Performance of Spatial-Modulation and Spatial ... - IEEE Xplore

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

Performance of Spatial-Modulation and SpatialMultiplexing Systems over Weibull Fading Channel Goutham Simha G.D. Shriharsha Koila, Neha N, U. Sripati Department of Electronics and Communication National Institute of Technology Karnataka (NITK), Surathkal Mangalore, India [email protected], [email protected]

spacing between constellation points which can degrade BER performance. Diversity techniques such as antenna or frequency diversity resolve the issue pertaining to poor channel reliability. Systems with multiple transmit and receive antennas are termed as MIMO systems. Spatial Multiplexing (SMX) [1] and Spatial Modulation (SM) [2], [3] are MIMO techniques that use antenna diversity for communication in an ingenious fashion. One of the impeccable advantages of MIMO SMX is the ability to provide enhanced spectral efficiency/ high data rates when compared to classical SISO systems. MIMO SMX has the potential to achieve higher data rates by utilizing multiple propagation paths and using them as an additional data pipes to carry information. A technique, referred to as Spatial Modulation (SM), discovered by Mesleh et.al in 2008 has the advantage of offering both spectral efficiency as well as energy efficiency [2]. This technique is designed to keep only one antenna active during each symbol interval. In this technique active antenna index is used as an additional dimension to convey information [2], [3]. This method simplifies the complexity of the overall system by reducing the number of transmit RF chains. This technique offers the additional benefit of nullifying Inter Channel Interference. Keeping these benefits of SM in mind, several researchers have conducted research work with the goal of improving SM so that it could serve as a viable alternative to SMX. These techniques emphasize the efficient use of spectrum as well as energy. Consequently various forms of SM that have been proposed in literature include Improved Spatial Modulation (ISM) or Extended Spatial Modulation (EXSM) [4], Enhanced Spatial Modulation (ESM) [5], Quadrature Spatial Modulation (QSM) [6]. These techniques have opened up new avenues in the field of MIMO communications and have reduced the complexity of receiver design to a great extent. A number of researchers have explored performance issues pertaining to the variants of SM in Rayleigh fading

Abstract—In this paper we have analyzed, quantified and compared the performance of variants of spatial modulation (SM) and spatial multiplexing (SMX) techniques over the GSM/3G frequency band. SMX systems use all the available transmit antennas for multiplexing the data symbols and hence achieve greater spectral efficiency. An SM system uses only one antenna at any given instant and achieves a reduction in the average energy consumption due to single RF chain activation. Some variants of (Spatial modulation (SM) namely Extended Spatial Modulation(EXSM), Enhanced Spatial Modulation (ESM) and Quadrature Spatial Modulation (QSM) use one or more antennas to provide a trade-off between spectral efficiency and energy efficiency. In battery operated devices, apart from increase in the spectral efficiency, energy efficiency also becomes a critical parameter of concern. This paper shows that EXSM provides superior BER performance in comparison to SMX systems. Thus, these schemes can be advantageously deployed in portable devices used in Mobile Wireless Communication Systems. In [9] it has been demonstrated that the Weibull distribution is a good fit to describe the multipath fading phenomenon in the GSM/3G band. In this paper, we have evaluated the performance of 2×2 and 2×4 SM, EXSM, ESM, SMX and QSM. We have also evaluated the performance of 3×3 SMX and EXSM systems. Our results indicate that a variant of SM specifically EXSM outperforms SMX systems by ~𝟒. 𝟕𝒅𝑩 in 2×2, 2×4 systems and ~𝟕𝒅𝑩 for 3×3 systems in a deep fading environment (Weibull with shape parameter=0.5). Keywords—Multiple Input Multiple Output (MIMO), Single Input Single Output (SISO) Inter Channel Interference (ICI).

I. INTRODUCTION The persistent need for increasing high data rates in wireless communications has been driven by the need to support a wide range of multimedia applications on mobile platforms. The most effective approach to address the need of higher spectral efficiency is the use of higher modulation schemes. However, higher order modulation schemes have the disadvantage of closer

978-1-4673-7309-8/15/$31.00 ©2015 IEEE

389

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

Fig 1: System Model for SMX

environment. In [7] authors have conducted performance analysis of SM and its variants in channels perturbed by Rician and Nakagami fading. The main contribution of this paper is the evaluation of the performance of SMX, SM and their variants in Weibull fading environment. Practical suburban and urban measurements made in GSM (EGSM) [8] and 3G band. Authors in [8] have demonstrated that the statistical distribution embedded in the observed data is well represented by the Weibull distribution. In [8], the authors have stated that the Weibull distribution is a good fit to represent multipath fading in an outdoor propagation environment. In addition, they have asserted that the Rayleigh distribution is unable to adequately represent multipath fading in urban and suburban environments [8] [9]. After an intense search, it was discovered that the Weibull distribution can be employed to model signal propagation in indoor environments [11]. Finally, the Weibull distribution has been judged to be appropriate for modeling digital enhanced cordless telecommunications for narrow-band (DECT) system at a reference frequency of 1.89 GHz [12].

