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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 NOISE REDUCTION IN FAST FADING CHANNEL USING OFDM/TDM Mr.A.Sagaya Selvaraj, Asst.Professor & Head Dr.R.S.D.Wahidabanu, Professor &Head Department of Electronics and Communication Engg . Department of Electronics and Communication Engg IFET College of Engineering, Villupuram -108 Govt.College of Engg. Salem-11 Research Scholar, Anna University, Chennai, India Anna University, Coimbatore, India E-mail: sagayam_a@yahoo.co.in E-mail: drwahidabanu@gmail.com ABSTRACT objectives of my paper is to design and evaluate Orthogonal Orthogonal Frequency Division Multiplex (OFDM) Frequency Division Multiplexing (OFDM) in a Multipath modulation is being used more and more in telecommunication, Fading Channel using computer simulation (MATLAB).To wired and wireless.. OFDM can be implemented easily, it is obtain and compare between the theoretical and simulation spectrally efficient and can provide high data rates with result for Orthogonal Division Multiplexing (OFDM) in sufficient robustness to channel imperfections. MMSE-FDE can Raleigh channel. To obtain and compare the Bit Error Rate improve the transmission performance of OFDM combination (BER) Performance of OFDM. with time division multiplexing (OFDM/TDM). To improve the tracking ability against fast fading robust pilot-assisted channel estimation is done that uses time-domain 2. OFDM/TDM TRANSMITTER RECEIVER MODEL filtering on a slot-by-slot basis and frequency-domain interpolation. The mean square error (MSE) of the channel 2.1 FDM TRANSMITTER CONFIGURATION estimator is obtained and then a tradeoff between improving the The following figure shows the configuration of an tracking ability against fading and the noise reduction is done. OFDM transmitter[1][2]. In the transmitter, the transmitted BER is calculated by mat lab simulator and compared with high speed data is first converted into parallel data of N sub conventional OFDM. It is proved that the OFDM/TDM using channels. Then, the transmitted data of each parallel sub MMSE-FDE achieves a lower BER and provides better tracking channel is modulated by BPSK based modulation. ability against fast fading. Keywords: Orthoganal Frequency Division Multiplexing(OFDM), BER (Bit Error Rate), MMSE (Minimum Mean Square Error), Feedback Decision Equalization, … 1. INTRODUCTION: In this paper, we focused on designing the mat lab code for particular channel conditions that affects the BER performance for Orthogonal Frequency Division Multiplexing (OFDM) [1]. The channel used is Raleigh Channel BPSK modulation has been used in this paper. We fig 2.1. OFDM Transmitter derive the mean square error and using MMSE-FDE, we again prove that the BER is reduced [4] [8] [9]. The main 203 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 2.1.1OFDM TRANSMITTER STRUCTURE S(t)=sk (t-kNm)for t=0~Nc-1, where k=[t/Nm] with [x] representing the largest integer smaller than or equal to x and s k(t) is the k-th OFDM signal with Nm subcarriers, is given by for t=0~Nm-1, where Es and Tc represent the symbol energy fig 2.2 OFDM Frame Structure and the sampling period, respectively. Before transmission, the last Ng samples in the OFDM/TDM frame are inserted as The OFDM/TDM transmission system model is the GI at the beginning of the frame. shown in the above Fig.2.1 Tc-spaced discrete time representation is used, where Tc represents the fast Fourier 3.2 GUARD INTERVAL transform (FFT) sampling period. To reduce the PAPR, the One key principle of OFDM is that since low rate inverse FFT (IFFT) time window for the conventional modulation scheme, where the symbols are relatively long OFDM is divided into K slots (which constitute the compared to the channel time characteristics suffer less from OFDM/TDM frame) shown in Fig 2.1. An OFDM signal inter symbol interference caused by multi path. It is the with reduced number of sub carriers (Nm=Nc/K)is advantageous to transmit a number of low rate streams in transmitted during each time slot without inserting guard parallel instead of a single high rate stream. Since