Mr.P.Sunil Kumar, Dr.M.G.Sumithra, Ms.M.Sarumathi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.1324-1330 Performance evaluation of Rayleigh and Rician Channels using M-DPSK Scheme in Simulink Environment

Mr.P.Sunil Kumar1, Dr.M.G.Sumithra2, Ms.M.Sarumathi3 1P.G.Scholar, Department of ECE, Bannari Amman Institute of Technology, Sathyamangalam 2Professor, Department of ECE, Bannari Amman Institute of Technology, Sathyamangalam 3Assistant Professor, Department of ECE, Bannari Amman Institute of Technology, Sathyamangalam

ABSTRACT The Computation of Bit Error Rate is a Estimation of path loss is very important for mandatory requirement for the analysis of designing and deploying wireless communication multipath fading channels in any modulation networks. Path loss is dependent on a number of scheme .Fading is nothing but the attenuation in factors such as the frequency used and the signal strength when it is obtained at the receiver nature of the terrain [2]. Since several of these factors side and it is broadly classified into two types as fast cannot be used to describe the characteristics of every fading and slow fading. If a line of Sight exists transmission. Therefore, in designing a network, between the transmitter and receiver then Rician several models are required to describe the variety of fading is modelled and in the absence of a line of transmission environments. The free space Sight path can be modelled. The propagation model is the simplest path loss model in multipath intensity profile of a mobile radio channel which there is a direct-path signal between the depends critically on the type of terrain. The transmitter and the receiver, with no atmospheric Performance comparison of the Rayleigh and attenuation or multipath components. In this model Rician Fading channels in Differential Phase Shift the relationship between the transmitted power Pt and Keying modulation using Simulink tool is dealt in the received power Pr is given by the following this paper. expression  P  PG G ( )2 (1) Keywords: Fading, Rayleigh, Rician, DPSK. r t t r 4d

where Gt and Gr are the transmitter and receiver I. AN INTRODUCTION TO antenna gains, respectively, in the direction from the CHARACTERISTICS OF THE WIRELESS transmitter to the receiver, d is the distance between CHANNELS c The wireless channel (transmission medium) the transmitter and receiver, and   is the is susceptible to a variety of transmission f impediments such as path loss, interference, and wavelength of the signal blockage. These factors restrict the range, data rate, FADING: Fading refers to the fluctuations in signals and the reliability of the wireless transmission. The strength when received at the receiver. Fading can be extent to which these factors affect these transmission classified into two types as fast fading/small-scale affect the transmission depends upon the fading, and slow fading/large-scale fading. Fast environmental conditions and the mobility of the fading refers to the rapid fluctuations in the transmitter and receiver. Typically, the transmitted amplitude, phase, or multipath delays of the received signal has a direct-path component between the signal, due to the interference between multiple transmitter and receiver [1]. Other components of the versions of the same transmitted signal arriving at the transmitted signal known as multipath components receiver at slightly different times. The time between are reflected, diffracted, and scattered by the the reception of the first version of the signal and the environment, and arrive at the receiver shifted in last echoed signal is called delay spread. The amplitude, frequency, and phase with respect to the of the transmitted signal, direct-path component. The various characteristics of which causes fast fading, is because of the three the wireless channel such as path loss, fading, propagation mechanisms described as reflection, interference, and Doppler shift along with the two diffraction and scattering. The multiple signal paths key constraints namely Nyquist’s and Shannon’s may sometimes add constructively or sometimes theorems, that govern the ability to transmit destructively at the receiver, causing a variation in information at different data rates, are presented. the power level of the received signal. The received signal envelope of a fast-fading signal is said to PATH LOSS: Path loss can be expressed as the ratio follow a Rayleigh distribution if there is no line-of- of the power of the transmitted signal to the power of sight path between the transmitter and the receiver the same signal received by the receiver, on a given and a Ricean distribution if one such path is path. It is a function of the propagation distance. available. Some of the common measures used for

