 50, no. 1, pp. 19–129, January 2002.
A PPENDIX I C OMPANION M ATRIX Let us define a matrix H as h11 h12 H= h21 h22 e as We can define another pair matrix H −hT22 hT12 e H= hT21 −hT11
(16)
(17)
e is an orthogonal pair. hij , ∀i, j, The matrix pair H and H e are matrices is a column vector of size m × 1, thus H and H of sizes 2m × 2 and 2 × 2m respectively.