the interval (GI) between consecutive OFDM signals, where Nc duration of each symbol is long, it can be affordable to insert is the number of sub carriers in the conventional OFDM[1]. a guard interval between the OFDM symbols and thus the Hence, the transmission data rate is kept the same as inter symbol interference can be eliminated. The transmitter conventional OFDM, while the number of sub carriers is sends s cyclic prefix during the guard interval. The guard reduced by a factor of K, thus reducing the PAPR[6]. interval also reduces the sensitivity to time synchronization 3.1 TRANSMIT SIGNAL problems[8]. A sequence of Nc data-modulated symbols The orthogonality of sub channels in OFDM can be {d(i);i=0~Nc-1} is transmitted during one OFDM/TDM maintained and individual sub channels can be completely frame(equal to the IFFT block size of the conventional separated by using an FFT circuit at the receiver when there OFDM). The data-modulated symbol sequence {d(i)} of Nc are no ISI and inter carrier interference (ICI) introduced by symbols is divided into K blocks of Nm=Nc/K symbols each. transmission channel distortion. The spectra of OFDM signal The k-th block symbol sequence is denoted by {dk(i); are not strictly band limited, the distortion due to multi path i=0~Nm-1},where dk(i)=d(kNm+i) for k=0~K-1. Nm-point fading causes each sub channel to spread the power into the IFFT is applied to generate a sequence of K OFDM signals adjacent channel. Moreover, the delayed wave with the delay with Nm subcarriers. The OFDM/TDM signal can be time larger than 11 symbol time contaminates the next expressed using the equivalent low pass representation as symbol. In order to reduce this distortion, a simple solution is 204 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 to increase the symbol duration or the number of carriers. r(t)=h(τ,t)s(t-τ)dτ+n(t) However, this method may be difficult to implement in terms Where h(τ,t) is the impulse response of the radio channel of carrier stability against Doppler frequency and FFT size. at time t, and n(t) is the complex AWGN. Another way to eliminate ISI is to create a cyclically extended guard interval, where each OFDM symbol is 3.3 FREQUENCY DOMAIN EQUALISATION preceded by a periodic extension of the signal itself. The GI inserted OFDM/TDM signal is transmitted over a The total symbol duration: wireless channel. We assume a Tc-spaced time-delay discrete Ttotal = Tg + Tn channel having L propagation paths with distinct time delays Where, {τl; l=0~L-1}. Tg = guard time interval Each symbol is made of two parts. The whole signal The discrete-time impulse response h(t) of the is contained in the active symbol, the last part of which is channel can be expressed as also repeated at the start of the symbol and is called a guard interval. When the guard interval is longer than the channel impulse response or the multi path delay, the effect of ISI can be eliminated. However, the ICI or in band fading still exists. The 3.4 OFDM RECEIVER CONFIGURATION ratio of the guard interval to the useful symbol duration is At the receiver, received signal r(t) is filtered by a application dependent[9][11]. The insertion of guard interval band pass filter, which is assumed to have sufficiently wide will reduce the data throughput; Tg is usually smaller than pass band to introduce only negligible distortion in the signal. Ts/4. An orthogonal detector is then applied to the signal where the After the insertion of a guard interval, the OFDM signal is signal is down converted to IF band. Then, an FFT circuit is given by applied to the signal to obtain Fourier coefficients of the s’(t)=∑∑di (k)exp(j2πfi(t-kTtotal))f’(t-kTtotal) signal in observation periods [iTTotal , iTTotal + Ts]. where f’(t) is the modified pulse waveform of each symbol defined as The OFDM signal is transmitted to the receiver; however, the transmitted data, s’(t) is contaminated by multi path fading and AWGN. At the receiver, the received signal FIG 3.4. OFDM Receiver is given by 205 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 The output, di’(k), of the FFT circuit of the ith OFDM