Spatial Modulation – OFDM

Spatial Modulation – OFDM R. Mesleh, H. Haas, C.W. Ahn and S. Yun

Abstract— In this paper, a novel multiple antennaOFDM transmission approach, called spatial modulation (SM)-OFDM is presented. SM entirely avoids inter-channel interference (ICI) at the receiver input, requires no synchronization between the transmitting antennas, and avoids correlation between them while maintaining high spectral efficiency. SM maps a block of information bits into a constellation point in the signal as well as the spatial domain. The spatial domain corresponds to a particular antenna location. Hence, for OFDM transmission, each subcarrier is mapped to one of the transmitting antennas. Only the corresponding antenna will be sending power on that subcarrier at an instant of time while all other antennas are transmitting zero power on this particular subcarrier. The receiver estimates the transmitted signal and the transmit antenna number and uses the two information to de-map the block of information bits. A comparison between SM-OFDM and V-BLAST-OFDM using optimum ordering (OR) and successive interference cancelation (SIC) in terms of system performance is presented in this paper. Index Terms— MIMO, OFDM, V-BLAST, Spatial Modulation, ZF, ICI.

I. I NTRODUCTION

T

HE need to improve the spectral efficiency and reliability of radio communication is driven by the ever increasing requirement for higher data rates and improved QoS (Quality of Service) across wireless links. Higher data rate and better spectral efficiency are of paramount importance in next generation cellular communication. OFDM is one of the most promising techniques for transmitting high speed data over wireless channels in future mobile communication systems. So far, OFDM is used in several wireless standards such as digital audio and video broadcasting (DAB) and (DVB-T), IEEE 802.11a [1], the IEEE 802.16a metropolitan area network (MAN), and the local area standard (LAN) [2]. R. Mesleh and H. Haas are with: International University Bremen, School of Engineering and Science, 28759 Bremen, Germany, {r.mesleh & h.haas}@iu-bremen.de. C.W. Ahn and S. Yun are with: C & N Lab., Samsung AIT, 11-4, Nongseo-ri, YoungIn-si, Kyeonggi-Do, KOREA, {cwan.ahn & sbyun}@samsung.com.

MIMO (multiple input multiple output) technology is another approach to attain high spectral efficiency by transmitting multiple data streams from multiple antennas [3]. Thus, a combination of MIMO and OFDM seems to be a very promising solution for fourth generation (4G) wireless communication systems. However, the capacity gain that results from MIMO transmission depends strongly on transmit and receive antenna spacing [4], [5], transmit antenna synchronization [6], and the used algorithm to reduce the interchannel interference (ICI) at the receiver input. Copious ICI reduction algorithms are reported in literature. The proposed Bell Labs Layered Space-Time Architecture (BLAST) [7] is one of the most promising MIMO detection algorithms. In its most basic form known as vertical (V)BLAST [8], multiple transmitted data streams are separated and detected successively using a combination of array processing (nulling) and interference cancelation techniques. It was demonstrated that with the V-BLAST algorithm spectral efficiencies of 20 − 40 bps/Hz can be achieved in an indoor rich scattering propagation environment assuming a practical SNR range, and bit-error performance respectively [8]. The high spectral efficiencies stem from parallel signal transmission resulting in a multiplexing gain. An alternative multiple antenna-OFDM transmission approach, called spatial modulation-OFDM (SM-OFDM), that entirely avoids ICI at the receiver input while maintaining high spectral efficiency is presented in this paper. Traditionally, modulation techniques such as BPSK (binary phase shift keying), QPSK (quadrature phase shift keying), 8PSK, 16-QAM (quadrature amplitude modulation), etc. map a fixed number of information bits into one symbol (b/s). Each symbol represents a constellation point in the complex, two dimensional signal plane. SM extends this two dimensional plane to a third dimension - the spatial dimension. SM maps multiple information bits into one information symbol and a corresponding antenna number. Thereby, the antenna array pattern can be interpreted as a spatial constellation diagram. The receiver estimates the symbol and the active antenna number and de-maps the original information bits. The number