1324 | P a g e Mr.P.Sunil Kumar, Dr.M.G.Sumithra, Ms.M.Sarumathi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.1324-1330 countering the effects of fading are diversity and example, if the voltage values used for transmission adaptive modulation. Diversity mechanisms are are 0,1,2 and 3, then each value can be used to based on the fact that independent paths between the convey two bits (00,01,10 and11). Hence the bit rate same transmitter and receiver nodes experience here would be twice the baud rate. The Nyquist independent fading effects, and therefore, by theorem gives the maximum data rate possible on a providing multiple logical channels between the channel. If B is the bandwidth of the channel (in Hz) transmitter and receiver, by providing multiple and L is the number of discrete signals levels/voltage logical channels between the transmitter and receiver, values used, then the maximum channel capacity C and sending parts of the signal over each channel, the according to the Nyquist theorem is given by error effects due to fading can be compensated. C  2 B  log L bits/sec (2) 2 The above condition is valid only for a noiseless INTERFERENCE: Wireless transmissions have to channel. counter interference from a wide variety of sources. SHANNON’S THEOREM: Noise level in the Two main forms of interference are adjacent channel is represented by the SNR. It is the ratio of interference and co-channel interference. In the signal power (S) to noise power (N), specified in adjacent channel interference case, signals in nearby S frequencies have components outside their allocated decibels, that is, SNR  10log ( ) . One of the ranges, and these components may interfere with on- 10 N going transmissions in the adjacent frequencies [3]. It most important contributions of Shannon is his can be avoided by carefully introducing guard bands theorem on the maximum data possible on a noisy between the allocated frequency ranges. Co-channel channel. According to Shannon’s theorem, the interferences, sometimes also referred to as narrow- maximum data rate C is given by the following band interference, is due to another nearby systems expression using the same transmission frequency. Intersymbol S interference is another type of interference, where C  B  log 2 (1 ( )) bits/sec, (3) distortion in the received signal is caused by the N temporal spreading and the consequent overlapping where B is the bandwidth of the channel (in Hz). of individual pulses in the signal. When this temporal spreading of individual pulses goes above a certain II. AN INSIGHT ABOUT RAYLEIGH limit, the receiver becomes unable to reliably AND RICIAN FADING CHANNELS distinguish between changes of state in the signal, Rayleigh fading occurs when there are that is, the bit pattern interpreted by the receiver is multiple indirect paths between the transmitter and not the same as that sent by the sender. receiver and no distinct dominant path, such as Line DOPPLER SHIFT: The Doppler Shift is defined as of Sight path. Fortunately, Rayleigh fading can be the change/shift in the frequency of the received dealt analytically, providing a clear understanding signal when the transmitter and the receiver are into performance characteristics that can be used in mobile with respect to each other. If they are moving arduous environments, such as downtown urban toward each other, then the frequency of the received settings [5]. In the context of mobile radio channels, signal will be higher than that of the transmitted the Rayleigh distribution is usually used to explain signal, and if they are moving away from each other, the statistical time varying nature of the envelope the frequency of the signal at the receiver will be detected at the receiver for a flat faded environment. lower than that at the transmitter. The Doppler Shift The Rayleigh probability density function (pdf) for a v distributed envelope s(t) can be expressed as follows fd is given by f  where v is the velocity d  s  s 2  p(s)  { exp } for0  s   between the transmitter and receiver, and λ is the  2  2 2  (4) wavelength of the signal.   TRANSMISSION RATE CONSTRAINTS: Two p(s)  {0} fors  0 important constraints that determine the maximum where γ is the rms value of the received voltage rate of data transmission on a channel are Nyquist’s signal and σ2 is the time average power at the theorem and Shannon’s theorem. The two theorems envelope detector respectively. The probability that are presented as follows the received signal is up to a specified given value S NYQUIST THEOREM: The signaling speed of a can be given as follows transmitted signal denotes the number of times per S  S 2  second the signal changes its value/voltage. The P(S)  p (s  S)  p(s)ds  1 exp  number of changes per second is measured in terms s   2 2  of baud. The baud rate is not the same as the bit 0   rate/data rate of the signal since each signal value (5) may be used to convey multiple bits [4]. For Similarly, smean for such distribution is given as the following expression

