BER PERFORMANCE OF GOLDEN CODED MIMO-OFDM SYSTEM OVER RAYLEIGH AND RICIAN FADING CHANNELS A Vamsi Krishna G Dhruva Department of ECE, LNMIIT Department of ECE, LNMIIT Jaipur-303012, India Jaipur-303012, India [email protected] [email protected] V Sai Krishna V Sinha Department of ECE, LNMIIT Fellow IEEE, Department of ECE, LNMIIT Jaipur-303012, India Jaipur-303012, India [email protected] [email protected] Abstract— In this paper, we analyze the Bit Error Rate (BER) Interference (ICI) and ensures efficient utilization of performance of Golden coded Multiple-Input Multiple-Output bandwidth. The MIMO-OFDM has a great potential to meet Orthogonal Frequency Division Multiplexing (MIMO-OFDM) up the stringent requirement for boosting up the transmit system over Rician multipath fading channel. We also compare diversity and mitigation of the detrimental effects due to the performance of the MIMO-OFDM system using Golden code frequency selective fading [5]. in Rayleigh and Rician multipath fading channels. We discuss the effects of the presence of line-of-sight (LoS) component in the Designing Space-Time Block Codes (STBC) for frequency multipath fading environment which renders the improvement in selective MIMO channels is well motivated by broadband the overall performance of the Golden coded MIMO-OFDM. applications, where multi-antenna systems have to deliver This paper discusses the performance of Golden codes in a multimedia information content at high data rates[6]. frequency selective Rician fading channel. To deal with the Furthermore, STBC are used to improve MIMO performances frequency selective fading channel, we use the OFDM by providing a temporal and spatial multiplexing modulation (Orthogonal Frequency Division Multiplexing) modulation. The [7], [8].The seminal code in this category is Alamouti space- BER performance of the Golden coded MIMO-OFDM system time block code which has been proposed in 1998 [9]. Many under several propagation conditions has been evaluated. other codes have been proposed in an attempt to achieve Keywords—MIMO, OFDM, Golden STBC, Rayleigh fading, maximum diversity in the channel at various transmission Rician fading. rates [10], [11]. The Golden STBC, which has been proposed in 2005 [12], is a full-rate, full-diversity perfect STBC that has I. ,20-"3!2'-, a maximum coding gain for 2X2 MIMO system. The Golden With the advent of next Generation (4G) broadband code has been studied in various MIMO-OFDM applications wireless communications, the combination of Multiple-Input [13]-[15]. Nevertheless, the performance of MIMO-OFDM Multiple-Output (MIMO) wireless technology with system using Golden STBC, in an environment where Orthogonal Frequency Division Multiplexing (OFDM) has multipath effect predominates, has not been thoroughly been recognized as one of the most promising techniques to studied. support high data rate and high performance [1]-[3].The In our work, we analyze the performance of MIMO- transmitted signal travels through several different paths OFDM system using the Golden STBC in Rayleigh and Rician toreach the receiver. The received signal includes multiple frequency selective fading channels. Further, we compare the versions of the transmitted waveform each of which is performance of Golden coded MIMO-OFDM system over attenuated by and delayed in time leading to the distortion of Rician frequency selective fading channels with different K the signal. The multipath effect causes the MIMO channels to factors, where K is the specular-to-diffuse ratio of the received be frequency selective for high data rate transmissions. signal. We show the expected significant improvement in the Orthogonal Frequency Division Multiplexing (OFDM) [4] has become a popular technique for transmission of signals over performance of the Golden Coded MIMO-OFDM system in wireless channels, which transforms frequency selective the presence of line-of-sight (LoS) component. fading channel into parallel flat fading channels. OFDM is a The rest of the paper is organized as follows. In the multicarrier modulation technique where the subcarriers are following section, we present the review of Golden STBC. In mutually orthogonal which in turn avoids Inter Carrier Section III, system model of Golden coded MIMO-OFDM is Proc. of the International Conference on Pervasive Computing and Communication (PCC) Editor In Chief Dr. R. K. Singh. Copyright © 2012 Universal Association of Computer and Electronics Engineers. All rights reserved. ISBN: 978-981-07-2579-2 doi:10.3850/978-981-07-2579-2 PCC-165 9 Proc. of the International Conference on Pervasive Computing and Communication (PCC) ͥ described in which we discuss transmitter, channel and where a,b,c and d are QAM modulated symbols