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![Raised Cosine Filter
If the transmitted signal is restricted to a certain bandwidth, then infinite bandwidth associated with a rectangular
pulse is not acceptable. The bandwidth of the rectangular pulse can be limited, however, by forcing it to pass through
a low-pass filter. The act of filtering the pulse causes its shape to change from purely rectangular to a smooth contour
without sharp edges. This filter is the well-known raised cosine filter and its frequency response is given by
H(w)= τ…………………………….0≤w≤c
τ{cos2[τ(w-c)/4α]}…………c≤w≤d
0…………………………….w>d
where w is the radian frequency 2πf, τ is the pulse period, α is roll off factor, c is equal to π(1-α)/τ , d is equal to
π(1+α)/τ.](https://image.slidesharecdn.com/pulseshapingfirfilterforwcdma-140216134232-phpapp02/85/Pulse-Shaping-FIR-Filter-for-WCDMA-11-320.jpg)
![Square Root Raised Cosine Filter
The frequency Response of the Square-Root Raised Cosine is given as below.
H(w)=√τ…………………………….0≤w≤c
√τ{cos[τ(w-c)/4α]}…………c≤w≤d
0…………………………….w>d
The consequence of pulse shaping is that it distorts the shape of the original time domain rectangular pulse into a
smoothly rounded pulse with damped oscillations (ripples) before and after the ½ To points. The ripples result from
the convolution of the rectangular pulse with the raised cosine impulse response (convolution is the process of
filtering in the time domain). Reduced bandwidth means larger ripple, which exacerbates ISI and increases the
likelihood of an incorrect decision (that is, error) at the receiver.](https://image.slidesharecdn.com/pulseshapingfirfilterforwcdma-140216134232-phpapp02/85/Pulse-Shaping-FIR-Filter-for-WCDMA-13-320.jpg)
Uploaded byBhagwat Singh Rathore
Pulse Shaping FIR Filter for WCDMA
This document analyzes the simulation parameters of a pulse shaping FIR filter for WCDMA. It simulates a square root raised cosine pulse shaping filter in MATLAB Simulink with varying group delay parameters. The simulation measures the number of bits, number of errors, and bit error rate at different group delays. It finds that the bit error rate is minimized at a group delay of 6 symbol periods. The optimal values found are a group delay of 6 and a roll off factor of 0.22.
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Pulse Shaping FIR Filter for WCDMA
- 1. Analysis of SimulationParameters of Pulse Shaping FIR Filter for WCDMA Digital Signal Processing And Digital Communication
- 2. Analysis of SimulationParameters of Pulse Shaping FIR Filter for WCDMA THE PROJECT DEALS WITH SIMULATION MODEL OF SQUARE ROOT RAISED COSINE PULSE SHAPING FILTER FOR WCDMA WITH DIFFERENT PARAMETERS OF THE FILTER AT 5MHZ. IT DEALS WITH STUDY OF SIMULATION PARAMETERS (NUMBER OF BITS, NUMBER OF ERRORS) OF PULSE SHAPING FIR FILTER AT DIFFERENT GROUP DELAY FOR WCDMA.
- 3. Introduction about WCDMA DigitalSignal processing techniques are being used to improve the performance of 3G systems. WCDMA (Wideband Code-Division Multiple Access), an ITU standard derived from Code-Division Multiple Access (CDMA), is officially known as IMT-2000 direct spread spectrum. W-CDMA is a third-generation (3G) mobile wireless technology that promises much higher data speeds to mobile and portable wireless devices. W-CDMA can support mobile/portable voice, images, data, and video communications at up to 2 Mbps (local area access) or 384 Kbps (wide area access). W-CDMA is one of several methods of multiplexing wireless users. In CDMA, users are multiplexed by distinct codes rather than by orthogonal frequency bands, as in frequency-division multiple access.