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  III. DPSK MODULATION SCHEME s  E s  sp(s)ds   (6) A differentially encoded phase-modulated mean    0 2 signal also allows another type of demodulation that does not require the estimation of the carrier phase. And the variance in Rayleigh distribution 2 (ac  S Instead, the received signal in any given signaling power in the envelope) can be derived as follows interval is compared to the phase off the received signal from the preceding signaling interval. To 2 2 2 elaborate, suppose that we demodulate the  s  E[s ]  E [s] (7) differentially encoded signal by, multiplying r(t) by   2  2 cos 2πf t and sin 2πf t integrating the two products  2  s 2 p(s)ds   2 2   0.429 2 c c s  2 2 over the interval T. At the kth signaling interval, the 0 demodulator output is expressed as follows (8) The middle value of the envelope is more r  [  cos( )  n  sin( )  n often useful for analysis of faded data under different k s k k1 s k k2 fading distributions as sometimes the mean value (13) varies widely. This middle value may be computed Where ϴk is the phase angle of the transmitted signal by treated P(S) as 0.5 and solving the following at the kth signaling interval, ϕ is the carrier phase, expression as follows and nk  nk  jnk 2 is the noise vector. Similarly, s 1 0.5  p(s)ds (9) the received signal vector at the output of the  demodulator in the preceding signaling interval is 0 expressed as follows This provides sm as 1.777γ, which differs slightly from the rmean value. Sometimes the dominant non j(k 1) fading signal due to line-of-sight in the channel rk1   s e  nk1 , (14) superimposes itself on the random multipath The decision variable for the phase detector components[6]. The effect of the dominant signal is the phase detector is the phase difference between over the weaker multipath weaker signal gives rise to these two complex numbers. Equivalently, the a Rician distribution. The Rician distribution projection rk onto rk-1 and use the phase of the degenerates to Rayleigh in the absence of a line of resulting complex number; that is, sight dominant signal. The Rician (pdf) can be expressed as follows * j(k k 1) j(k ) *  j(k1) * s s2  A2 A rk rk1   se   s e nk1   s e nk  nk nk1 p(s)  { exp  ( )I ( s )} for A  0,s  0  2 2 2 0  2 (15) (10) which, in absence of noise, yields the phase * difference k  k 1 . Thus, the mean value of rk rk1 p(s)  {0} for s<0 (11) is independent of the carrier phase. Differentially encoded PSK signaling that is demodulated and Here A is the peak amplitude of the direct Line of detected as described above is called differential PSK Sight (LOS) signal and I0(x) is the modified Bessel (DPSK). The main differential PSK (DPSK) function of the first kind with zero order. The Rician sometimes needs clarification because two separate distribution is described by a parameter K, which is aspects of the modulation/demodulation format are the ratio between the direct signal power and the being referred to, namely the encoding procedure and variance of the multipath. This may be expressed in the detection procedure. The term differential dB as given below encoding refers to the procedure of encoding the data differentially; that is, the presence of a binary one or A2 zero is manifested by the symbol’s similarity or dB (12) difference when compared with that of the preceding K  10log 2 2 symbol [7]. The term differentially coherent detection This shows that for the absence of direct line-of-sight of differentially encoded PSK, the usual meaning of signal K  -  and Rician distribution degenerates DPSK, refers to a detection scheme often classified into Rayleigh. In digital wireless systems, channel as non coherent because it does not require a impairment due to fading is solved using error reference in phase with the received carrier. control codes, equalizers, or appropriate diversity Occasionally, different encoded PSK is coherently schemes. Random fluctuating signals cause fades detected. With non coherent systems, no attempt is which randomly cross a given specific signal level. made to determine the actual value of the phase of the incoming signal. Therefore, if the transmitted waveform is expressed as