of information bits that can be transmitted using spatial modulation depends on the used constellation diagram and the given number of transmit antennas. For instance, six information bits can be mapped into 32-QAM and two transmit antennas. Alternatively, if the channel and interference environment do not allow the use of 32-QAM, the same spectral efficiency can be achieved with 16-QAM and four transmit antennas, etc.. In view of the fact that information is not only included in the transmitted symbol, but also in the actual physical location of the antenna, a combination with OFDM transmission is not straightforward. The proposed solution is as follows: The output block of symbols from the spatial modulation is grouped into Nt vectors, where Nt is the number of transmit antennas. Each vector corresponds to one of the transmitting antennas. For instance, all the subcarriers that should be transmitted from the first antenna are included in the first vector and all other subcarriers are set to zero. This is done by grouping the mapped symbols at the output of the spatial modulator in vectors corresponding to their assigned transmit antenna number and setting all other symbols in that vector to zero. The OFDM modulator is applied to each vector; thus, resulting in Nt OFDM blocks to be transmitted simultaneously from the Nt transmit antennas. However, at each instant of time and for each subcarrier only one transmit antenna will be active and all other transmit antennas are off. As a result, ICI is completely avoided at the receiver input. In addition to eliminating ICI at the receiver, SM produces no mutual coupling between the transmit antennas and it requires no synchronization between them. Furthermore, in SM, the symbol duration is unchanged even though the transmitted symbol carries different number of information bits due to the described working mechanism. As a consequence, the bandwidth occupied is unchanged which effectively results in the desired increase in spectral efficiency. The rest of the paper is organized as follows: In Section II, the SM-OFDM system model is presented. Simulation results are shown in Section III. Finally, conclusions are provided in Section IV.

pose, of a matrix or a vector respectively, and (·)−1 denotes the inverse of a matrix. hν, κ is the channel vector between transmit antenna κ and receive antenna ν . The number of receive antennas is denoted as, Nr . Finally, for M -QAM modulation, m = log2 (M ) is the number of bits/symbol and Q(·) is the constellation quantization (slicing) function. The SM-OFDM system model is shown in Fig. 1. Q(k) is an n × m binary matrix to be transmitted; where n is the number of OFDM subcarriers. This matrix is mapped into another matrix X(k) of size Nt × n. The mapping procedure is the basic concept of the SM technique. First, the Q(k) matrix is mapped into another vector containing n M -QAM symbols. Each symbol in the resulting vector corresponds to a single transmit antenna, ` ∈ [1 : Nt ]. For example, as seen in Fig. 2, an initial three-bit input sequence of 0 1 0 is mapped to ant11−i , where ant11−i means that the QPSK-symbol 1 − i is transmitted from the first transmit antenna. The second antenna transmits zero power on that respective sub-carrier. Similarly, the second three-bit block of 1 1 1 is mapped to ant2−1−i , and so forth. Thus, rearranging the resultant symbol vectors results in the X(k) matrix, where each row xν (k) contains the symbols to be transmitted from transmit antenna ν . All the other symbols that do not belong to this antenna are set to zero as seen in Fig. 2. Afterwards, each row vector xν (k) is modulated using an OFDM modulator.

II. S YSTEM M ODEL Throughout the paper, the following notations and assumptions are used. Bold and small letters 0 a0 denote vectors. Bold and capital letters 0 A0 denote matrices. The notations, (·)∗ , (·)+ , (·)H , and (·)T denote conjugate, pseudoinverse, Hermitian, and trans-

At the OFDM modulator output, sν (t) vector is created. Each sν (t) vector contains a unique and disjoint set of OFDM sub-carriers. The resultant vectors are transmitted simultaneously from the Nt transmit antennas over the MIMO channel, H(t). The channel matrix is a block matrix and can be

Data belong to 1st. antenna

0 1 0

x1(k)

1 1 1 Q (k ) 1 1 0 0 0 0

Input bits

1 1 1

Mapping

a n t1

0 0

0 0

1+i 0 o a n t 1- 1 + i o 1

0 0

1 1

+ 1 -i 0 o a n t 1- 1 - i o 1

1 1 1 1

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1+i 0 o a n t -21 + i 1 o a n t 2+ 1 - i 0 o a n t -21 - i 1 o

Fig. 2.

>1-i

0

0 1i

0@

OFDM Modulator

-1-i@

OFDM Modulator

Spatial Modulation

a n t1

x2 (k)

>0

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0

Data belong to 2nd. antenna

Tx antennas

ant1 ant 2

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Symbol: 4-QAM

ant1

ant2

ant2 Spatial Modulation Mapping table

Spatial Modulation-OFDM Transmission Approach

Data belong to st 1 . antenna

OFDM Modulator

Spatial Modulation

q (k)

OFDM Modulator

X (k)

s1 (t)

OFDM Demodulation

s2 (t)

OFDM Demodulation



 OFDM Modulator

s N t (t)

 

1

1

IFFT

xi (k)

Fig. 1.

