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Pulse Shaping In Wireless Communication Computer Science Essay

The application of signal processing techniques to wireless communications is an emerging area that has recently achieved dramatic improvement in results and holds the potential for even greater results in the future as an increasing number of researchers from the signal processing and communication areas participate in this expanding field. Due to intensive use of FIR filters in video and communication systems, high performance in speed, area and power consumption is demanded. Basically digital filters are used to modify the characteristics of signal in time and frequency domain and have been recognized as primary digital signal processing operations.The present paper deals with critical analysis of pulse shaping in wireless communication.

Keywords: WCDMA,Pulse Shaping.

1. Introduction: The rapidly increasing popularity of mobile radio services has created a series of technological challenges. One of this is the need for power and spectrally efficient modulation schemes to meet the spectral requirements of mobile communications. Linear modulation methods such as QAM,QPSK, OQPSK have received much attention to their inherent high spectral efficiency However for the efficient amplification of transmitted signal, the Radio Frequency Amplifier is normally operated near the saturation region and therefore exhibit non linear behaviour. As a result significant spectral spreading occurs, when a signal with large envelope variations propagates through such an amplifier and creates large envelope fluctuations. Pulse shaping plays a crucial role in spectral shaping in the modern wireless communication to reduce the spectral bandwidth. Pulse shaping is a spectral processing technique by which fractional out of band power is reduced for low cost, reliable , power and spectrally efficient mobile radio communication systems.Signal processing techniques, such as Equalization, Detection, and Fast Fourier transform, have been successfully used in communication systems to improve the quality of communication.

The applications of signal processing techniques to wireless communication is an emerging area that has recently achieved dramatic improvement in results and holds the potential for even greater results in the future as an increasing number of researchers from the signal processing and communication areas participate in this expanding field [1-5].From an industrial viewpoint also, the advanced signal processing technology cannot only dramatically increase the wireless system capacity but can also improve the communication quality including the reduction of all types of interferences. As an example, a recent field test by Lucent Technologies demonstrated that adaptive signal processing for antenna arrays can be effectively used in mobile communication systems to mitigate the co-channel interference and increase the system capacity, setting a milestone for signal processing in wireless communications.[6-10]Currently, different wireless technologies (e.g. GSM, CDMA, and TDMA) are used through out the world for Second Generation(2G),Second and Half Generation(2.5G), and eventually Third Generation (3G) Networks. Researchers are continuing their ideas for the development of an undefined wireless world, which could become operational by 2010 [6]. The next generation systems based on the DS-CDMA, FDMA/TDMA and GSM concepts are projected to provide transmitting high speed data, video and multimedia traffic for both indoor and outdoor systems, new technologies like Wideband Code Division Multiple Access (WCDMA), already in service, are providing users with high data rate services options like they have never experienced previously.

1.1 Application Domain

Signal Processing Techniques are being employed in the field of wireless communication to enhance the performance of the system. There are many areas varying from First Generation(1G)to Fourth Generation (4G). The recent trends in the Research and Development are in the cutting edge technologies such as IS-95,GSM,CDMA,CDMA 2000,WCDMA,MIMO,SDR etc and the commonly employed different air interface techniques such as TDMA, FDMA ,WCDMA etc.[7]

1.1.1 Access Schemes

For radio systems, there are two resources, frequency and time. Division by frequency, so that each pair of communicators is allocated part of the spectrum for all of the time, results in Frequency Division Multiple Access (FDMA). Division by time, so that each pair of communicators is allocated all (or at least a large part) of the spectrum for part of the time results in Time Division Multiple Access (TDMA). In Code Division Multiple Access (CDMA), every communicator will be allocated the entire spectrum all of the time. CDMA uses codes to identify connections.Fig 1 shows the different multiple access schemes used in the communication systems.

Figure 1. Multiple Access Schemes

CDMA uses unique spreading codes to spread the baseband data before transmission. The signal is transmitted in a channel, which is below noise level. The receiver then uses a correlator to despread the wanted signal, which is passed through a narrow bandpass filter. Unwanted signals will not be despread and will not pass through the filter. The rate of spreading code is referred to as chip rate rather than bit rate.

