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Performance of Downlink CDMA-SFBC Over Weibull Fading Channels

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Performance of Downlink CDMA-SFBC Over Weibull Fading Channels JOURNAL OF COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2012 321 Performance of Downlink CDMA-SFBC Over Weibull Fading Channels Taimour Aldalgamouni1,AmerM.Magableh2, and Salsabeel Al-Theiabat Electrical Engineering Department Jordan University of Science and Technology Irbid, Jordan 22110 Email: [email protected]; 2 [email protected] Abstract—In this paper, we consider code division multiple codes with lengths larger than the number of OFDM tones and access (CDMA) - space frequency block coded (SFBC) downlink hence the system can serve larger number of users compared system and evaluate its performance over independent and to direct sequence (DS)-CDMA [5]. In the literature, there are identically distributed (i.i.d) Weibull fading channels. Specifically, we drive closed form bit error rate (BER) expressions for the several schemes that combine MIMO with OFDM, STBCs, M-ary quadrature amplitude modulation (MQAM) and M-ary and CDMA. In [6], J. young et al. proposed an adaptive phase shift keying (MPSK). We study the outage probability of constrained minimum mean square error (CMMSE) receiver the system by numerically inverting the Laplace transform of for single carrier STBC-CDMA systems. In [7], Vook et al. the cumulative distribution function of the instantaneous signal proposed a cyclic prefix single carrier CDMA system with to noise ratio. The derived expressions are evaluated considering different amounts of channel estimation error, different M- antenna diversity at both the transmitter and the receiver. In ary size, different fading severities and different SFBC forms. [8], Auffray and Helard studied the performance of multi- Numerical results are provided to show the tradeoff between the carrier (MC)-CDMA combined with STBC over Rayleigh different system parameters. The derived expressions can be used fading channel for one or two transmit antennas. In [9], Torabi to assign channels to different users in a cross-layered fashion et al. derived closed form expressions for the bit error rate based on the conditions of their channels. (BER) of SFBC-OFDM system over Rayleigh fading channels. Index Terms—Code division multiple access (CDMA), Space In [10], Aldalgamouni et. al. proposed and studied the BER frequency block code (SFBC), Orthogonal frequency division performance of CDMA-SFBC downlink system over Rayleigh multiplexing (OFDM), Multiple input multiple output (MIMO), Weibull fading channel, BER, Estimation error. fading channel. Most of the previous works in the literature studied the BER I. INTRODUCTION performance over Rayleigh fading channels. Digital communi- cations over Weibull fading channels has recently received the Wireless communication links equipped with multiple an- interest of several researchers (see, for example [11]–[15]). It tennas at both transmitter and receiver known as (MIMO) was found in [16]–[19] that the Weibull distribution has the systems are gaining popularity in the next generation wireless flexibility to fit experimental fading channel measurements for networks. MIMO systems can be used to increase the diversity both indoor and outdoor environments. The Weibull and the gain of the link to overcome the fading nature of the wireless Nakagami-m models have been recommended by the IEEE channel or can be used to increase the bit rate of the sys- Vehicular technology society committee on radio propagation tem through spatial multiplexing. Therefore, MIMO systems to theoretically study slope changes in the tail of the model have been adapted in many communication systems such as distribution to compensate for some of the weaknesses of the WiMAX, IEEE802.11n and 3GPP long term evolution. Rayleigh distribution [18]. Moreover, space time block codes (STBC) are used to get Several numerical methods have been suggested to compute maximum diversity gain. Several STBCs have been designed the outage probability of orthogonal STBC systems over [1]–[3] in order to get maximum diversity gain in MIMO generalized fading channels. In [20], Alouini et al. evaluated systems. The use of orthogonal STBCs allows low complexity the outage probability of diversity systems with maximal- maximum likelihood (ML) decoding. Orthogonal frequency ratio combining (MRC) over generalized fading channels division multiplexing (OFDM) technique is used to divide the using a moment generating function-based technique. Their frequency selective fading channel into multiple flat fading approach is based on numerical inversion of Laplace transform sub-channels. It is also used to mitigate the effects of ISI [4], which was originally presented in [21]. In [22], the authors and to support variable rates for different users. The advan- introduced a general and simple Fixed-Talbot algorithm to tages of OFDM and STBC can be combined together in what numerically