The remaining part of the paper is organized as follows: System model is discussed in section II and the performance analysis of SMX system and SM along with its variants is discussed in Section III. Simulation results and comparison of relative performance of various schemes is discussed in Section IV. Finally Section V concludes the paper.

We have analyzed the performance of SMX, SM and its variants in moderate and deep (m=0.5, 5) Weibull fading environment. These modulation techniques have been evaluated with spectral efficiency and energy efficiency serving as performance metrics.

The received signal can then be written as

II. SYSTEM MODEL A. Spatial Multiplexing In SMX independent streams of information are transmitted through multiple transmit antennas. The spectral efficiency with 𝑁𝑡 transmit antennas is 𝑁𝑡 × log 2 𝑀 where 𝑀 is the constellation size. The transmitted symbol vector 𝑋 of length 𝑁𝑡 × 1 is represented as 𝑋 = [𝑥1 , 𝑥 2, , … … 𝑥𝑁𝑡 ]𝑇 . Here 𝑥𝑖 refers to the transmitted symbol from ith transmit antenna. The System model is represented in Fig1. 𝑁𝑟 denotes the number of receive antennas and 𝑯 represents the Weibull channel matrix with dimension 𝑁𝑟 𝑋 𝑁𝑡 . The elements of 𝑯 are denoted as ℎ𝑖𝑗 where 1 ≤ 𝑖 ≤ 𝑁𝑟 𝑎𝑛𝑑 1 ≤ 𝑗 ≤ 𝑁𝑡 and are according to the distribution stated in (3). 𝒚(𝑡) = √𝜌𝑯𝒙(𝑡) + 𝒏(𝑡)

(1)

where 𝒚 = [𝑦0 𝑦1 . . . . 𝑦𝑁𝑟 ]𝑇 denotes the received symbol vector of length 𝑁𝑟 × 1. 𝜌 denotes average signal to

Fig 2: System Model for SM

390

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

noise ratio (SNR) at each receive antenna. 𝒏 = [𝑛1 𝑛2 . . . 𝑛𝑁𝑟 ]𝑇 represents noise vector of length 𝑁𝑟 × 1. The entries of 𝒏 are sample values of independent and identically distributed (iid) complex Gaussian random variables with zero mean and unit variance (𝒞𝒩 (0, 1)).The transmitted symbols are decoded using the optimal maximum likelihood (ML) decoder.

𝑁𝑡 = 2 which provides a spectral efficiency of 2 bits per channel use (bpcu) has been described. The Spectral efficiency of EXSM system is given by η = 𝑁𝑡 + log 2 𝑀. We have extended this scheme in order to obtain a spectral efficiency of η=6bpcu. ii.

The principal idea behind ESM is to use multiple constellation symbols in order to increase the information transfer rate. A higher order modulation scheme is employed when single antenna is chosen and two lower order modulation schemes (with a significant phaseoffset between the two employed symbols) are used while transmitting from more than one antenna thereby increasing the spectral efficiency as compared to classical SM system. In [5], the authors have specified an ESM arrangement that uses QPSK and BPSK for systems with 𝑁𝑡 = 2,4. Spectral efficiency of ESM system is also represented by η = 𝑁𝑡 + log 2 𝑀. In addition the authors claim that the performance of ESM is superior to that of conventional SM over channels perturbed by Rayleigh fading. In our study, we have analyzed the performance of SMX and various variants of SM systems in an environment perturbed by Weibull fading. In order to obtain higher spectral efficiency, we have used 16QAM and QPSK. The number of transmit antennas is selected as 𝑁𝑡 = 2.