- 4. Contd… The information isspread over a band of approximately 5 MHz. This wide bandwidth has given rise to the name Wideband CDMA or WCDMA. In WCDMA, the CDMA technology (Code Division Multiple Access) air interface is implemented along with GSM networks. WCDMA is a Third Generation (3G) technology and works towards the interoperability between the various 3G technologies and networks being developed worldwide. WCDMA transmits on a 5 MHz wide radio channel and hence is called Wideband CDMA. This 5 MHz wide radio channel is in contrast to CDMA which transmits in one or more pairs of 1.25 MHz wide radio channel. WCDMA uses Direct Sequence spreading spectrum (DSSS), where spreading process is done by directly combining the baseband information to high chip rate binary code. The Spreading Factor is the ratio of the chips (Universal Mobile Telecommunication System, UMTS = 3.84Mchips/s) to baseband information rate.
- 5. Need of efficientPulse Shaping In communications systems, two important requirements of a wireless communications channel demand the use of a pulse shaping filter. These requirements are: 1) Generating band limited channels 2) Reducing inter symbol interference Both requirements can be accomplished by a pulse shaping filter which is applied to each symbol. In fact, the sync pulse, meets both of these requirements because it efficiently utilizes the frequency domain to utilize a smaller portion of the frequency domain.
- 6. Contd… The sinc pulseis periodic in nature and it has maximum amplitude in the middle of the symbol time. It appears as a square wave in the frequency domain and thus can effectively limit a communications channel to a specific frequency range.
- 7. Contd… A. Reducing Channel Bandwidth Modulationof a carrier sinusoid results in constant transitions in its phase and amplitude. Below, figure shows the time domain of a carrier sinusoid with a symbol rate that is half of the carrier. It is clear that phase/amplitude transitions occur at every two periods of the carrier and sharp transitions occur, when filtering is not applied. The sharp transitions in any signal result in high-frequency components in the frequency domain. By applying a pulse shaping filter, the sharp transitions are smoothed and the resulting signal is limited to a specific frequency band.
- 8. Contd… Fig shows smoothedphase and amplitude transitions in a filtered modulated signal. It happens much more gradually when filtering is implemented. As a result, the frequency information of the sinusoid becomes more concentrated into a specified frequency band. The sharp transitions do cause high frequency components in the frequency domain. Now, once a filter has been applied to the carrier signal, These high frequency components of the signal have been removed. Thus, the majority of the channel power is now limited to a specific defined bandwidth. It is clear that the required bandwidth for a channel is directly related to the symbol rate and is centered at the carrier frequency.
- 9. Contd… B. Reducing Inter-SymbolInterference (ISI) In band limited channels, intersymbol interference (ISI) can be caused by multi-path fading as signals are transmitted over long distances and through various mediums. This characteristic of the physical environment causes some symbols to be spread beyond their given time interval. As a result, they can interfere with the following or preceding transmitted symbols. To solve this problem we apply the pulse shaping filter. By applying this filter to each symbol that is generated, it is possible to reduce channel bandwidth while reducing ISI. Fig (A) shows the output in time domain. It is clear that the maximum amplitude of the pulse-shaping filter occurs in the middle of the symbol period. In addition, the beginning and ending portions of the symbol period are attenuated. Thus, ISI is reduced by providing a pseudo-guard interval which attenuates signals from multipath reflections.
- 10.
- 11. Raised Cosine Filter Ifthe transmitted signal is restricted to a certain bandwidth, then infinite bandwidth associated with a rectangular pulse is not acceptable. The bandwidth of the rectangular pulse can be limited, however, by forcing it to pass through a low-pass filter. The act of filtering the pulse causes its shape to change from purely rectangular to a smooth contour without sharp edges. This filter is the well-known raised cosine filter and its frequency response is given by H(w)= τ…………………………….0≤w≤c τ{cos2[τ(w-c)/4α]}…………c≤w≤d 0…………………………….w>d where w is the radian frequency 2πf, τ is the pulse period, α is roll off factor, c is equal to π(1-α)/τ , d is equal to π(1+α)/τ.
- 12.