and ͬ)ʚ͟ʛ, ͦ receiver models considered in this work. In section IV, we ͬ)ʚ͟ʛ are Golden modulated symbols sent to OFDM present simulation results for different channel models and modulators at transmitter 1 and 2 respectively. t, t +T denote compare them. Finally a conclusion is given in section V. the tth and (t+T)th time slots. The modulator consists of an Inverse Fast Fourier II. #4'#5 -$ -*"#, Transform (IFFT) block. The output of the IFFT block after two time slots at each transmitter are OFDM symbols in The 2X2, Golden Code is represented as [12], 1 ʚ͕ ƍ ͖ʛ ʚ͗ ƍ ͘ʛ ͒Ɣ Ƭ ư discrete time domain and are given by √5 ͝ʚ ʛʚ͗ ƍ ͘ʚʛʛʚ ʛʚ͕ ƍ ͖ʚʛʛ vŗ ͥ ͯͥ $ &) t + Ć ̾+,& Ɣ Ȕͬ) ʚ͟ʛ ͙ t ͤ ą ʞ1, ͈/ʟ (3) where a, b, c and d are information symbols which can be t )Ͱͤ taken from any M-QAM constellation and i = √Ǝ1 After IFFT operation, a parallel to serial conversion is used ͥͮ√ͩ and a Cyclic Prefix (CP) is added. In order to avoid OFDM θ = = 1.618 (Golden number). ͦ Inter Symbol Interference (ISI), the CP is assumed to be ͥͯ√ͩ σ θ θ longer than largest multipath delay spread. The resulted ( ) = ͦ = 1- MIMO-OFDM symbol is transmitted over a frequency α = 1+i-iθ=1+iσ(θ) selective fading channel. σ α σ θ θ ( ) = 1+i-i ( ) = 1+i B. &,,#* We assume that the MIMO-OFDM symbols are III. 712#+ -"#* transmitted over a frequency selective Rayleigh and Rician fading channels. We also assume that the channel taps remain A.0,1+'22#0S constant during transmission. We can represent the received Following the terminology of [18], let us consider system signal as with Nt=2 transmit antennas and Nr=2 receive antennas, r(t) = s(t) * h(t) + n(t)(4) signaling over a frequency selective MIMO channel using where * represents Convolution and h(t) is the impulse Fig. 1. Golden STBC MIMO-OFDM Transceiver. OFDM modulation per antenna as shown in Fig. 1. We first response of the random channel and n(t) is Additive White generate binary sequence which is then Quadrature Amplitude Gaussian Noise (AWGN). Modulation (QAM) modulated. The QAM symbol streams are If there is no line-of-sight (LoS) component between encoded via Golden STBC. Once we obtain Golden coded transmitter and receiver, the constructive and destructive symbols, 2M0 complex valued symbolsare grouped to form nature of multipath components can be approximated by parallel input set to the OFDM modulator. For Golden STBC Rayleigh distribution and hence the envelope of h(t) follows we can write Rayleigh distribution. The probability distribution function ͥ ͬ)ʚ͟ʛ ʞ ʚ͕ ƍ ͖ʛ/ ʚ͗ ƍ ͘ʛ/ͮʟ (1) (pdf) of Rayleigh distribution is given by ĥv ͦ - v ͬ)ʚ͟ʛ ʞ͝ʚ ʛʚ͗ ƍ ͘ʚʛʛ/ ʚ ʛʚ͕ ƍ ͖ʚʛʛ/ͮʟ (2) ͤʚͦʛ ͙vř ͦ ƚ 0 av (5) 10 Proc. of the International Conference on Pervasive Computing and Communication (PCC) where σ2 is the average power of the received signal [15]. When there is a line-of-sight (LoS), direct path component gets added to multipath components. This type of signal can be approximated by Rician distribution and hence the envelope of h(t) follows Rician distribution. As the direct path component experience deeper fading, the signal characteristics goes from Rician to Rayleigh distribution. The probability distribution function (pdf) of Rician distribution is given by [17, (2.15)] v ʚͥͮ ʛ Ą- ʚu~Ąʛĥ ʚ ͮͥʛ ͤʚͦʛ Ɣ ͙ řv ̓ ʦ2ͦǯ ʧ ͦ ƚ 0 av ͤ av (6) where K is the specular-to-diffuse ratio of the received signal I0(•) is the modified Bessel function of the first kind and zero- order. We assume channel coefficients to be varying slowly such that they are almost constant over two transmission time instants. The channel frequency response of the kth subcarrier Fig. 2. Golden STBC (4-QAM) in Flat Fading Vs Golden is Coded MIMO-OFDM (4-QAM) in Frequency Selective 'ͯͥ vŗĞŘ RayleighWe compare fading the Channels. performance of 2X2 Golden coded MIMO- % ͂ʚ͟ʛ ȕ͜ʚʛ͙ ġ ʚ7ʛ OFDM systems in frequency selective Rayleigh fading +Ͱͥ channel with 2X2 Golden coded MIMO systems in Rayleigh where h(ρ) is the complex channel gain of the ρth multipath flat fading channel and we observe that the two graphs component. coincide. It implies that the deployment of OFDM effectively combats the frequency selective conditions of the channel. C.#!#'4#0 We analyze the performance of 2X2 Golden coded MIMO- At the receiver, after removing cyclic prefix (CP), we OFDM systems in frequency selective Rician fading channels perform FFT operation. The signal at the output of FFT block with different K factors. We observe that, the overall BER can be expressed as performance of the system improves with increase in K factor. ͦ The increase in K factor implies the increase in the power of ͭ,ʚ͟ʛ ȕ͂ ʚ͟ʛͬ+ʚ͟ʛ ƍ ͫ,ʚ͟ʛ ͥ Ɣ 1,2 ʚ8ʛ dominant LoS signal which renders the improvement of BER ) ,+ ) ) performance of the system.