1.1.2 Wideband CDMA

Wideband Code Division Multiple Access (WCDMA) technology has emerged as the most widely adopted 3G air interference. Its specification has been created in the 3rd Generation Partnership Project (3GPP), which is the joint standardization project of the standardization bodies from Europe, Japan, Korea, the USA and China [7-8].

WCDMA is considered to be wideband technologies based on the direct sequence spread spectrum transmission scheme, where user information bits are spread over a wide bandwidth by multiplying the user data with quasi-random bits called chips derived from CDMA spreading codes. In order to support very high bit rates (upto 2 Mbps), the use of a variable spreading factor and multicode connection is supported. The chip rate 3.84 Mcps used to leads a carrier bandwidth of approximately 5 MHz. The relatively high bandwidths occupied by CDMA systems are responsible for the significant advantages of WCDMA over traditional narrowband systems.

1. The spread of information over a very high bandwidth causes the CDMA signal to have power levels comparable to those of the noise floor. This guarantees high resistance to jamming and lower intercept probability.

2. The high bandwidth also ensures inherent resistance to multipath which causes significant signal attenuation in narrowband systems.

3. The soft handoff ensures that there are fewer “dropped” calls as the mobile moves from one cell to another.

4. The interference added by each user in the system can be considered as AWGN by the others. The whole system can therefore be designed using the average interference conditions. The ability to use the same set of frequencies within each cell results in an increase in the capacity of CDMA systems as compared to TDMA/FDMA systems.

5. The wide carrier bandwidth of WCDMA supports high user data rates and increased multipath diversity. Each user is allocated frames of 10 ms duration, during which the user data rate is kept constant [7]. However, the data capacity among the users can change from frame to frame as shown in Figure 2.

Figure 2. Allocation of Bandwidth in WCDMA in the time–frequency code space [7]

1.1.3 W-CDMA Radio Parameters

The main radio parameters that define in WCDMA radio interface are given in Table 1.1 [7,9]

WCDMA

PARAMETERS

Channel bandwidth

5,10, 20 MHz

Chip rate

3.84 *(1,2,4) Mcps

Multiple Access

DS CDMA

Frame length

Variable-rate speech

10 or 20ms

Packet Data

10-80 ms

Modulation

Spreading

Balanced QPSK (downlink)

QPSK (Uplink)

Complex spreading circuit

Data

QPSK (downlink)

BPSK (Uplink)

Coherent detection

Pilot Symbol assisted

Channel Coding

Convolutional and turbo coding

Scrambling code

10ms

Interleaving

10/20/40/80 ms

Multirate

Variable spreading and multicode

Spreading factor

4-512

Spreading

Downlink

Variable length orthogonal sequences for channel separation.

Gold sequence218 for user and cell separation

Uplink

Variable length orthogonal sequences for channel separation.

Gold sequence 241 for user separation

Inter base station timing

Asynchronous

Table 1.1. Radio parameter of WCDMA system [9]

1.1.4 SPREADING PROCESS

WCDMA uses Direct Sequence spreading, 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 (UMTS = 3.84Mchips/s) to baseband information rate. Spreading factors vary from 4 to 512 in FDD UMTS. Spreading process gain can in expressed in dBs (Spreading factor 128=21dBgain).

Figure 3.CDMA spreading

2.Pulse Shaping in Wireless Communication

Due to increasing demand for video signal processing and transmission of high speed and higher order FIR filters have frequently been applied for performing adaptive pulse shaping and signal equalization on received data in real time. Pulse shaping for wireless communication over time as well as frequency selective channels is the need of hour for 3G and 4G systems. Due to intensive use of digital filters in video and communication systems, high performance in speed, area and power consumption is demanded.

