NA TDMA Standard IS 95 Computer Science Essay

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This chapter presents the theory that is related to a CDMA forward link cellular system. The chapter first examines the history of wireless communication and then present a comparison of the CDMA cellular system with previously adopted systems. Finally, concluding with a brief introduction of the current state-of-the-art research on new CDMA cellular systems.

CDMA development started in early 1989 after the NA-TDMA standard (IS-95) was established. A CDMA demonstration to test its feasibility for digital cellular systems was held in November 1989. The CDMA mobile station-base station compatibility standard for dual mode wideband spread spectrum cellular system was issued as IS-95. CDMA uses the idea of tolerating interference by spread spectrum modulation. The power control scheme in a CDMA system is a requirement for digital cellular application.

The CDMA systems manage the power levels of all mobiles so that the power level of each mobile is below a certain required level and is about the same whether the mobile is very close to the base station or far at the edge of the cell. Multipath and fading also attenuate power levels so the system maintains a power control loop. The figure given below is the basic block diagram of communication system.

http://www.ece.virginia.edu/~mv/edu/ee136/Lectures/comm-system-block-diagram.gif

Figure 1.1: Block diagram of communication system

Interim standard 95 (IS-95) is the first CDMA based digital cellular standard pioneered by Qualcomm. The brand name for IS-95 is CDMAOne. It is a 2G mobile telecommunications standard that uses CDMA, a multiple access scheme for digital radio to send voice, data and signalling data between mobile telephones and cell sites. IS-95 defines transmission of signals in both the forward and reverse directions. In the forward direction radio signals are transmitted by base stations.

CELLULAR CONCEPT

One of many reasons for developing a cellular mobile developing system and deploying it in many cities is the operational limitations of conventional mobile telephone systems: limited service capability, poor service performance and inefficient frequency spectrum utilization. IS 95 is a cellular phone system based on Direct Sequence CDMA multiple access. Thus, multiple users simultaneously share the same (wideband) channel. The technology behind cellular systems has developed from first generation (1G) systems to second generation (2G) systems and then to the third generation (3G) systems. At each stage performance was improved and further facilities were available. There are a number of basic concepts behind cellular communication systems. These include the idea of cells themselves as well as how the networks are setup, what is in a mobile and how some of the technologies such as CDMA, TDMA operate.

THE ADVANCED MOBILE PHONE SERVICE (AMPS)

The AMPS cellular system was very popular. However, with the gigantic increase in Subscribers in order of million each year, the AMPS cellular systems began to over loading capacity and became incapable of delivering sufficient air time to reach user .To overcome the problem, more effective multiple access techniques were invented. AMPS (Advanced Mobile Phone Service) were the first cellular mobile system in the United States. AMPS operate as an analog system using 30 kHz wide channels. An AMP was later enhanced to NAMPS (Narrowband Advanced Mobile Phone Service), a version of AMPS that uses 10 kHz channels and by doing so triples cellular capacity. AMPS were released in 1983 using the 800-MHz to 900-MHz frequency band and the 30 kHz bandwidth for each channel as a fully automated mobile telephone service. It was the first standardized cellular service in the world and is currently the most widely used standard for cellular communications. Designed for use in cities, AMPS later expanded to rural areas. It maximized the cellular concept of frequency reuse by reducing radio power output. The AMPS telephones (or handsets) have the familiar telephone-style user interface and are compatible with any AMPS base station. This makes mobility between service providers (roaming) simpler for subscribers.

AMPS are used throughout the world and are particularly popular in the United States, South America, China, and Australia. AMPS use frequency modulation (FM) for radio transmission. In the United States, transmissions from mobile to cell site use separate frequencies from the base station to the mobile subscriber. Since analog cellular was developed, systems have been implemented extensively throughout the world as first-generation cellular technology. In the second generation of analog cellular systems, Narrow Analog Mobile Phone Services (NAMPS) was designed to solve the problem of low calling capacity. NAMPS is a U.S. cellular radio system that combines existing voice processing with digital signalling, tripling the capacity of today's AMPS systems. The NAMPS concept uses frequency division to get three channels in the AMPS 30-kHz single channel bandwidth. NAMPS provides three users in an AMPS channel by dividing the 30-kHz AMPS bandwidth into three 10-kHz channels. This increases the possibility of interference because channel bandwidth is reduced.