B. Spatial Modulation The generalized system model for spatial modulation is shown in figure 2.The SM transmitter with 𝑁𝑡 transmit antennas requires a single transmit RF chain. The Receiver consists of 𝑁𝑟 receive antennas. The transmitted and received symbol vectors are denoted as defined in the previous section for SMX. In SM systems, since a single transmit antenna is active at any given instant of time, the transmit vector X has only one nonzero element. The information sequence is divided into two streams namely, selection stream and transmission stream. Depending upon log 2 𝑁𝑡 bits from the selection stream, SM switching circuitry activates only one antenna and hence uses the active antenna index as one of the information dimensions. This approach gives the benefits of spectrally efficient transmission and avoidance of Inter Channel Interference (ICI). In SM systems, the number of bits per channel use is quantified as log 2 𝑁𝑡 + log 2 𝑀. Assuming availability of perfect Channel State Information (CSI) and antenna index, the transmitted symbol is decoded using Maximum Likelihood (ML) decoder.

iii.

Quadrature Spatial Modulation (QSM)

Exploiting an extra spatial dimension in an SM system enhances the overall throughput. This scheme that was proposed by Mesleh in [6] is referred to as Quadrature Spatial Modulation (QSM). Spatial dimension is subdivided into in-phase and quadrature components. Spectral efficiency of the channel is given by

C. Variants of SM A few variants of SM have been proposed. In these systems, the number of active antennas can vary from symbol interval to symbol interval. The number of active transmit antennas depends upon the information bearing bit stream. These techniques require the use of more than one RF chain at the transmitter side when multiple antennas are active. Hence compared to SMX schemes, variants of SM consume lesser energy because not all RF chains are active all the time. The system model for variants of SM is similar to SMX excluding the multiplexing block. The multiplexing block is replaced by spatial mapper block or multiple-antenna switching circuitry. The notations for transmitted and received vectors remain the same. We have described the variants of SM system in subsections i.

Enhanced Spatial Modulation (ESM)

η = 2 × log 2 𝑁𝑡 + log 2 𝑀

(2)

In [6], the authors have claimed that the QSM system requires 3 dB less signal power as compared to classical SM systems. With the use of RF circuits such as spatial de-multiplexers and phase discriminators, it is possible to have a single RF chain structure similar to that employed in conventional SM system. Due to lack of availability of these devices, we are forced to employ multiple RF chains in QSM systems.

Extended spatial modulation (EXSM).

III. CHANNEL MODEL

The primary idea of EXSM is to activate one or more antenna at the transmitter corresponding to the input data pattern [4]. EXSM scheme make use of all transmit antennas to convey information though not all antennas are active at each instant of time. The RF chains connected to inactive antennas can be switched off to enable improvement in efficiency of energy usage. EXSM does not require that the number of transmit antennas be a power of 2. In this sense, it has an advantage over classical SM. EXSM technique was first proposed in [4]. In this paper, a scheme corresponding to

The Weibull fading model is characterized by the PDF given by

𝑝(𝑎; 𝜆, 𝑚) =

𝑚 𝑎 𝑚−1 −(𝑎)𝑚 ( ) 𝑒 𝜆 𝜆 𝜆

(3)

Where m, 𝜆 denote the shape parameter and scale parameter respectively. For the simulations presented in this paper, the Weibull fading channel is realized using 1

𝑊 = 𝜆(− ln( 𝑈)𝑚 . In this equation, 𝑈 represents a uniformly distributed Random Variable with zero mean

391

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

of m=0.5 indicates the deep fade situation and m=5 indiactes non fading environment. Table. I indicates the modulation schemes which were employed to design the SMX, SM, EXSM, ESM and QSM schemes (both 2×2 and 3×3 antenna configurations) systems for η = 6bpcu. A spectral efficiency of 6 bpcu is achieved by employing the digital modulation schemes as shown in the table. These configurations are so selected that maximum Euclidean distance between the symbols is maintained. Table. II shows the active antenna combination for individual digital modulation schemes

and unit variance (𝑈(0, 1)). In Weibull fading, deep fading scenario is depicted by parameter 𝑚 taking on a value of 0.5 (m=0.5). The Weibull distribution can be related to other distributions such as the exponential and Rayleigh distributions. For values of m = 1, 2, the Weibull distribution reduces to the exponential distribution and Rayleigh distributions respectively [9]. The main aim of this paper is the performance analysis of SMX, SM and variants of SM under the Weibull fading model. IV. SIMULATION RESULTS AND PERFORMANCE ANALYSIS