The rapidly increasing popularity of mobile radio services has created a series of technological challenges. One of this is the need for power and spectrally efficient modulation schemes to meet the spectral requirements of mobile communications. Linear modulation methods such as QAM,QPSK, OQPSK have received much attention to their inherent high spectral efficiency However for the efficient amplification of transmitted signal, the Radio Frequency Amplifier is normally operated near the saturation region and therefore exhibit non linear behaviour. As a result significant spectral spreading occurs, when a signal with large envelope variations propagates through such an amplifier and creates large envelope fluctuations. Pulse shaping plays a crucial role in spectral shaping in the modern wireless communication to reduce the spectral bandwidth. The aim of investigation is to achieve the following:

1 Good error performance

2 Small Envelope variations as possible

3 A compact power spectrum

Pulse shaping is a spectral processing technique by which fractional out of band power is reduced for low cost, reliable , power and spectrally efficient mobile radio communication systems. It is clear that the pulse shaping filter not only reduces intersymbol interference (ISI), but it also reduces adjacent channel interference.To satisfy the ever increasing demands for higher data rates as well as to allow more users to simultaneously access the network, interest has peaked in what has come to be known as wideband code division multiple access (WCDMA).The basic characteristics of WCDMA waveforms that make them attractive for high data rate transmissions are their advantages over other wireless systems. It emphasizes that how the choice of spread bandwidth affects the bit error rate of system [10]

The WCDMA has emerged as the most widely adopted 3G air interface and its specification has been created in 3GPP .In this system the user information bits are spread over much wider bandwidth by multiplying the user data bits with quasi random bits called as chips derived from CDMA spreading codes. In order to support very high bit rates (up to 2 Mbps) the use of variable spreading factor and multimode connection is supported. Block diagrams of WCDMA Transmitter and Receiver are shown in figure 4 and figure 5 respectively. The figures shown below are the generic block configuration of radio transmitter and receiver in WCDMA. Layer 1 (physical layer) adds a cyclic redundancy check(CRC) code for detecting block errors, to each transport block(TB)which is the basic unit of data that is subject to processing.This is followed by channel encoding (Forward Error Correction) and interleaving. The interleaved bit sequence is subject to overhead conditions (e.g.: pilot bits for channel estimation), followed by data modulation. In-phase & Quadrature phase components in the phase plane mapped following data modulation are spread across the spectrum by two layers of spreading code sequences.

CRC Attachment

Data Mapping

Rate Matching

Channel Encoding

Code Block Segmentation

Interleaving

MUX

Spreading

DAC

Square Root Raised CosineNyquist Pulse Shaping filter

Quadrature Modulator

Up Converter

Transmitting Amplifier

Tx Data

To Antenna

TPC bits

Pilot bits

Figure 4. WCDMA Transmitter

AGC Amplifier

From Antenna

Low Noise Amplifier

Down Converter

Quadrature Detector

ADC

Despreader Bank

Square Root Raised CosineNyquist Pulse Shaping filter

TPC Command Generator

SIR Measurement

Path Searcher

Coherent Rake Combiner

Code Block Multiplexing

Channel Decoding

Demultiplexing

Block Error Detection

Interleaver

Recovered Data

Figure 5.WCDMA Receiver

The resulting chip data sequence is restricted to 5Mhz band by a square root raised cosine nyquist filter(roll off factor=0.22) and then converted to analog signals through D/A converter so as to undergo orthogonal modulation. The orthogonally modulated IF signals are further converted into RF signals in 2 GHz band and are subject to power amplification thereafter. The signals received by destination mobile are amplified by LNA and converted into IF signals, to further undergo linear amplification by Automatic Gain Control (AGC) amplifier. The amplified signals are subject to quadrature detection to generate in phase and quadrature phase components. The analog signals of these components are converted into digital signals through A/D converter. The digitized in phase and quadrature components are bound within the specified band by square root raised cosine nyquist pulse shaping filter and are time divided into a number of multipath components with different propagation delay times through a despreading process that uses the same spreading code as the one used for spreading the reception signals. The time divide paths are combined through a coherent rake combiner, after which the resulting data sequences are deinterleaved and are subject to channel decoding(error correction decoding). [10] The design and analysis of transmit and receive pulse shaping filter is an important aspect of digital wireless communication since it has a direct effect on error probabilities.The pulse shaping digital filter is a useful means to shape the signal spectrum and avoid interference. Basically digital filters are used to modify the characteristics of signal in time and frequency domain and have been recognized as primary digital signal processing operations.In the radio environment, transmitted signals arrive at the receiver via a direct, unobstructed path, or via multiple paths from the reflection, diffraction and scattering of surrounding objects such as buildings and trees. This multipath propagation causes the signal at the receiver to distort and fade significantly, leading to inter-symbol interference (ISI)[11-12].