EVOLUTION OF MULTIPLE ACCESSES: Satellites are always built with the intension that many users will share the bandwidth. The ability of the satellite to carry many signals at the same time is known as multiple accesses. It allows the communication capacity of the satellite to be shared among a large number of earth stations. The signals that earth stations transmit to a satellite may differ widely in there character but they can be sent through the same satellite using multiple access and multiplexing techniques. Multiplexing is the process of combining multiple signals into a single signal so that it can be processed by a single amplifier or transmitted over a single radio channel. The corresponding technique the recovers the individual signal back is called as demultiplexing. The distinction between multiplexing and multiple accesses is that multiplexing is done at one location whereas multiple accesses refer to the signals from a number of different geographic locations. Multiplexing is done at the earth stations then after modulating the signals at the earth stations it is transmitted to the satellite. At the satellite the signals will share the satellite transponder by different multiple access techniques. There are basically three multiple access techniques. They are:

Frequency division multiple access (FDMA)

Time division multiple access (TDMA)

Code division multiple access (CDMA)

The reason of using such techniques is to allow all users of a cellular system to be able to Share the available bandwidth in a cellular system simultaneously.

FREQUENCY DIVISION MULTIPLE ACCESS (FDMA)

Frequency division multiple access is a technique in which all the earth stations share the satellite transponder bandwidth at the same time but each earth station is allocated a unique frequency slot. Each station transmits its signals within that piece of frequency spectrum. FDMA was the first multiple-access technique deployed for cellular systems, the AMPS Cellular systems. In Figure below, it can be seen that each user is assigned a unique channel (frequency band). In other words, no other user can share the same frequency channel during the period of the Call using FDD (Frequency Division Duplexing). FDMA is an analog FM multiple-access technique, which transmission for any user is continuous. FDD is a frequency domain duplexing technique, that is, FDD provides two distinct frequency bands for forward (base station to mobile) and reverse (mobile to base station) for every user.

Figure1.2 FDMA channels

TIME DIVISION MULTIPLE ACCESS (TDMA)

Time division multiple access is a technique in which each earth station is allocated a unique time slot at the satellite so that signals pass through the transponder sequentially. TDMA causes delay in the transmission. TDMA is a digital multiple-access technique, which divides the radio spectrum in to time slots (channels), and only one user is allowed to either transmit or receive in each slot. In Figure below, it can be seen that each user occupies a particular time slot with in every frame, where a frame comprises of N times slots. In TDMA, time domain duplexing (TDD) and FDD are the two possible duplexing Techniques can be used. In TDMA/TDD systems, multiple users share the same frequency channel by taking turns in the time domain .TDD is a duplexing technique which sectors time instead of frequency to provide both the forward and reverse link channels. Each user is assigned a forward and reverse time slot in each frame and only allowed to access the radio channel in these assigned slots. Furthermore, time slots in a frame are divided equally between the forward and reverse link channels.

On the other hand, in TDMA /FDD systems, an identical or similar frame structure is used Entirely for either forward or reverse transmission, but in this case the carrier frequencies are Different for the forward and reverse links In TDMA systems, data is transmitted in a buffer-and burst method, which means Transmission for any user is non-continuous. Digital data and digital modulation is used With TDMA, leading to data being transmitted in discrete packets

Figure1.3 TDMA channels

CODE DIVISION MULTIPLE ACCESS (CDMA)

Code division multiple access is a technique in which all the earth stations transmit signals to the satellite on the same frequency and at the same time. The earth station transmits the coded spectrum which is then separated or decoded at the receiving earth station. Due to the daily demand of higher user capacity, FDMA and TDMA systems were unable to with stand high system over load and system problems. In particular, in FDMA systems, non-linear effects were observed when the power amplifiers or the power combiners operate at or near saturation for maximum power efficiency and adjacent-channel interference occurs.