Par





n

n+g

Periodic exte nsion

ZF Detection

Spatial demodulation

 (k) X "

Y (k)



h1 Nt (t) º h2 Nt (t) » » » » hNrNt (t) ¼

OFDM Demodulator Ser

 (k) "

qˆ(k)

Nr

h12 (t) ª h11 (t) « h (t) h22 (t) H (t)= « 21 «  « ¬ hNr1 (t) hNr 2 (t)

Data belong to N t . antenna

Estimated transmit antenna number

Y (t)

OFDM Demodulation

Estimated transmitted symbol

OFDM Demodulator Par

Ser

1

Ser

si (t)

y (t)

Par

Par

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FFT





n+g

n

One Period Ser

 " (k) x

Spatial Modulation-OFDM System Model

viewed as a collection of Nr × Nt vectors of length p, where p is the number of channel paths for each channel link between each transmit and receive antenna. The received matrix Y(t) = H(t) ⊗ S(t) + R(t), where R(t) is the additive white Gaussian noise matrix and ⊗ denotes time convolution. A. Multipath Channel Model H(t) is a block matrix containing a set of Nr ×Nt vectors each of length p. Each vector corresponds to the multipath channel gains between each transmit and receive antenna as follows:   h11 (t) h12 (t) · · · h1Nt (t)  h21 (t) h22 (t) · · · h2N (t)  t   H(t) =   .. .. .. . .   . . . . hNr 1 (t) hNr 2 (t) · · · hNr Nt (t) (1) hκ ν is a size p × 1 channel vector between receive antenna κ and transmit antenna ν containing all the multipath channel gains and can be written as follows: hκ ν (t) = [h1κ ν (t) h2κ ν (t) · · · hpκ ν (t)]T

(2)

In this paper, the multipath channels between different links are statistically independent and modeled by the Monte Carlo method (MCM) [9]. An indoor multipath channel with maximum propagation delay of 0.45µs is considered. Then, each channel path gain is given by: N X

1 hϕ ej(2πfϕ,q t+θϕ,q ) δ (τ − τϕ ) κ ν (τϕ , t) = √ ρ[ϕ] N q=1 (3)

where fϕ,q = fd sin (2πuϕ,q ), θϕ,q , and N are called the discrete Doppler frequencies, the Doppler phases, and the number of harmonic functions respectively. The propagation delay related to the ϕth channel path is τϕ . The qualities uϕ,q are independent random variables, each with a uniform distribution in the range (0, 1] for all ϕ = 1, 2, · · · , p and generated independently for each link. The maximum Doppler frequency of the frequency selective multipath channel is given by fd . Finally, the coefficients of the discrete multipath profile are modeled by ρ[ϕ]1 [10]. B. OFDM detection and spatial demodulation A conventional OFDM zero-forcing (ZF) detection is considered. The ZF detection can be viewed as an element-wise division of the OFDM demodulated signal by the transfer function of the discrete time channel, which is computed by a DFT of the zero-padded discrete time channel impulse response. However, for SM another source of information needs to be estimated at the receiver, namely, the spatial location (the transmit antenna number) from which the symbol was transmitted. This is done by finding the location of the maximum of the absolute value of the output vector from the ZF equalizer for each subcarrier as follows: `˜% = arg max |y% | % : 1, 2, · · · , n.

(4)

where y% is the output vector from the ZF equalizer for the subcarrier %. Then, the symbol detection is 1 The channel profile used in this paper is ρ [1, 0.849, 0.766, 0.788, 0.666, 0.564, 0.517, 0.054, 0.046].

=

(5)

1) Example: SM-OFDM transmission and detection: The following example considers the transmission of three bits/sub-carrier using SM-OFDM transmission approach and a 2x4 MIMO configuration. Hence, a 4-QAM constellation diagram is to be used to achieve the required bit rate. The following bits sequence is to be transmitted using four OFDM sub-carriers,   0 1 1  1 1 1   Q(k) =   1 0 0  0 1 0 Using the mapping table in Fig. 2, the Q(k) matrix is mapped into another matrix µ ¶ −1 − i 0 0 1−i X(k) = 0 −1 − i 1 + i 0 Each row in X(k) contains all the symbols to be transmitted from the corresponding transmit antenna. The OFDM modulator is applied to each row and the resulting vectors are transmitted simultaneously from the transmit antennas. A free noise transmission is assumed in this example and the receiver has full channel knowledge. The received vectors on each receive antenna are demodulated using an OFDM demodulator followed by a ZF equalizer. As a result, the output matrix Y(k) is the same as X(k). Applying eqn. (4) results in the following vector containing the estimated transmit for each ¡ antenna number ¢ OFDM sub-carrier, 1, 2, 2, 1 . Using these values, the transmitted symbol on each sub-carrier ¡is estimated as given in eqn. (5) ¢and results in, −1 − i, −1 − i, 1 + i, 1 − i . The two estimated vectors are jointly used in combination with the mapping table in Fig. 2 to retrieve the transmitted information bits. The V-BLAST detection for OFDM is the same as the V-BLAST detection used for flat Rayleigh fading channels and can be applied on each subcarrier [11].