decomposed into Nc frequency components {R(n); n=0~Nc- subchannel is given by 1}by applying Nc-point FFT as di’(k) = 1/Ts r(t) exp (-j2ðfi(t-kTtotal))dt R(n)=S(n)H(n)+∏(n) If the characteristics of delayed wave, hi’(k) in a where S(n), H(n) and Π(n) are the signal component, the multipath fading environment can be estimated, therefore the channel gain and the noise component at the nth frequency, received data also can be equalized as respectively, given by follows: di’’ (k) = (hi’ * (k)) / (hi’(k)hi’ * (k) )) (di’(k)) where * indicates the complex conjugate. By comparing dk and di’’ (k), the BER performance can be calculated. The BER depends on the level of the receiver’s noise. In OFDM transmission, the orthogonal is preserved and the BER performance depends on the modulation scheme in each sub channel. One-tap FDE is applied as Here w(n) is the equalization weight for the nth frequency and Πˆ (n) is the noise component after equalization. We consider MMSE-FDE. 4. DIGITAL MODULATION SCHEMES 4.1 DIGITAL MODULATION FIG 3.4.1. OFDM Receiver Structure Nowadays, digital modulation is much popular The received signal can be expressed as compared to analog modulation. The move to digital modulation provides more information capacity, compatibility with digital data services, higher data security, better quality communications, and quicker system availability. Developers of communications systems face these constraints: for t=-Ng~Nc-1, where η(t) is the additive white Gaussian Available bandwidth noise (AWGN) process with zero mean and variance 2N0/Tc Permissible power with N0 being the single-sided power spectrum density. After Inherent noise level of the system removing the GI, the received signal {r(t); t=0~Nc-1} is 206 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 The RF spectrum must be shared, yet every day there modulate a cosine (or sine) wave and the amplitude along the are more users for that spectrum as demand for quadrature axis to modulate a sine (or cosine) wave. communications services increases. Digital modulation schemes have greater capacity to convey large amounts of information than analog modulation schemes. 4.2 PHASE SHIFT KEYING (PSK) PSK is a modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (i.e. fig 4.2. Constellation Diagram the phase of the carrier wave is changed to represent the data In PSK, the constellation points chosen are usually signal). A finite number of phases are used to represent positioned with uniform angular spacing around a circle. This digital data. Each of these phases is assigned a unique pattern gives maximum phase-separation between adjacent points of binary bits; usually each phase encodes an equal number and thus the best immunity to corruption. They are positioned of bits. Each pattern of bits forms the symbol that is on a circle so that they can all be transmitted with the same represented by the particular phase. energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes There are two fundamental ways of utilizing the phase of a needed for the cosine and sine waves. Two common signal in this way: examples are binary phase-shift keying (BPSK) which uses two phases, and quadrature phase shift keying (QPSK) which (i) By viewing the phase itself as conveying the information, uses four phases, although any number of phases may be in which case the demodulator must have a reference signal used. Since the data to be conveyed are usually binary, the to compare the received signal's phase against; (PSK) or PSK scheme is usually designed with the number of constellation points being a power of 2. (ii) By viewing the change in the phase as conveying information – differential schemes, some of which do not 4.3 BIT RATE AND SYMBOL RATE need a reference carrier (to a certain extent) (DPSK). To understand and compare different PSK A convenient way to represent PSK schemes is on a modulation format efficiencies, it is important to first constellation diagram. This shows the points in the Argand understand the difference between bit rate and symbol rate. plane where, in this context, the real and imaginary axes are The signal