Developed by Qualcomm Incin1995, CDMA is a recently developed digital multiple access technique. CDMA or Code Division Multiple Access was standardized by the Telecommunications Industry Association (TIA) as an Interim Standard (IS-95). Compared to TDMA and FDMA, CDMA is superior in terms of user capacity, signal quality, security, power consumption and reliability. It enables allocation of data in increments of 8 kilo bits per second with in the1.25MHz CDMA channel bandwidth. As a bench mark, CDMA is able to offer up to 6 times the capacity of TDMA, and about7-10 Times the capacity of analog technologies such as AMPS and FDMA, and now holds over 600 million subscribers worldwide. In CDMA systems, all user so that the system are allowed to use the same carrier frequency band May transmit simultaneously as depicted inFigure2.4, through the use of Direct-Sequence Spread Spectrum. Therefore, CDMA is also known as DSMA - Direct Spread Multiple Access.

Figure1.4 CDMA channels

A narrow band message is multiplied with a much larger bandwidth signal, which is called the Spreading signal, which is uncorrelated to the message signal. Then the transmitted signal will have a bandwidth, which is essentially equal to the bandwidth of the spreading signal the spreading signal is comprised of symbols that are defined by a pseudorandom sequence, which is known to both the transmitter and the receiver. These symbols are called chips. Typically the chip rate is much greater than the symbol rate of the original data sequence. The pseudorandom chip sequence is also known as the PN (Pseudo Noise) sequence as the power spectral density of the pseudorandom chip sequence looks approximately like white noise.

FREQUENCY HOPPED MULTIPLE ACCESS (FHMA)

Like CDMA, Frequency Hopped Multiple Access (FHMA) is another spread spectrum Technique which uses long PN codes or signal spreading and de spreading. FHMA is a digital multiple access technique, in which the carrier frequency of each user transmitting varies in a pseudo random fashion with in the system's available bandwidth. As a spread spectrum technique, FHMA allows users of the system to transmit simultaneously. FHMA allows multiple users to access the system spectrum simultaneously, as each user occupies a specific non-over lapping portion of the spectrum determined by their unique long PN code at a particular instance of time. In contrast, each CDMA user is allocated the same portion of the spectrum all the time. The major advantage of using FHMA over CDMA is the level of security which it provides, especially when a large number of channels are used.

Aims and Objectives:

The main aim of this project is to investigate the MMSE based decision feed back equalizers for multi users in DS-CDMA systems for minimizing the error in multiple access interference. The receiver type we use here is a non coherent type, which uses a certain window to generate non coherent decision variable. Varying the size of the window can provide the gain in the power, for this reason we opt to go for DFE. The equalizer here is used to suppress the multipath and MAI effects based on the received signals.

Project Deliverables: After completion of project these deliverables has to be achieved successfully

Results obtained from using the simulation package to study the effects of noise and multipath fading has on a received signal.

For an infinite number of feedback symbols, the optimum weight can be derived analytically

CHAPTER 2

Problem Analysis:

Problem analysis discusses the fundamental system requirements. The elementary system necessities and the environment for the development of the system were studied. It mainly focuses on the basic information like input, output and so on, which are very much essential for the task in order to get the predicted output.

A cellular communication system uses a large number of low power wireless transmitters to create cells-the basic geographic service area of a wireless communications system. Variable power level allows cells to be sized according to the subscriber density and demand within a particular region. As the population grows cells can be added to accommodate that growth. Frequencies used in the one cell cluster can be reused in the other cells. Direct Sequence (DS) Spread Spectrum System utilizes the PN-sequence as a code, the user with this special code doesn't suffer from interference disturbance in a high degree as a normal system do.

Pseudo Noise (PN) Sequences:

Spread spectrum systems are constructed in much the same way as conventional systems but there are differences. The main difference is that the system includes two identical pseudorandom sequence generators. One interfaces with the modulator at the transmitting end and the second which is located in the receiver. These two generators produce a pseudorandom or pseudo noise (PN) binary-valued sequence that is used to spread the transmitted signal in frequency at the modulator and to de spread the received signal in the receiver. This sequence is in our system in fact a sequence of random 1's and -1's that is white with good correlation properties. This sequence is still the same in all transmissions though, i.e. the PN-sequence of length 8 is always the same and so on. A critical factor of the system is that a time synchronization of the PN sequence generated at the receiver, and the PN sequence contained in the received spread-spectrum, signal must be achieved. The PN sequence generated at the modulator is used in conjunction with the PSK modulation to shift the phase of the PSK signal pseudo randomly, at a rate that is an even multiple of the bit rate.