receiver is assumed to have full channel knowledge and perfect time and frequency synchronization is considered. The receive antennas are assumed to be separated wide enough to avoid correlation. The total signal power on each transmitted subcarrier is 1 W. For V-BLAST transmission, the transmit antennas are assumed to be synchronized and separated wide enough to avoid correlation. The bandwidth of the system is BW = 20 MHz and the sampling interval is ta = 1/BW = 50 ns. The channel delay spread is 0.45 µs and the guard interval is 0.5 µs. A. Three bits transmission A three bits/sub-carrier transmission can be obtained using different configurations, for SM, a 4x4 BPSK or a 2x4 4-QAM configuration transmits three bits per subcarrier. Alternatively, a 3x4 BPSK VBLAST configuration transmits the same number of information bits per subcarrier. These three configurations are simulated and the BER (bit-errorratios) are plotted in Fig. 3. SM 4x4 BPSK shows a degradation in performance as compared to SM 2x4 4-QAM. This is mainly due to the behavior of the ZF equalizer when Nt ≈ Nr . On the other hand, 3x4 BPSK V-BLAST demonstrates the worst performance and exhibits an error floor. Three bits transmission using spatial modulation and V−BLAST

0

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estimated using the following equation: ´ ³ x ˜%` = Q y[(j=`˜% ),%]

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SM−3bits 4x4 BPSK SM−3bits 2x4 4QAM V−BLAST 3x4 BPSK

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Fig. 3. Three bits transmission using spatial modulation and V-BLAST

B. Four bits transmission III. R ESULTS In the simulation, the channel model presented in II-A is considered with a maximum Doppler frequency of 30 Hz. A frame length of 20 OFDM symbols with each symbol having 256 OFDM subcarriers. The simulation is carried out with the presence of additive white Gaussian noise (AWGN). The

Four bits transmission can be obtained by using SM 4x4 4-QAM or SM 2x4 8-QAM and 2x4 4QAM V-BLAST. The BER simulation results are plotted in Fig. 4. 2x4 4-QAM V-BLAST outperforms SM 4x4 4-QAM, but it shows a degradation in performance when compared to SM 2x4 8-QAM. At 20 dB SNR the obtained gain is around 4 dB.

Four bits transmission using spatial modulation and V−BLAST

0

efficiency in bits/sub-carrier can be achieved. A notable BER performance gain over V-BLAST-OFDM has been demonstrated. More than 3dB SNR gain for six bits/sub-carrier transmission and a 4dB SNR gain for four bits/sub-carrier transmission are observed. It is expected that the obtained gain with respect to VBLAST will be more significant under more realistic channel conditions taking into considerations spatial correlation and mutual antenna coupling. This will be subject to future studies.

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SM−4bits 4x4 4QAM SM−4bits 2x4 8QAM V−BLAST 2x4 4QAM

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Fig. 4.

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Four bits transmission using SM and V-BLAST

ACKNOWLEDGEMENT The authors would like to thank Samsung, and in particular the Samsung Advanced Institute of Technology (SAIT) in Korea for supporting this work.

C. Six bits transmission Fig. 5 shows the BER performance of SM 4x4 16-QAM transmission and SM 2x4 32-QAM transmission compared to 2x4 8-QAM and 3x4 4-QAM V-BLAST transmission. Six bits transmission using spatial modulation and V−BLAST

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SM−6bits 4x4 16QAM SM−6bits 2x4 32QAM V−BLAST 2x4 8QAM V−BLAST 3x4 4QAM

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Fig. 5.

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Six bits transmission using SM and V-BLAST

Again, SM 2x4 32-QAM outperforms all other scenarios and the 3x4 4-QAM V-BLAST system results in an error floor. IV. C ONCLUSION In this paper, a novel spectral efficient multiple antenna transmission scheme that utilizes spatial information in an innovative fashion in combination with OFDM transmission has been presented. SM considers the antenna pattern as a “spatial constellation” diagram and uses this novel concept to increase the spectral efficiency. It has been shown that the conventional signal modulation can be traded-off against “spatial modulation” such that a constant spectral

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