Table I : Modulation schemes employed for SMX and SM

The performance analyses of variants of SM techniques have been evaluated. Monte Carlo simulations for 105 channel realizations (except for simulations shown in fig.3 where 104 channel realizations have been employed as the best BER are of the order of 10−3 ) have been performed and Average Bit Error Rate (ABER) versus SNR is plotted. This has been compared with the performance of conventional SMX systems. The channel fading has been described by the Weibull distribution Targeting high data rate applications in small scale handheld devices, we consider MIMO systems with 𝑁𝑡 = 𝑁𝑟 = 2,3. For the purpose of providing fair comparison all the systems compared offer a spectral efficiency of 6 bpcu. Table. I shows the modulation schemes used for SMX, SM and its variants for 2X2 and 3X3 systems. Maximum likelihood detection strategy is used for SMX and variants of SM. The ML estimates are provided by, 2 ‖𝑦 − 𝐻𝑆̂‖𝐹 𝑆̂𝑀𝐿 = 𝑎𝑟𝑔 min 𝑚 𝑠ɛ𝑠

MODULATION SYSTEM

=

− 2𝑅𝑒{𝒚† 𝒈𝑗𝑞 }

SMX

EXSM

ESM

QSM

2×2

32QA M

8PSK

16QAM

16QAM, QPSK0, QPSK1

16QAM

3×3

NA

BPSK

8PSK

NA

NA

Table II: Antenna Requirement SM

SMX

EXS M

ESM

QSM

Min

1

𝑁𝑡

1

1

1

Max

1

𝑁𝑡

𝑁𝑡

2

2

In Fig 3, we have illustrated the performance of EXSM, SM, SMX, ESM and QSM systems in deep Weibull fading environment characterized by m=0.5. We see that that the performance of EXSM is superior to all other schemes. Further, an inspection of the plot reveals that the performance of QSM, EXSM, and ESM is similar. These schemes offer a performance advantage of ~4.7𝑑𝐵 when compared to SMX at a BER of 10−2 . The performance in a non-fading environment (m=5) is examined in Fig 4. From Fig 4 for a 2×2 system it is shown as m=5. In this environment, SM and EXSM schemes perform well because of high channel gains. From the plot, it is seen that the performance of SM and EXSM is superior to the performance of SMX by ~1.7 dB. The performance of SM and EXSM is superior by about ~3 dB when compared to QSM and ESM at a BER of 10−4 .

(4)

Optimal ML detection strategy for conventional SM as described in Jegannathan et.al [10] has been adopted for SM demodulation. The ML estimates are described by, [𝑗̂𝑀𝐿 , 𝑞̂𝑀𝐿 ] = 𝑎𝑟𝑔𝑚𝑎𝑥 𝑝𝒀 (𝒚|𝑥𝑗𝑞 , 𝑯) 𝑗,𝑞 2 𝑎𝑟𝑔𝑚𝑖𝑛√𝜌‖𝒈𝑗𝑞 ‖𝐹 𝑗,𝑞

SM

(5)

where 𝒈𝑗𝑞 = 𝒉𝑗 𝑥q , 1 ≤ 𝑗 ≤ 𝑁𝑡 , 1 ≤ 𝑞 ≤ 𝑀, 𝑀 is the modulation order. 𝑗̂𝑀𝐿 , 𝑞̂𝑀𝐿 , gives information about the estimated active transmit antenna index and signal constellation symbol respectively [10]. The performance of the system is measured using Average Bit Error Ratio (ABER). ML decoder provides a significant enhancement in bit error rate (BER) performance over sub-optimal MRRC detection method [10].

SMX perform better compared to QSM and ESM because of higher channel gains. However, it must be noted that the non-fading environment described by m=5, represents a very ideal situation which is not realizable in practice. Mesleh [2] has shown that receive diversity plays an important role in an SM MIMO systems. He has also demonstrated that there is a significant performance gap of approximately 10 dB at

Performance analysis of 2×2, 2×4 and 3×3 systems A comparison of the performance of 2×2 2×4 and 3x3 systems in non fading and deep fading Weibull environments has been discussed in this section. A value

392

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

Fig.3. BER performance of SMX and variants of SM for a 2×2 system in quasi-static-Weibull flat fading environment with m=0.5

Fig.5. BER performance of SMX and variants of SM for a 2×4 system in quasi-static-Weibull flat fading environment with m=0.5

A similar analysis has been carried out for 2×4 system in a non- fading environment (m=5). From figure 6 it is seen that SMX schemes outperforms all the other techniques because of the highest net channel gain at the receiver. Again it must be noted that the probability of the channel getting into this state is highly improbable. A 3×3 antenna configurations can be supported only by EXSM and SMX schemes.

a BER of 10−5 between SM 2×2 and SM 2×4 systems [2]. This is because of the performance advantage brought about by the use of additional receive-diversity.