3. Multipath Effects:

Multipath propagation through linear dispersive media introduces distortion in signal during the wireless transmission. Due to this, there is degradation in BER performance, unless it is compensated with some suitable techniques at the receiver. In addition to frequency selectivity, the wireless channel also experiences time variations, which arise due to relative motion between transmitter and receiver which in turn needs to acquire mobile channel states and needs to be optimized. In a digital communication system, digital information can be sent on a carrier through changes in its fundamental characteristics such as: phase, frequency, and amplitude. In a physical channel, these transitions can be smoothed, depending on the filters implemented in transmission. In fact, the use of a filter plays an important part in a communications channel because it is effective at eliminating spectral leakage, reducing channel width, and eliminating interference from adjacent symbols (Inter Symbol Interference, ISI)[1-9].Transmitting a signal at high modulation rate through a band-limited channel can create intersymbol interference. As the modulation rate increases, the signal's bandwidth increases. When the signal's bandwidth becomes larger than the channel bandwidth, the channel starts to introduce distortion to the signal. This distortion is usually seen as intersymbol interference. The signal's spectrum is determined by the pulse shaping filter used by the transmitter. Usually the transmitted symbols are represented as a time sequence of dirac delta pulses.

4.Constraints in Modern Communication System

The following are the constraints in communication system:

(1)Data rate/Bandwidth Interrelationship is a major constraint in a modern data communication system The challenge is to obtain the highest possible data rate in the bandwidth allotted with least number of errors.

(2)The data in the form of pulses are sent from transmitter and detected at receiver keeping in view to maximize the probability of an accurate binary decision.

(3)To provide non interference as well as need to limit the pulse width is a major factor in a wireless communication.

5. Need of Efficient Pulse 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, and

(2) Reducing Inter Symbol Interference (ISI) arising from multi-path signal reflections.

Both requirements can be accomplished by a pulse shaping filter which is applied to each symbol. In fact, the sinc pulse, shown below, meets both of these requirements because it efficiently utilizes the frequency domain to utilize a smaller portion of the frequency domain, and because of the windowing affect that it has on each symbol period of a modulated signal. A sinc pulse is shown below in figure 6 along with an FFT spectrum of the givensignal.

Figure 6 Time vs. Frequency Domain for a Sinc Pulse

The sinc pulse is periodic in nature and is has maximum amplitude in the middle of the symbol time. In addition, it appears as a square wave in the frequency domain and thus can effectively limit a communications channel to a specific frequency range. [11]

5.1 Reducing Channel Bandwidth

Fundamentally, modulation of a carrier sinusoid results in constant transitions in its phase and amplitude. Below, figure 7. 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. [11]

Figure7. Phase and Amplitude Transitions in an Unfiltered Modulated Signal

The sharp transitions in any signal result in high-frequency components in the frequency domain. By applying a pulse-shaping filter to the modulated sinusoid, the sharp transitions are smoothed and the resulting signal is limited to a specific frequency band. Below, it is shown time-domain modulated sinusoid.

Figure 8. Smoothed Phase and Amplitude Transitions in a Filtered Modulated Signal

Fig 8 shows smoothed phase 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. [10]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.

5.2 Reducing Inter-Symbol Interference (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. More specifically, 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. One solution to this problem is the application of the pulse shaping filter. By applying this filter to each symbol that is generated, it is possible to reduce channel bandwidth while reducing ISI. In addition, it is common to apply a match filter on the receiver side to minimize these affects. Fig 9 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 multi-pathreflections[10].

Figure9 Filter Output in the Time Domain.

5.3 Pulse Shaping and Matched Filtering

The matched filter is perhaps equally as important as the pulse-shaping filter. While the pulse shaping filter serves the purpose of generating signals such that each symbol period does not overlap, the matched filter is important to filter out what signal reflections do occur in the transmission process. Because a direct-path signal arrives at the receiver before a reflected signal does, it is possible for the reflected signal to overlap with a subsequent symbol period. This is shown in the fig 10. It is clear, the matched filter reduces this affect by attenuating the beginning and ending of each symbol period. Thus, it is able to reduce intersymbol interference. One of the most common choices for a matched filter is the root raised cosinefilter[10].Figure10. ISI Caused by Multi-Path Distortion