Spreading of the Signal

The spreading of the signal is done by using the pseudo noise sequence. Let's say that a binary information sequence with an information rate of R bits per second is to be spread. The bit interval of the signal is Tb = 1/R seconds and the available channel bandwidth is Bc Hz, where Bc >> R.

At the modulator the bandwidth of the information signal is expanded to W = Bc Hz by shifting the phase of the transmitted signal pseudo randomly at a rate of W times per second according to the pattern of the PN generator. The effective bit rate will therefore depend on the available bandwidth Bc, and the length of the PN-sequence N as

The information-bearing signal can be expressed as

Where and gt(t) is a rectangular pulse of duration Tb. This signal is multiplied by the signal from the PN sequence generator. This sequence can be expressed as where {cn} represents the binary PN code sequence of ±1 and p(t) is a rectangular pulse of duration Tc.

org.bmp

FIGURE 2.1Spreading of the signal

The product signal v(t)c(t) is then used to amplitude modulate the carrier Acos(2fct) and, thus generate the DSB-SC signal.

Because v(t)c(t) = ±1 for any t, the carrier-modulated signal may also be expressed as u(t)=Accos(2fct + (t))

where (t) = 0 when v(t)c(t) = 1 and (t) =  when v(t)c(t) = -1. Therefore it can easily be seen that the transmitted signal is actually a BPSK-modulated signal. This procedure can also be viewed in figure

+1

-1

t

+1

-1

t

+1

-1

t

c(t)

v(t)c(t)

v(t)

PN signal

Product Signal

Data signal

Figure 2.2

The rectangular pulse p(t) is commonly known as a chip, and its time duration Tc is called the chip interval. And analogously the expression 1/Tc is called the chip rate and is approximately the same as the bandwidth W of the transmitted signal. The ratio of the bit interval Tb to the chip interval Tc is expressed as where Lc is usually chosen to be an integer. In other words, Lc is the number of chips of the PN code sequence per information bit. In the system Lc can take on three different values, namely 8, 16 and 32. A lesser value will be too small to be effective against interference and a larger value. The de-spreading of the signal is performed in the receiver by first multiplying it with a replica of the waveform c(t) generated by the PN code sequence generator. This generator is synchronized to the PN code in the received signal. Thus we have since c2(t) = 1 for all t. The resulting signal occupies a bandwidth of approximately R Hz, which is the bandwidth of the information-bearing signal

The resistance towards interfering signals is one of the CDMA based communication system biggest benefits. In our project the resistance against interference is one of the major parameters to deal with. A sinusoidal signal is to be used as a disturbance when the transmission is performed, suppose that the received signal is

Where i(t) denotes the interference. The de spreading operation at the receiver yields

The effect to multiplying the interference i(t) with c(t), is to spread the bandwidth of i(t) to W Hz. For example, consider the sinusoidal interfering signal

Where fJ is a frequency with in the bandwidth of transmitted signal. The multiplication with c(t) results in a wideband interference with a power spectral density J0 = PJ/W, where PJ = A2J/2 is the average power of the interference. The desired signal is demodulated by a matched filter or a correlator with a bandwidth of R. This means that the total power in the interference at the output of the demodulator is

Therefore, the power in the interfering signal is reduced by an amount equal to the bandwidth expansion factor, W/R. This factor, W/R = Tb/Tc = Lc is called the processing gain of the spread-spectrum system. Thus the effect of the interfering signal on the transmission is significantly reduced.

Building Blocks of the Communication System

In this section the focus will be on deseparate building blocks of the discrete communication system. There will not be a complete mathematical account of all the different blocks but rather a description of what the blocks do and how they function. For a more complete mathematical description the consultation could be helpful.

One of the most important parts in this CDMA communication system is the PN-generator, which performs the signal spreading.

The PN-generator

When the information sequence has been mapped to the data sequence , it is passed through a base band modulator, depicted below in figure , which outputs a signal centred at the DC frequency.

The base band Modulator

The first operation that is done in the modulator is an up sampling of the data sequence by a factor, i.e. between every symbol in zeros are inserted. This up sampling process is done in order to introduce sufficient space between the symbols so that they can be separated from each other in the receiver and to achieve a much smoother signal. The up sampled data sequence is then passed through the pulse-shaping filter, which outputs a base band pulse for every symbol in the data sequence.