bandwidth for the communications channel termed the in-phase and quadrature axes respectively due to needed depends on the symbol rate, not on the bit rate. their 90° separation. Such a representation on perpendicular Symbol rate=bit rate \ the number of bits transmitted axes lends itself to straightforward implementation. The with each symbol amplitude of each point along the in-phase axis is used to Bit rate is the frequency of a system bit stream. Take, for example, a radio with an 8 bit sampler, sampling at 10 207 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 kHz for voice. The bit rate, the basic bit stream rate in the radio, would be eight bits multiplied by 10K samples per second, or 80 Kbits per second. (For the moment we will ignore the extra bits required for synchronization, error correction, etc.). . 4.4 BIT ERROR RATE FOR BPSK MODULATION We will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. With Binary Phase Shift Keying (BPSK), the binary digits 1 and 0 maybe represented by the analog levels and respectively. The system model is as shown in the Figure below. fig 4.4.1. conditional probability density function with bpsk modulation .If the received signal is greater than zero(y>0), then the receiver assumes that binary “1” was transmitted. If the received signal is less than zero(y<0),then the receiver assumes that binary “0” was transmitted. i.e., y>0, s1 is transmitted and fig 4.4. Simplified Block Diagram with BPSK Transmitter- y<=0, s0 is transmitted Receiver Probability of error given S1 was transmitted With this 4.4.1 COMPUTING THE PROBABILITY OF ERROR threshold, the probability of error given S1 is transmitted is p(e\s1)(the area in the blue region) Probability of error given The received signal is, S0 was transmitted Similarly the probability of error given S0 when bit 1 is transmitted and is transmitted is p(e\s2)(the area in the green region) Total probability of bit error: when bit 0 is transmitted. The conditional probability distribution function (PDF) of for the two cases are: . 208 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 Given that we assumed that s1and s0are equally ionospheric layers, reflection from the earth’s surface or from probable i.e. p (s1)=p(s0)=1/2, the bit error probability is, more than one ionospheric layer, and so on. Multipath fading occurs when a transmitted signal divides and takes more than . one path to a receiver and some of the signals arrive out of phase, resulting in a weak or fading signal. Some where, transmission losses that effect radio wave propagation are ionospheric absorption, ground reflection and free space losses. Electromagnetic interference (EMI) both natural and man made, interfere with radio communications. The maximum useable frequency (MUF) is the The given function is the complementary error function highest frequency that can be used for communications 5.1 MULTIPATH between two locations at a given angle of incidence and time In wireless communications, multipath is the of day. The lowest usable frequency (LUF) is the lowest propagation phenomenon that results on radio signals frequency that can be used for communications between two reaching the receiving antenna by two or more paths. Causes locations. of multipath include atmospheric ducting, ionospheric reflection and refraction and reflection from terrestrial object 5.3MULTIPATH CHANNEL CHARACTERISTICS such as mountains and buildings. The effects of multipath Because there are obstacles and reflectors in the include constructive and destructive interference and phase wireless propagation channel, the transmitted signal arrivals shifting of the signal. This causes Rayleigh Fading named at the receiver from various directions over a multiplicity of after Lord Rayleigh. Rayleigh fading with a strong line of paths. Such a phenomenon is called multipath. It is an sight is said to have a Rician distribution or tobe Rician unpredictable set of reflections and/or direct waves each with fading. its own degree of attenuation and delay. Multipath is usually In digital radio communications such as GSM described by: Line-of-sight (LOS): the direct connection Multipath can cause errors and affect the quality of between the transmitter (TX) and the receiver (RX). communications. The errors are due to Inter symbol Non-line-of-sight (NLOS): the path arriving after reflection interference (ISI). Equalizers are often used to correct the ISI. from reflectors. The illustration of LOS and NLOS is shown Alternatively, techniques such as orthogonal frequency below. division modulation and Rake receivers may be used. 5.2 MULTIPATH FADING Multipath Fading is simply a term used to describe the multiple paths a radio wave may follow between transmitter and receiver. Such propagation paths include the ground wave, ionospheric refraction, re radiation by the fig 5.4. Effect Of Multipath On Mobile Station 209 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 Characteristics of a Multipath Channel are As shown in the model above, the path between base – this is the interval for which a symbol remains inside a station and mobile stations of terrestrial mobile multipath channel communications is characterized by various obstacles and with one line of sight (LOS) path & several multipath, the reflections. The radio wave transmitted from the base station signals from the multipath being delayed and attenuated radiates in all directions. version of the signal from the LOS path Multipath will cause These radio waves, including reflected waves that are amplitude and phase fluctuations, and time delay in the reflected off of various objects, diffracted waves, scattering received signal. waves, and the direct wave from the base station to the mobile station. 6 COMMUNICATION CHANNEL Therefore the path lengths of the direct, reflected, 6.1 RAYLEIGH FADING CHANNEL diffracted, and scattering waves are different, the time each Rayleigh fading is a statistical model for the effect takes to reach the mobile station is different. The phase of the of a propagation environment on a radio signal such as that incoming wave also varies because of the reflection. used by wireless devices. It assumes that the power of a As a result, the receiver receives a superposition signal that has passed through such a transmission medium consisting of several waves having different phase and time (also called a communications channels will vary randomly of arrival. The generic name of a radio wave in which the or fade according to a Rayleigh distribution – the radial time of arrival is retarded in comparison with this direct wave component of the sum of two uncorrelated Gaussian random is called a delayed wave. variables. It is reasonable model for tropospheric and Then, the reception environment characterized by a ionospheric signal propagation as well as the effect of heavily superposition of delayed waves is called multipath built up urban environment on radio signals. Rayleigh fading propagation environment. is most applicable when there is no line of sight between the transmitter and receiver. 7. CHANNEL ESTIMATION TECHNIQUES FOR PILOT 7.1 VARIOUS CHANNEL ESTIMATION TECHNIQUES Channel estimation can be done in 3 ways. They are: 1. Channel estimation with TDM pilot. 2. Channel estimation with FDM pilot. 3. Channel estimation TDM pilot with first order filtering. Fig 6.2. Principle Of Multipath Channel 210 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 7.1.2 CHANNEL ESTIMATION WITH TDM-PILOT AND TDFF Fig 7.1.2. Channel Estimation With TDFF The pilot signal {p(i); i = 0 ∼ Nm−1} is inserted into(K − 1)th slot (i.e., dK−1(i) = p(i) for i = 0 ∼ Nm −1)and into the Fig 7.1. General Pilot Symbol Assisted OFDM GI as a cyclic prefix .Since the same pilot is used for all frames, the (g − 1)th frame’s pilot slot acts as a cyclic prefix 7.1.1 CHANNEL ESTIMATION WITH TDM-PILOT for the gth frame’s GI. Thus, the channel estimation can be For OFDM/TDM with pilot-assisted channel performed using the gth frame’s Nm-sample GI. Similar estimation using TDM-pilot ,a pilot signal is transmitted frame structure was presented for SC transmission. The followed by Nd OFDM/TDM data frames is given below. Nc channel gain estimate and noise variance estimate to