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2E number of bits per integer parameter value present in the integer to bit convertor block defines how many si (t)  cos[w0t  i (t)] 0  t  T and T bits are mapped for each integer-valued input. For i=1,….., M (16) fixed-point inputs, the stored integer value is used. Then the received signal can be characterized by the This block is single-rated and so the input can be following mathematical expression either a scalar or a frame-based column vector. For sample-based scalar input, the output is a 1-D signal 2E with ‘Number if bits per integer’ elements. For frame-based column vector input, the output is a r(t)  cos[w0t i (t)  ]  n(t) T column vector with length equal to ‘Number of bits 0  t  T and i=1,…….,M (17) per integer’ times larger than the input signal length. where α is an arbitrary constant and is typically DIFFERENTIAL ENCODER: Differential assumed to be a random variable uniformly encoder differentially encodes the input data. The distributed between zero and 2π, and n(t) is an differential encoder object encodes the binary input AWGN process. For coherent detection, matched signal within a channel. The output is the logical filters are used, for non coherent detection, this is not difference between the current input element and the possible because the matched filter output is a previous output element. function of the unknown angle α. However, if we CONVOLUTIONAL INTERLEAVER: This assume that α varies slowly relative to two period block permutes the symbols in the input signal. times (2T), the phase difference between two Internally, it uses a set of shift registers. The delay value of the kth shift register is (k-1) times successive waveforms and is  j (T1 )  k (T2 ) the register length step parameter. The number of independent of α; that is expressed as the following shift registers is the value of the rows of shift equation registers parameter. DPSK MODULATOR BASEBAND: This block modulates the input signal using the differential [ k (T2 )  ] [ j (T1 )  ]   k (T2 )  j (T1 )  i (T2 ) phase shift keying method. The inputs can be either (18) bits or integers. The basis for differentially coherent detection of DPSK DEMODULATOR BASEBAND: This differentially encoded PSK (DPSK) is as follows. block demodulates the input signal using the The carrier phase of the previous signaling interval differential phase shift keying method. For sample- can be used as a phase reference for demodulation. based input, the input must be a scalar. For frame- Its use requires differential encoding of the message based input, the input must be a column vector. sequence at the transmitter since the information is BUFFER: The buffer converts scalar samples to a carried by the difference in phase between two frame output at a lower sample rate. The conversion successive waveforms. In general, DPSK signaling of a frame to a larger size or smaller size with performs less efficiently than PSK, because the errors optional overlap is possible. It is then passed to the in DPSK tend to propagate due to the correlation multipath Rician fading between signaling waveforms. One way of viewing CONVOLUTIONAL DEINTERLEAVER: The the difference between PSK and DPSK is that the Convolutional deinterleaver block recovers a signal former compares the received signal with a clean that was interleaved using the Convolutional reference, in the latter, however, two noisy signals interleaver block. are compared with each other. Thus there is twice as DIFFERENTIAL DECODER: The differential much noise associated with DPSK signaling decoder block decodes the binary input signal. compared to PSK signaling. BIT TO INTEGER CONVERTER: The bit to integer converter maps a vector of bits to a IV. PERFORMANCE ANALYSIS OF corresponding vector of integer values. The number RAYLEIGH AND RICIAN FADING of bits per integer parameter defines how many bits CHANNELS USING M-DPSK are mapped for each output. MODULATION SCHEME ERROR RATE CALCULATION: The error rate The environment is created as shown in the calculation is done by computing the error rate of the fig. 1. respectively using Simulink tool. received data by comparing it to a delayed version of RANDOM INTEGER GENERATOR: The the transmitted data. random integer generator generates random SIGNAL TRAJECTORY SCOPE: The discrete- uniformly distributed integers in the range [0, M-1], time signal trajectory scope is used to display a where M is the M-ary number. modulated signal constellation in its signal space by INTEGER TO BIT CONVERTER: In the integer plotting the in phase component versus the to bit convertor unit, a vector of integer-valued or quadrature component. fixed valued type is mapped to a vector of bits. The