6. Different Pulse Shapes

Rectangular Pulse

Raised Cosine Pulse

Square Root Raised Cosine Pulse

Gaussian Pulse

Flipped Exponential Pulse

Flipped Hyperbolic Secant Pulse

Flipped Inverse Hyperbolic Secant Pulse

Data transmission systems that must operate in a bandwidth-limited environment must contend with the fact that constraining the bandwidth of the transmitted signal necessarily increases the likelihood of a decoding error at the receiver. Bandwidth limited systems often employ pulse-shaping techniques that allow for bandwidth containment while minimizing the likelihood of errors at the receiver. The response of a digital filter, as compared to analog, is solely dependent on the filter coefficients, which are invariant to both temperature and aging. Therefore, digital pulse-shaping filters have become an integral part of many digital data transmission systems.[12]

6.1 Rectangular Pulse

The most basic information unit in a digital transmission scheme is a rectangular pulse. It has a defined amplitude, A, and defined duration, T. Such a pulse is shown in Figure 11, where A = 1, T = To, with the pulse centered about the time origin at t = 0. Typically, a sequence of such pulses (each delayed by T seconds relative to the previous one) constitutes the transmission of information. The information, in this case, is encoded in the amplitude of the pulse. The simplest case is when a binary 0 is encoded as the absence of a pulse (A = 0) and a binary 1 is encoded as the presence of a pulse (A = constant). Since each pulse spans the period T, the maximum pulse rate is 1/T pulses per second, which leads to a data transmission rate of 1/T bits per second. In more sophisticated data transmission schemes, the pulse amplitude can take on both positive and negative values with multiple discrete amplitudes used to encode more than one bit into the pulse. Four levels can be used to encode two bits in which each level is uniquely associated with one of the four possible bit patterns[12].

Figure 11. A Single Rectangular Pulse (T=T0, A=1)

The pulses used to transmit symbols occupy a fixed time interval, T .Thus, the pulse rate is 1/T pulses per second, which leads to a symbol rate of 1/T symbols per second. The unit, symbols per second, is often referred to as baud. The data transmission rate in bits per second is the baud rate multiplied by the number of bits represented by each symbol. For example, if a symbol represents four bits, then the bit rate is four times the symbol rate. This means that a lower transmission rate can be used to transmit symbols as opposed to directly transmitting bits, which is the primary reason that the more sophisticated data transmission systems encode groups of bits into symbols. The logic 1 is represented by the presence of a pulse of unit amplitude and a logic 0 by the absence of a pulse (that is, zero amplitude).

Spectrum of a Rectangular Pulse

The frequency content (or spectrum) associated with the pulse of Figure 6 is shown in Figure 7 The spectrum of the pulse is obtained by applying the Fourier transform to the time domain waveform of Figure 11. The shape of the spectrum is the well-known sin(x)/x response, which is often referred to as the sinc response. The null points (where the spectral magnitude is zero) always occur at integer multiples of fo, which is the pulse (or symbol) rate. Therefore, the null points are solely determined by the pulse period, T. In theory, the nulls and peaks extend in frequency out to ±∞ with the peaks approaching zero magnitude. However, because the frequency span of Figure 2.7 is only ±4 fo, only four null points are evident on each side of the f = 0 line.

Figure 12. Spectrum of Single Rectangular Pulse of Duration T0

The general shape of the spectrum that appears in Figure 7 is the same regardless of the amplitude of the rectangular pulse. Although the amplitude of the rectangular pulse proportionally affects the magnitude of the peaks, it has no effect on the frequency location of the null points. Therefore, encoding schemes that rely on pulse amplitude variations still produce a spectrum similar to that of Figure12 even though the pulse amplitude may vary from pulse to pulse.