- 13. Square Root RaisedCosine Filter The frequency Response of the Square-Root Raised Cosine is given as below. H(w)=√τ…………………………….0≤w≤c √τ{cos[τ(w-c)/4α]}…………c≤w≤d 0…………………………….w>d The consequence of pulse shaping is that it distorts the shape of the original time domain rectangular pulse into a smoothly rounded pulse with damped oscillations (ripples) before and after the ½ To points. The ripples result from the convolution of the rectangular pulse with the raised cosine impulse response (convolution is the process of filtering in the time domain). Reduced bandwidth means larger ripple, which exacerbates ISI and increases the likelihood of an incorrect decision (that is, error) at the receiver.
- 14.
- 15. Pulse Shaping inWCDMA Code-division multiple access is one of several methods of multiplexing wireless users. In CDMA, users are multiplexed by distinct codes rather than by orthogonal frequency bands, as in frequency-division multiple access. The processing gain factor is defined as the ratio of the transmitted bandwidth to information bandwidth and is given by: Gp=Bt/Bi Correlating the received signal with a code signal from a certain user will then only despread the signal of this user, while the other spread-spectrum signals will remain spread over a large bandwidth.
- 16. Simulation model ofWCDMA The performance in terms of the Bit Error Rate can be examined for different values of Group Delay “D” of the pulse shaping filter against a sinusoidal interference. The information signal in wideband CDMA system is generated by Bernoulli Binary Generator and the PN sequence is used for spreading the signal at certain bandwidth. The signal is passed from different parameters block and at the end BER is calculated by comparing the transmitted data and received data. On the basis of block diagram, a simulation model will be developed by using Matlab Simulink.
- 17. Block diagram forWCDMA system
- 18. Block diagram inSIMULINK
- 19. Description of allelements used in SIMULINK model Bernoulli Binary Generator: Bernoulli Binary Generator is used to generate information signal appropriate with the standard for WCDMA from simulink library. Bernoulli Binary Generator block as shown in figure generates random binary numbers using Bernoulli Distribution. The Bernoulli distribution has mean value=(1-p) and variance=p(1-p).The probability of a zero parameter specifies p and can be any real number between zero and one. PN Sequence Generator: The PN Sequence is produced by pseudo random noise generator that is simply a binary linear feedback shift register consisting of XOR gates and a shift register. This PN Sequence has the ability to create an identical sequence for both transmitter and receiver and yet retaining the desirable properties of a noise like randomness bit sequence. In Direct Sequence Spread Spectrum System, to generate a chip rate of 3.84Mbps for 5Mhz bandwidth in WCDMA system PN Sequence Generator has been used.
- 20. Contd… Data Type ConversionBlock: It converts input to data type and scaling of output. This conversion has two possible goals. One goal is to have real world values of input and output be equal. Other goal is to have stored integer values of input and output be equal. Overflows and Quantization errors can prevent goal from being fully achieved. XOR Logical Operator: For single input operators are applied across input vector. For multiple inputs operators are applied across inputs. Differential Encoder: It differentially encodes the input data. The output of this block is a logical difference between present input to this block and previous output of this block. The input can be a scalar, vector or frame based matrix.
- 21. Contd… Modulator baseband: Itmodulates the input signal using the offset quadrature phase shift keying (OQPSK) method. The input can be either bits or integers. For sample based integer input, input must be a scalar. For frame based integer input, input must be a column vector. In case of sample based input, output sample time equals symbol period divided by 2. There are different variants such as QPSK, orthogonal QPSK (OQPSK). BFFT Scope: This spectrum scope computes and displays the periodogram of each input signal. Non frame based inputs to this block should use buffering option. Upsampling Block: It upsamples the integer sampling rate by a factor of 8. Square Root Raised Cosine Transmit Filter: It upsamples and filters the input signal. The group delay is specified as the number of symbol periods between start of filter response and its peak. This delay also determines the length of filter impulse response which is 1+2*N*Group Delay.