In this way the base band modulator modulates the data sequence as a series of pulses and thereby outputs the base band signal Sbb. The amplitude of each pulse is determined by the corresponding symbol. Since in most communication systems, especially in wireless ones, the available bandwidth is very limited, it is of great importance that the pulse-shaping filter outputs pulses with good spectral properties. In other words we want a pulse-shaping filter with an impulse response that falls off relatively smooth in the time-domain and thereby implies band-limited spectral properties in the frequency-domain. One impulse response that is commonly used in real-time applications and satisfies the requirements above is the raised cosine function

,

Where the parameters and determines the bandwidth of the impulse response of the transmitting filter. The bandwidth is given by In other words the bandwidth of p(n) can be varied by varying and Lt.

If a choice of is made, reduces to a sinc-pulse with a rectangular frequency response and a bandwidth given by

But if, a frequency response with a much smoother roll off is obtained, i.e. an impulse response that decays faster in the time-domain.

But if , a frequency response with a much smoother roll off is obtained, i.e. an impulse response that decays faster in the time-domain.

To translate the frequency band of the base band signal to the pass band of the channel, i.e. to transform the base band signal to a band pass signal, modulation by a carrier wave is employed. This is accomplished by multiplying the base band signal with a sinusoidal carrier wave with frequency,

2.bmp

Carrier wave Modulation

This operation has the effect that the spectrum of the base band signal is now shifted in frequency and centred on the carrier frequency, i.e. the base band signal has been transformed to the pass band signal. The figure 4.8 shows the spectrum of the pass band signal.

QUADRATURE MODULATION

The final processing before transmitting the user's information involves Quadrature modulation of the Walsh coded data chip stream. Quadrature modulation allows easy acquisition and synchronization at the mobile receiver. Quadrature modulation involves separating the incoming data chip stream into an L data chip stream and a Q data chip stream and mixing each with their corresponding short PN sequences. The IQ modulation block carries out the In phase and Quadrature phase modulation of the Data chips stream from the Walsh coding block before it is transmitted from the base station to the mobile. The Walsh coded data chips stream enters the IQ modulator block, and get divided into the In Phase Stream, which contains the odd number indexed bits, and the Quadrature phase Stream, Which contains the even indexed bits. Then the data bits in each of the streams get modulated by the respective pilot PN sequences. Each of the I and Q pilot PN sequence generators are 15-stage shift registers. The initial state of the I and Q pilot PN sequence shift registers is defined as an output of a"One"after14 consecutive "Zeros". The I and Q pilot PN sequences are generated by repeatedly running a FOR-LOOP for 24576 times and obtaining the output of the irrespective shift register at each iteration.

The feedback value of each shift register is calculated by performing modulo-2 addition of Bit value of selected stages of the shift registers in each iteration. Bit values in the shift Registers stages are shift redone stage to the right after each iteration. The output signal vector Of the IQ modulation block consists of 12288 elements, with each element consists of a real and imaginary component. Finally, the transmitter transmits the output signal in a number of Multi paths, and with different propagation path distances. The band pass signal is transmitted over the acoustic channel, which distorts the signal i.e. introduces ISI, and adds white Gaussian noise.

s(n)

h(n)

n(n)

r(n)

Figure 2.3 Channel adds white Gaussain noise

MULTIPATH FADING CHANNEL

The communication channel is the medium which the transmitting radio signal goes through in order to reach the receiver. The channel can be modelled as a linear filter with a time varying channel impulse response. A channel impulse response describes the amplitude and phase effects that the channel will impose on the transmitting radio signal, as it transmits through the medium. IS-95 CDMA communication channels are often modelled as a multipath fading channel, as it is the best modelling for a mobile communication channel. The term fading describes the small-scale variation of a mobile radio signal. As each transmitting signal is represented by a number of multipaths and each having different propagation delays, the channel impulse response is different for each multipath. Therefore, not only the channel response is time varying, the channel response is also functional dependent on the propagation delay.