6.2 Raised Cosine Pulse

As shown in Figure 7, the spectrum of a rectangular pulse spans infinite frequency. In many data transmission applications, the transmitted signal must be restricted to a certain bandwidth. This can be due to system design constraints In such instances, the 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. Therefore, the act of filtering rectangular data pulses is often referred to as pulse shaping. Unfortunately, limiting the bandwidth of the rectangular pulse necessarily introduces a damped oscillation. That is, the rectangular pulse exhibits nonzero amplitude only during the pulse interval, whereas the smoothed (or filtered) pulse exhibits ripples both before and after the pulse interval. At the receiver, the ripples can lead to incorrect decoding of the data, because the ripples associated with one pulse interfere with the pulses before and after it. However, the choice of a proper filter can yield the desired bandwidth reduction while maintaining a time domain shape that does not interfere with the decoding process of the receiver.[12]

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

A plot of the raised cosine frequency response is shown in Figure 12 (normalized to τ = 1). The raised cosine filter gets its name from the shape of its frequency response, rather than its impulse (or time domain) response.

Figure 12. The Raised Cosine Frequency Response

The response characteristic of the raised cosine filter is adjustable via a parameter known as the roll off factor represented by the symbol α, where 0 ≤ α ≤ 1. In the case of α = 0, the frequency response is confined to ½ fo(the green trace). For α = 1, the frequency response is confined to fo (the blue trace). For values of α between 0 and 1, the frequency response is restricted to an intermediate range between ½ fo and fo (the red trace shows the response for α = ½). The dashed black trace is the spectrum of a rectangular pulse and is included for the sake of comparison. There are three significant frequency points associated with the raised cosine response. The first is known as the Nyquist frequency, which occurs at ½ fo (that is half the pulse rate). According to communication theory, this is the minimum possible bandwidth that can be used to transmit data without loss of information. It is clear that the raised cosine response crosses through the 1/2 amplitude point at ½ fo regardless of the value of α. The second significant frequency point is the stop band frequency (fstop) defined as the frequency at which the response first reaches zero magnitude. It is related to α by:

Fstop=(1+α)f0/2

The third, and final, significant frequency point is the pass band frequency (fpass) defined as the frequency at which the response first begins to depart from its peak magnitude. The raised cosine response is perfectly flat from f = 0 (DC) to fpass, where:

Fpass=(1-α)f0/2

Ideal Response of Raised Cosine Filter is shown in figure 13. below[10]

Figure 13. Ideal Response of Raised Cosine Filter

Ideal Raised Cosine filter frequency response consists of unity gain at low frequencies,raised cosine function in the middle and total attenuation at high frequencies.The root raised cosine filter is generally used in series pairs so that total filtering effect is that of raised cosine filter.Sometimes it is desirable to implement the raised cosine response as the product of two identical responses, one at the transmitter and the other at the receiver. In such cases, the response becomes a square-root raised cosine response since the product of the two responses yields the desired raised cosine response.

6.3 Square Root Raised Cosine

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 variable definitions are the same as for the raised cosine response.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).This is a source of decision-making error at the receiver known as Intersymbol Interference (ISI). Reduced bandwidth means larger ripple, which exacerbates ISI and increases the likelihood of an incorrect decision (that is, error) at the receiver.[12] Obviously, a trade off exists between bandwidth containment in the frequency domain and ripple attenuation in the time domain. It is this trade off of bandwidth containment vs. ripple amplitude that must be considered by design engineers when developing a data transmission system that employs pulse shaping.Ideal response of Square Root Raised Cosine filter is shown in figure 14 below.[10]

Figure 14. Ideal Square Root Raised Cosine Filter frequency Response

6.4 Gaussian Pulse

This gives an output pulse shaped like a Gaussian function. The Gaussian filter is a pulse shaping technique that is typically used for Frequency Shift Keying (FSK) and Minimum Shift Keying (MSK) modulation. This filter is unlike the raised cosine and root raised cosine filters because it does not implement zero crossing points. The impulse response for the Gaussian filter is defined bythefollowingequation:

Graphical representation of the impulse response of gaussian filter is shown in figure11. As described above, it is clear that there are no zero crossings for this type of filter[10].

Figure 15. Impulse Response of Gaussian Filter

6.5 Flipped Exponential Pulse

This pulse is proposed by Beaulieu(fexp)[11]. It is known as flipped-exponential pulse.In this pulse a new parameter,β=ln 2/αβ has been introduced .The frequency and impulse responses of this family are given as below.