invert the laplace transform. is known as space frequency block coding (SFBC). OFDM can In this paper, we adapt the downlink CDMA-SFBC system be also combined with code division multiple access (CDMA) which was proposed in [10] to combine the advantages of producing what is called multi-tone (MT)-CDMA [5]. In MT- MIMO, STBC, OFDM and CDMA systems in one system. CDMA spreading is done in the time domain using spreading The adapted CDMA-SFBC system exploits time, space, Manuscript received February 21, 2012; revised March 25, 2012. code, and frequency diversities of the channel which will © 2012 ACADEMY PUBLISHER doi:10.4304/jcm.7.4.321-328 322 JOURNAL OF COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2012 greatly improve reception. We analyze the performance of first tone, the second symbol transmitted from each antenna is the system assuming independent and identically distributed transmitted on the second tone and so on. See Table 1. (i.i.d) Weibull fading channels. We derive and evaluate closed form expressions for the BER of the system considering M- TABLE I FREQUENCY MAPPING ary quadrature amplitude modulation (MQAM) and M-ary phase shift keying (MPSK) modulation techniques. These Subcarrier Antenna 1 Antenna 2 expressions show the effects of channel estimation errors, 2Ks(2K) s(2K +1) fading severity, number of transmit and receive antennas and 2K +1 −s∗(2K +1) s∗(2K) the alphabet size of the modulation scheme on the BER per- formance. In our analysis, we assume the effects of frequency selectivity in fading channels are neglected; this assumption The slow variation of the fading channel in usual indoor is acceptable when the cyclic prefix is larger than the delay environments allows us to assume the channel to be a quasi- spread of the channel and the spreading codes resolve the static Weibull fading channel (i.e. the channel remains fixed frequency selective channels [23]. The derived expressions can for the duration of one OFDM block). be used to assign channels to different users in a cross-layer The envelope of Weibull fading channel has the following fashion. Moreover, we study the outage probability perfor- probability density function (pdf), [24]: mance of the system by numerically inverting the Laplace βxβ−1 −xβ transform of the cumulative distribution function (CDF) of fX (x)= exp [ ],x≥ 0 (1) the instantaneous signal to noise ratio (SNR) using the simple Ω Ω and accurate algorithm presented in [21]. The reminder of this where β represents the fading parameter and Ω is the mean paper is organized as follows: the system model is shown and of xβ (i.e. E[xβ ]). At the receiver, the signal will be multiplied explained in Section II. BER performance for MQAM and by its corresponding Walsh function, and then filtered by a MPSK downlink CDMA-SFBC systems over Weibull fading low pass filter (LPF). OFDM demodulation is done using fast channel are studied in Sections III and IV respectively. Perfor- Fourier transformation (FFT).The STBC decoder utilizes the mance over Rayleigh fading channel is illustrated in Section channel state information (CSI) to decode the received signal V. Outage probability is presented in Section VI. Numerical and generate an estimate of the transmitted signal (S˜)using results are provided in Section VII while concluding remarks ML detection. Following that, the signal will be demodulated are drawn in Section VIII. by the MQAM/MPSK demodulator and converted into serial format. II. SYSTEM MODEL The system model considered in this paper is illustrated in III. BER PERFORNACE OF THE DOWNLINK Figure 1. It shows a downlink system, i.e. from the base station CDMA-SFBC MQAM SYSTEM OVER WEIBULL to the mobile station, for one user only with MT transmit and FADING CHANNEL MR receive antennas. At the transmitter side, the data bits are Assuming MQAM modulation with Gray coding and M = first converted from serial to parallel and then modulated using b th b 2 , the instantaneous BER of the K sub-channel can be MQAM/MPSK modulator where M =2 and b is the number expressed as in [25]: of allocated bits per symbol to generate a signal vector S. 1 The generated vector S includes L × Rc information symbols 1 − √ 2b 1.5γ [qK] where L is equal to the total number of available OFDM tones BERMQAM [qK]=2 erfc (2) b 2b − 1 and Rc is the rate of the STBC code. The signal vector S is then provided as an input to the Where erfc(x) is the complementary error function i.e. ∞ 2 × T −t STBC encoder. The STBC encoder is defined by its q M erfc(x)= x e dt. γ[qK] is the instantaneous SNR derived generating matrix. The STBC encoder generates MT blocks, in [10] as S ...SM . Each one of these blocks has a length of L 1 T MT MR | |2 and consists of F sub-blocks, such that F = L/q and γs i=1 j=1 Hi.j [qK] γ [qK]= 2 (3) each sub-block has a length of q. Then, using inverse fast RcM T (γsσe +1) Fourier transform (IFFT), OFDM modulation is performed Where Hi.j (qK) is the discrete Fourier transform (DFT) S ...SM X ...XM th on 1 T .
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