Hence, the channel impulse response should actually be summarized as h (t, t), which't' is the specific time instance, and't' is the multipath delay for a fixed value of't'. As a result, the received signal in a multipath channel consists of a number of attenuated, time delayed, and phase shifted versions of the original signal, and the base band impulse response of a multipath channel can be written as

h (bt ,t) = Æ’a (t,t )exp[ j(2pf t (t) +f (t,t ))]d (t -t (t))

where a i(t,t ) and t i(t) are the amplitude and delay, respectively, of the ith multipath component at time t. The phase term 2pf t (t) +f i (t, t) represents the phase shift due to free space propagation of the i multipath component, plus any additional phase shift which it encountered in the channel. And d (t -t i (t)) is the unit impulse function for the multipath component with delay t and at time instance t. The communication channel is implemented as a multipath channel. It is represented by a Number of randomly distributed objects, and each with an amplitude and phase gain. When a Multipath signal reflects on one of these objects along its propagation, the multipath signal Experiences amplitude and phase attenuations according the respective gains of the object, Due to the interaction between the multipath signal and the object. The objects are randomly generated and distributed in the channel. Both the amplitude and Phase gain of each object are manually assigned.

Chapter 3

Problem Solutions:

In last chapter the problems and issues were studied. The main aim of this section of the report was to discuss the solutions how this task has been completed by involving the selected components from the analysed ones and solution of the available inputs and outputs.

The first thing that is done in the receiver is to translate the frequency spectrum of the received band pass signal, centred around the carrier frequency , back to the base band, i.e. centred around DC-frequency. This is accomplished by multiplying the received signal with the expression 2cos (2fct/fs), followed by a low pass filtering of the resulting signal. This filtering is done in order to remove the double frequency terms introduced by the multiplication operation.

Figure 3.1 Demodulation of the received band pass signal

The signal resulting from these operations, , is called the low pass (base band) equivalent signal of the received signal . The low pass equivalent is the band pass signal shifted to zero frequency.

Down sampling and Equalization

The acoustic channel introduces ISI and the low pass equivalent is thus a distorted version of have been introduced.

Where

If we try to extract the transmitted data sequence from by sampling at the sampling rate we obtain

Where the first term is the desired symbol, scaled with the constant c(0), the second term is the ISI contribution introduced by the channel and last term is a sample noise process. An optimal detector is given by the MAP-detector which when assuming equi probable signal alternatives is equivalent with a ML-detector with decision threshold zero. Thus, assuming that the symbol was sent, the contribution from the ISI and the noise will result in a detection error if

and similar if was sent a detection error occur if the sum above is greater than zero. The acoustic channel introduces an ISI and this, as well as the noise, has to be reduced before a detector can be employed to detect the received symbols. An equalizer, shown in figure below can do this

Eq

rd(n)

Figure 3.2The equalizer

Before the signal enters the equalizer it is down sampled with a factor L1, i.e. only every L1:th value of the signal is kept. The reason for this down sampling is that a lot of signal processing and computations are being done in the equalizer and to do this in a less time consuming manner as possible, it is important that the equalizer gets less data to process.

When choosing the down sampling factor L1 a trade-off has to be considered. For a large value on, fewer computations have to be done in the equalizer, which implies less delay. But on the other hand, the more samples ignored, the more information is lost which in turn leads to a greater distortion of the signal. The experiments made have shown that a good result is reached with L1 = 4. The down sampled version of is then passed through the equalizer, in which another down sampling is made, this time with the factor L2 =2, which must be chosen so that the relation Lt = L1L2 is satisfied. By this second down sampling, the output sequence from the equalizer., is at symbol rate. The equalizer is implemented as a FIR-filter and to compute the filter coefficients various criterions can be used. We have chosen to implement an MMSE-equalizer, i.e. the filter coefficients are chosen so that the difference (error) between the desired transmitted data sequence and the estimated data sequence is minimized in the mean-square sense.

Note that when the training of the equalizer occurs the data sequence d(n) is a training sequence that is known to the receiver prior to the transmission.

The error is defined as

And the filter coefficients should be chosen so that the mean square error is

Minimized. Furthermore, in this communication system a time variant channel (a channel whose impulse response changes with the time) has been assumed to exist. An adaptive algorithm to compute the equalizer filters coefficients, i.e. something that adaptively updates the filter coefficients when the channel change is to be used to conquer this. For this to be possible a decision to include a small training sequence in each transmitted data block has been made. This will help to train the equalizer so that any necessary changes in the equalizer can take place.