S2(f)=1…………………f≤B(1-α);

S2(f)=exp(β(B(1-α)-f))……………B(1-α)<f≤B

S2(f)=1-exp(β(f-B(1+α)))………...B<f≤B(1+α)

S2(f)= 0………… ……………….B(1+α)<f

S2(t)=(1/T)sinc(t/T)(4βπtsin(παt/T)+2β2cos(παt/T)-β2)/[(2πt)2+β2]

Two more pulses have been derived from from flipped exponential pulse[14]

6.6 Flipped Secant Hyperbolic Pulse

The first one is known as flipped-hyperbolic secant (fsech) pulse, has frequency and impulse responses defined as S3(f)=1…………………….f≤B(1-α);

=sech(γ׀f׀-B(1-α)))…...B(1-α)<f≤B

=1-sech(γ(B(1+α)-f))….B<f<≤B(1+α)

= 0……………………..B(1+α)<f

S3(t)=(1/T)sinc(t/T){8πtsin(παt/T)F1(t)+2cos(παt/T)[1-2F2(t)]+4F3(t)-1}

where γ=ln(√3+2)/αβ

The impulse response has been obtained through an expansion in series of exponentials.

6.7 Flipped Inverse Secant Hyperbolic Pulse

The second pulse is referred to as flipped-inverse hyperbolic secant (farcsech) pulse. It has frequency response defined as

S4(f)=1…………………………………………….f≤B(1-α)

=1-(1/2αβγ)arcsech(1/2αβ(B(1+α)-f))………..B(1-α)<f≤B

=(1/2αβγ)arcsech(1/2αβ(f-B(1-α)))…………...B<f≤B(1+α)

= 0…………………………………………….B(1+α)<f

Its impulse response s4(t)can be evaluated through a numerical inverse Fourier transform. The plot of frequency responses of the above pulses is shown in figure16 below. It is clear that the pulses are real and even, with optimum time sampling.

Figure 16. Frequency Responses of the different pulses with roll-off factor α= 0.35

7. Solution to the constraints of modern communication system

The unbounded frequency response of rectangular pulse is not suitable for data transmission. The Gaussian pulse shaping technique is unlike the raised cosine and root raised cosine filters because it does not implement the zero crossing points. So out of all these pulse shapes which pulse will fulfill the requirements of:

(1)Limiting the bandwidth

(2)Decaying as quickly as possible

(3)Providing zero crossing point at the optimal pulse shaping point for sake of non interference.

8.Impact of Study

The study is useful to improve the performance of WCDMA Network.

In the planning of WCDMA Network.

To achieve the flexibility in use of data rates in different environments.

Design of future cellular mobile communication network.

The proposed WCDMA Simulator can be used for optimization of parameters in various environments, with various mobile distributions and different services.

9.Future Scope of Work:

The following points have to be concentrated to extend its application to wide range of future directions:

Different multipath fading channels can replace AWGN channel in the model to simulate the system under different mobile radio channels.

More influencing parameters can be incorporated in the simulation model using adaptive signal processing.

The simulation model can be developed for Tan, Beaulieu and Damen pulse shaping families by incorporating more variables.

DSP algorithms can be developed for performance enhancement of WCDMA based wireless system using optimized values of parameters of pulse shaping filters.

Simulation study can be extended to different data rates such as 144 kbps, 384 kbps & 2Mbps.

10.Conclusion:The application of signal processing techniques to wireless communications is an emerging area that has recently achieved dramatic improvement in results and holds the potential for even greater results in the future as an increasing number of researchers from the signal processing and communication areas participate in this expanding field. Due to intensive use of FIR filters in video and communication systems, high performance in speed, area and power consumption is demanded. Basically digital filters are used to modify the characteristics of signal in time and frequency domain and have been recognized as primary digital signal processing operations.Digital Signal 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 than commonly offered in today's market.

Acknowledgement:The first author is thankful to Dr B S Sohi,Director UIET,Sec-25,PANJAB UNIVERSITY Chandigarh for discussion and valuable suggestions during technical discussion at WOC conference at Panjab Engg College Chandigarh during presentation of research paper,”Digital Processing and Analysis of Pulse Shaping Filter for wireless communication “The help rendered by S Harjitpal Singh,a research scholar of NIT Jalandhar as well as Mr Hardeep Singh,Research Scholar, Communication Signal Processing research Lab, Deptt of Electronics Technology GNDU Amritsar is also acknowledged.

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