Fig.4. BER performance of SMX and variants of SM for a 2×2 system in quasi-static-Weibull flat fading environment with m=5 Fig.6. BER performance of SMX and variants of SM for a 2×4 system in quasi-static-Weibull flat fading environment with m=5

We have also examined the performance of a 2×4 system under conditions of deep fading (m=0.5). Comparing Figures 3 and 5, it is seen that 2×4 systems yield a performance gain of the order 10 dB over 2×2 systems under conditions of deep fade. Similarly, EXSM scheme offer a performance advantage of ~4.7dB at a 𝐵𝐸𝑅 𝑜𝑓 10−3 over SMX schemes.

393

2015 Intl. Conference on Computing and Network Communications (CoCoNet'15), Dec. 16-19, 2015, Trivandrum, India

V. CONCLUSIONS Several variants of spatial modulation techniques can be used in Mobile wireless communication systems as an alternative to standard SMX systems. Variants of SM systems offer an advantage in terms of spectral efficiency and energy consumption over comparable SMX schemes. In this paper, the wireless communication medium is modeled using the Weibull distribution because it provides a close fit to the channel perturbations observed in the GSM/3G band [8] [9]. From the results obtained, we conclude that SM or variants of spatial modulation techniques especially EXSM can be advantageously used in applications that require efficient use of spectral and energy (battery) resources such as mobiles, tablets etc. They are better suited to replace SMX systems under operating conditions well modelled by the Weibull distribution. Fig.7. BER performance of SMX and variants of SM for a 3×3 system in quasi-static-Weibull flat fading environment with m=0.5

References

In a deep fading environment (Figure 7), we see that EXSM systems perform better than SMX systems by about ~7 dB for 𝐵𝐸𝑅 𝑜𝑓 10−3 . This is a significant improvement for a 3×3 system.

[1]

Siavash M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, 16(8):1451{1458}, October 1998. [2] R. Y. Mesleh, H. Haas, S. Sinanovic, C. W. Ahn, and S. Yun, ‘‘Spatial modulation,’’ IEEE Trans. Veh. Technology, vol. 57, no. 4, pp. 2228–2241, Jul. 2008. [3] M. Di Renzo, H. Haas, A. Ghrayeb, S. Sugiura, and L. Hanzo, “Spatial-modulation for generalized MIMO: Challenges, opportunities, implementation,” Proc. IEEE, vol. 102, no. 1, pp. 56–103, Jan. 2014. [4] J.M. Luna-Rivera and M. G. Gonzalez-Perez, “An Improved Spatial Modulation Scheme for MIMO Channels, EuCAP 2012. [5] Chien-Chun Cheng, Hikmet Sari, Serdar Sezginert, and Yu T. Su, Enhanced Spatial Modulation with Multiple Constellations. IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom) 2014. [6] R. Mesleh et al, “Quadrature spatial modulation,” IEEE Trans. Veh. Technol., early access, 2014. [7] Abdelhamid Younis, Spatial Modulation: Theory to practice 2013. [8] Tzeremes, G. and Christodoulou, C. G. (2002). Use of Weibull distribution for describing outdoor multipath fading. Proceedings of the IEEE Antennas and Propagation Society International Symposium, San Antonio, Texas, Vol. 1, pp. 232–235. [9] Fading and InterferenceMitigation in WirelessCommunications Stefan R. Panić Mihajlo Stefanović,Jelena Anastasov,Petar Spalević 2011. [10] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial modulation: optimal detection and performance analysis,” IEEE Commun. Lett., vol. 12, no. 8, pp. 545-547, Aug. 2008. [11] Babich, F. and Lombardi, G. (2000). Statistical analysis and characterization of the indoor propagation channel. IEEE Transactions on Communications, 48( 3), 455–464.

In Figure 8 (non-fading environment, ( m=5), it can be seen that SMX systems perform better than EXSM systems by about ~1.4𝑑𝐵 at 𝐵𝐸𝑅 𝑜𝑓 10−4 . Again, it must be emphasized that this type of fading environment is not likely to be encountered often in wireless systems.

Fig.8. BER performance of SMX and variants of SM for a 3×3 system in quasi-static-Weibull flat fading environment with m=5

394