Therefore, a suitable algorithm for computing and continuously updating the filter coefficients is needed. The normalized least mean squares (NLMS) algorithm is an algorithm that is well suited for what this system needs. For a complete description of the NMLS algorithm, the reader is referred to.

The NMLS algorithm:

Where wn are the filter coefficients and is a small positive number used to prevent that the denominator of becomes zero and thus

The difference between the NLMS algorithm and the LMS type is that the adjustment term is normalized with the squared norm of the received signal vector R(n).

Feedback Equalizer

Suppressing inter symbol interference, or equivalently removing the effect of a frequency selective channel is known as equalization. In the process, the spectrum of the received signal becomes flat, hence the name equalization. The intersymbol interference can be quite severe. As an example, consider the QPSK modulated signal, transmitted over a four-tap channel. The received complex-valued sampled signal Introduction is displayed before and after equalization. Without intersymbol interference, the received signal should appear as small clouds, centred around the points in the symbol constellation, depicted.

Figure 3.3 Scatter plots of the received signal before and after equalization. Prior to equalization, it is impossible to see that the transmitted signal is QPSK modulated.

Here we have to compensate for the intersymbol interference. Any attempt to detect the transmitted symbols without such compensation would be futile: There is no trace of the QPSK constellation. The first attempt to solve the equalization problem was the linear transversal equalizer, which is depicted. The received sampled base band signal, corrupted by ISI and noise, is used as input to an FIR filter. The coefficients of this filter are adjusted to produce an estimate of the transmitted symbol.

Figure 3.4 Block Diagram of a Decision Feedback Equalizer (DFE)

Figure 3.4 shows a simplified block diagram of a DFE where the forward filter and the feedback filter can each be a linear filter, such as transversal filter. The nonlinearity of the DFE stems from the nonlinear characteristic of the detector that provides an input to the feedback filter. The basic idea of a DFE is that if the values of the symbols previously detected are known, then ISI contributed by these symbols can be cancelled out exactly at the output of the forward filter by subtracting past symbol values with appropriate weighting. The forward and feedback tap weights can be adjusted simultaneously to fulfil a criterion such as minimizing the MSE.

The advantage of a DFE implementation is the feedback filter, which is additionally working to remove ISI, operates on noiseless quantized levels, and thus its output is free of channel noise.

Figure 3.5 The Scalar Decision Feedback Equalizer

An equalizer that performs almost as well as the MLSE at a complexity only slightly higher than the linear equalizer is the decision feedback equalizer (DFE). Thus, the DFE - depicted in Figure above constitutes an attractive compromise between complexity and performance. The received signal is here used as an input to the feed forward filter. From the output of the feed forward filter, the interference from previously detected symbols are removed via the output of the feedback filter.

The difference between these two filter outputs constitutes an estimate of the transmitted symbol. This estimate is sometimes called soft, since it is not yet quantized. The decision device quantizes the soft estimate and the resulting hard estimate is used as input of the feedback filter to remove its effect on future symbol estimates and the constant known as the decision delay. It specifies how many future measurements which are processed before a decision is made on the present symbol. For a thorough understanding of the equalization process, we will study the impulse response between the transmitted symbols and the various signals in Figure above Starting at the channel output, we, of course, obtain the impulse response of the channel, as depicted in Figure below

.

.

Figure3.6: The impulse response of the channel.

The partly equalized channel at the output of the feed forward filter is depicted in Figure 1.8. The purpose of the feed forward filter in a DFE is to suppress the first "O" taps in the equalized channel impulse response, the so-called precursor ISI. The feed forward filter must also try to keep tap Ã-, the so-called reference tap close to unity.

Figure3.7 The signal at the output of the feed forward filter: The precursor has been suppressed, whereas the reference tap is close to one and the remaining taps are arbitrary.

The feedback filter will be tuned so that its impulse response matches the post cursor ISI, that is, the taps "O" .and so forth in the partly equalized channel. When the output of the feedback filter is subtracted from the output of the feedback filter, we obtain the impulse response shown in Figure below. This impulse response relates the symbol estimate to the transmitted symbols.

Figure 3.8 the Complete Equalized Channel

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