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SCATTER PLOT SCOPE: The discrete-time characteristics such as pulse shaping, as well as scatter plot scope is used to display a modulated channel distortions of the signal. signal constellation in its signal space by plotting the SNR ESTIMATION: The SNR estimation block in phase component versus the quadrature gives the estimated SNR in decibels. component. DISPLAY: This unit gives the total number of bits EYE DIAGRAM SCOPE: The discrete-time eye transmitted, the number of errors and finally displays diagram scope displays multiple traces of a the Bit Error Rate. modulated signal to reveal the modulation

Fig. 1. Simulink Scenario for the Performance Analysis of Rician Fading Channels in M-DPSK modulation

Fig. 3. Scatter plot for the Performance Analysis of Fig. 2. Signal Trajectory for the Performance Rician Fading Channels in M-DPSK modulation Analysis of Rician Fading Channels in M-DPSK scheme modulation scheme

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Table 1. Bit Error Rate Analysis of Rician Fading Channels in MDPSK Modulation Scheme

RICEAN SNR BER FACTOR 200 100 0.008676 400 200 0.008605 600 300 0.008339 800 400 0.008147

Fig. 4. Eye diagram for the Performance Analysis of Rician Fading Channels in MDPSK modulation scheme

Fig. 5. Simulink Scenario for the Performance Analysis of Rayleigh Fading Channels in MDPSK modulation

Fig. 6. Signal Trajectory for the Performance Analysis of Rayleigh Fading Channels in MDPSK modulation scheme Fig. 7. Scatter plot for the Performance Analysis of Rayleigh Fading Channels in MDPSK modulation scheme

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Saddle River, NJ:Prentice Hall PTR,2002). [4] A.G.Molisch, Wireless Communications (Chichester : Wiley-IEEE, 2005). [5] A.A.M.Saleh and R.A.Valenzuela, A statistical model for indoor multpath propagation. IEEE J.Sel.Areas Commun., 5:2(1987), 1281C-137. [6] G.L.Stuber, Principles of Mobile Communication, 2nd edn (Boston, MA:Kluwer, 2001). [7] John G.Proakis, Digital Communications, Fig. 8. Eye diagram for the Performance Analysis fourth edn (McGraw-Hill International of Rayleigh Fading Channels in MDPSK Edition, 2000). modulation scheme

Table 2. Bit Error Rate Analysis of Rayleigh Fading Channels in MDPSK Modulation Scheme

SNR BER 100 0.009015 200 0.008994 300 0.008972 400 0.008677

V. CONCLUSIONS An introduction to the characteristics of the wireless channels followed by a review on Rayleigh and Rician fading channels is provided. It is obvious from table 1 that when the Ricean factor and Signal to Noise Ratio increases, the Bit Error Rate decreases gradually. Similarly from table 2 it can be inferred that when the Signal to Noise ratio increases, the Bit Error Rate decreases. It is observed from table 1 and table 2 that for a very high Signal to Noise Ratio a low bit error rate is achieved. The Differential Phase Shift Keying modulation technique can produce a very low bit error rate for the same signal to noise ratio in Rician fading channels than in the Rayleigh fading channels. The signal trajectory, scatter plot and the eye diagrams for the Simulink scenario is also provided. Future implementations may include the effective utilization of different modulation schemes for different fading channels in the Simulink scenario to produce a very low bit error rate.

References [1] L.Boithias, Radio Wave Propagation (New York:McGraw-Hill, 1987). [2] A.Goldsmith, Wireless Communications (Cambridge, UK:Cambridge University Press, 2005). [3] T.S.Rappaport, Wireless Communications: Principles and Practise, 2nd edn (Upper

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