be used subcarriers are used as pilots. First, by reverse modulation, for FDE are denoted by He,g(n)and 2σ2e,g respectively. the instantaneous channel gain estimate Hg(n) at the nth Hg(n) and σ2g are replaced by He,g(n) and σ2e,grespectively. subcarrier is obtained .Then, Nc-point IFFT is applied to { The received pilot {rg(t); t = −Nm ∼ −1} in the GI is filtered Hg(n); n=0∼ Nc−1} to obtain the instantaneous channel on a slot-by-slot basis by the time-domain first-order filtering impulse response {h(τ); τ =0∼ Nc−1}. Assuming that the to increase the signal-to-noise power ratio (SNR) of the pilot actual channel impulse response is present only within the signal. The filtered pilot signal is obtained as GI, the estimated channel impulse response beyond the GI is replaced with zeros to reduce the noise Finally, Nc-point FFT is applied to obtain the improved channel gain estimates {He,g(n); n=0∼ Nc−1}. for t=−Nm∼ −1, where γ is the forgetting factor with the initial condition r0(t) = r0(t). Then, Nm-point FFT is applied to decompose {rg(t); t = −Nm ∼ −1} into Nm sub carrier components {Rg(q); q=−Nm∼ −1} as Fig 7.1.1. OFDM Pilot Block Insertion 211 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 With q=n\k for n=0 and the initial condition domain interpolation is used to obtain the channel gains for R0(q)=R0(q). The instantaneous channel gain estimate at the all frequencies (i.e., n=0∼ Nc−1). Nm-point IFFT is qth subcarrier is obtained by removing the pilot modulation performed on { Hg(q); q = 0 ∼ Nm −1} to obtain the as instantaneous channel impulse response {h(τ); τ =0∼ Nm−1} and then, Nc-point FFT is applied to obtain the interpolated channel gain estimates {He,g(n); n=0∼ Nc−1}. 7.2 PILOT SEQUENCE SELECTION where ,P(q) and P(q) denotes the qth frequency component of {p(t); t=0∼ Nm−1}.Since the channel estimates are obtained only at the frequencies n=0, Nm, 2Nm,. . ., (Nc-1) . Hence, an interpolation is necessary to obtain the channel gains for all frequencies (i.e., n = 0 ∼ Nc −1). Frequency-domain interpolation is applied. First, Nm-point IFFT is performed on { Hg(q); q = 0 ∼ Nm−1} to obtain the instantaneous channel impulse response {h(τ); τ = 0 ∼ Nm−1} as Then, Nc-point FFT is applied to obtain the interpolated channel gain estimates {He,g(n); n = 0 ∼ Nc −1} for all Nc frequencies as Fig 7.2. Pilot Amplitude (a) constant amplitude in frequency-domain (FD), 7.1.3 CHANNEL ESTIMATION WITH FDM-PILOT (b) constant amplitude in time-domain (TD) and For pilot-aided channel estimation with FDM-pilot (c) constant amplitude in both time- and frequency domains using frequency-domain interpolation an Nm equally-spaced (Chu). pilot subcarriers among Nc subcarriers are used. First, by A selection of pilot sequence is an important design reverse modulation, the instantaneous channel gain estimate { issue. If the amplitude of P(n) drops at some frequencies, the Hg(q); q = nNm for n =0 ∼ Nc−1} at the pilot subcarriers is noise component in the channel estimate will be enhanced and obtained. where Nm is the number of pilot subcarriers. Since thereby, the estimation accuracy will degrade leading to poor q = nNm , the channel estimates are obtained only at the performance. To avoid the noise enhancement, it is desirable frequencies n=0, Nm, 2Nm,. . ., (Nc-1)Hence, the frequency- that P(n) has constant amplitude irrespective of n. On the 212 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 contrary, if P(n) is constant for all n, a large amplitude 8. SIMULATION RESULTS AND ANALYSIS variation may appear in p(t) and consequently, the pilot signal We assume BPSK data-modulation with Nc=256 may be distorted due to nonlinear power amplification. So chu and Nm=16. Chu sequence is used as the pilot given by sequence is used as the pilot which makes amplitude constant for t=0∼ Nm−1 . in both time and frequency domain. (R2-1)The propagation channel is an L=16-path block Rayleigh fading channel having exponential power delay 7.3 NOISE POWER ESTIMATION profile with decay factor α as shown below. The zero-mean The noise component at the qth pilot subcarrier can independent complex path gains {hl; l=0∼ L−1} remain be estimated by subtracting the received pilot component constant over one OFDM/TDM frame length and vary frame- He,g(q) P(q) from Rg(q) as by-frame. Without loss of generality, we assume τ0 = 0 < τ1 < · · · < τL−1 and that the lth path time delay is τl = lΔ, where Δ (≥ 1) denotes the time delay separation between for q=0 ∼ Nm−1. adjacent paths. The maximum time delay of the channel is equal to the GI length (i.e., L=Ng). The noise variance estimate can be obtained as 7.4 OFDM DEMODULATION By applying Nc-point IFFT after FDE, we obtain the time-domain OFDM/TDM signal rˆ(t) , which can be expressed as for t=0~Nc-1. Then, the decision variable for the ith data symbol in the k th Fig 8.1. Average BER Performance slot can be obtained using Nm-point FFT as We plot the average BER performance using the proposed channel estimation as a function of Eb/N0 for fDTs=0.0001 and α=0 dB. The optimum γ is used for each Eb/N0 value. It for i=0~Nm-1 and k=0~K-1. can be seen from the above figure that the OFDM/TDM with 213 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 the proposed channel estimation achieves a much better BER 8.1 TRADE OFF BETWEEN THE NOISE REDUCTION performance than OFDM; the required Eb/N0 for BER=10−3 AND ROBUSTNESS AGAINST THE CHANNEL TIME SELECTIVITY reduces by about 6.5 dB in comparison with OFDM using TDM-pilot when fDTs=0.0001. The The MSE equation is given by, Eb/N0 degradation of OFDM/TDM in comparison to ideal channel estimation is only about 0.6 dB. Since γ is one of the key parameters in the estimator, the robustness of the algorithm is discussed when γ is fixed. The MSE of channel estimator with time-domain first-order filtering and frequency-domain interpolation is not a function of the channel frequency-selectivity and it is only a function of Es/N0 and the channel time selectivity. The first term of the above equation represents the influence of AWGN, while the second term represents the influence of the channel time-selectivity. Thus, a trade-off is present; as the filter coefficient γ increases (decreases), the channelestimator becomes more (less) robust against the channel time selectivity while on the other hand, the estimator ability to reduce the noise decreases (improves). (R2-1) This trade-off property computed using the above equation and is plotted as a graph . Fig 8.1.1. BER In Raleigh Channel BER for BPSK modulation with 2x2 MIMO and MMSE equalizer (Rayleigh channel) theory (nTx=2,nRx=2, ZF) The above figure illustrates the average bit error -1 theory (nTx=1,nRx=2, MRC) 10 sim (nTx=2, nRx=2, MMSE) rate (BER) performance with: (i) ideal CE, (ii) optimum γ (i.e., γopt) and (iii) fixed γ. BER performance is plotted as a -2 10 function of Eb/N0 at fDTs=10−2. The figure shows that, for a Bit Error Rate lower Eb/N0 (i.e., Eb/N0<15 dB), the BER with fixed γ=0.5 is almost the same as with γopt. As expected, γopt and fixed -3 10 γ=0.5 give the same BER atEb/N0=15 dB because γ=0.5 is optimum value at Eb/N0=15 dB and fDTs=10−2. However, -4 10 as Eb/N0 increases (i.e., Eb/N0>15 dB) the BER with fixed γ=0.5 approaches a floor value of about BER=10−3, while -5 10 the performance with γopt consistently improves. 0 5 10 15 20 25 Average Eb/No,dB Fig 8.1.2 . MMSE Equalization 214 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 8, August 2011 9 CONCLUSION [5] M. Hsieh and C. Wei, ”Channel estimation for OFDM Thus the performance evaluation of OFDM/TDM systems based on comb-type pilot arrangement in frequency using MMSE-FDE with practical channel estimation in a fast selective fading channels,” IEEE Trans. Consumer Electron., fading channel was presented. A tracking against fast fading Vol. 44, No. 1, Feb. 1998. is improved by robust pilot-assisted channel estimation that uses time-domain first-order filtering on a slot-by-slot basis [6] (R1) W. Zeng, X. Xia and P. C. Ching, ”Optimal training and frequency-domain interpolation. The MSE of the channel and pilot pattern design for OFDM systems in Rayleigh estimator using time-domain first-order filtering and fading,” IEEE Trans. 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