- 22. Contd… dB Gain: Herewe apply the amplitude gain specified in dB. Here 5dB and 10 dB gain have been taken in present study for subsequent analysis. Gaussian Noise generator: It generates the Gaussian distributed noise with given mean and variance values. AWGN Channel: It adds white Gaussian noise to the input signal. The input and output signals can be real or complex. This block supports multichannel input and output signals as well as frame based processing. Here in AWGN channel block, we can change Eb/No from 5dB to 10dB. Square Root Raised Cosine Receive Filter: It filters the input signal and downsamples using Square root raised cosine FIR filter. The group delay is specified as the number of symbol periods between start of filter response and its peak. This delay also determines the length of filter impulse response which is 1+2*N*Group Delay.
- 23. Contd… Downsampling Block: Itdownsamples the input sample rate by integer factor of 8. Demodulator Baseband: It demodulates the input signal using the offset quadrature phase shift keying (OQPSK) method. The input can be either bits or integers. For sample based integer input, input must be a scalar. For frame based integer input, input must be a column vector. In case of sample based input, output sample time equals symbol period divided by 2. This block has variants such as QPSK, orthogonal QPSK. Differential Decoder: It differentially decodes the input data. The output of this block is a logical difference between present input to this block and previous input of this block. The input can be a scalar, vector or frame based matrix. Unit Delay: It samples and hold with one sample period delay.
- 24. Contd… Error Rate CalculationBlock: It computes the error rate of received data by comparing it to the delayed version of transmitted data. The block output is a three element vector consisting of error rate followed by number of errors detected and total number of symbols compared. Display: It is for the numeric display of values input to it from error rate calculation block. Here one can get data display in different formats.
- 25. Snapshots of SIMULINKmodel parameters Bernoulli Binary Generator:
- 26.
- 27.
- 28.
- 29. Results The simulation studyhas also been carried out for different values of D i.e.2,4,6 and 8. The readings of the simulation model for number of bits, number of errors and Bit Error Rate at different values of D have been taken at different time instants during the simulation runs. The parameters of the simulation model are given as below: 1. Eb/No=5dB 2. PN Sequence Generator Sample time=1/3840kbps 3. Bernoulli Binary Generator Sample time=1/64kbps(data services) 4. Interpolation Factor M=5 5. Roll Off Factor =0.22(Optimum) It is also observed that BER decreases as the group delay is increased from 2 to 4 and then from 4 to 6. The BER is found to increase as the value of group delay D is varied from 6 to 8. Hence the group delay should be controlled at D=6 by RF design engineer. Hence the optimum value of D=6 is taken for subsequent analysis in WCDMA system.
- 30.
- 31. Conclusions The present studyhas proposed the WCDMA communication link employing the pulse shaping filters using matlab simulink. The group delay (D) plays a crucial role in pulse shaping digital finite impulse response filter. The value of group delay should be minimal for efficient performance of digital pulse shaping filter. The effects of change in group delay on number of errors have been studied for square root raised cosine pulse shaping filter at 5 MHz band The effect of variation of group delay D i.e. number of symbols spanned by impulse response is studied at fix value of Roll Off Factor (alpha)=0.22 as well as at fix value of interpolation M=5. The study has impact on analysis & simulation of pulse shaping families in WCDMA based wireless communication system.
- 32. Contd… The study willbe useful to improve the performance of WCDMA based network by using the modified and improved design of square root raised cosine pulse shaping filter. Design of new type of filter of higher or different order will be useful to get better root raised cosine approximation thereby improving the performance parameters like increased Capacity, reduced BER, better S/N ratio, and Reduced ISI (noise) as a consequence of pulse shaping. The future work will involve the incorporation of interpolation factor for tradeoff between D and M at fix roll off factor as well as study of parameters of pulse shaping filter on the bit error rate performance analysis for WCDMA based wireless communication.
- 33. References Simon Haykin, “CommunicationsSystems” , Tata McGraw Hill. B.P. Lathi, Modern Digital and analog Communications Systems, John Wiley & Sons. John G. Proakis, Digital Communications. McGraw Hill. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5044827&url=http%3A%2F%2Fieeexplore.ieee.org%2Fx pls%2Fabs_all.jsp%3Farnumber%3D5044827 http://www.ijcaonline.org/archives/volume40/number8/4981-6675 http://www.mathworks.in/help/comm/ug/digital-modulation.html