Concept Of Signal Spreading In Cdma Computer Science Essay

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Spread-spectrum communication systems have been developed since the mid-1950. The initial application was limited to military anti-jamming, guidance systems, and experimental multi-path systems. A definition of spread spectrum that adequately reflects the characteristics of this technique is as follows: Spread spectrum is a means of transmission in which the signal occupies a bandwidth in excess of the minimum necessary to send the information.

There are three ways to spread the bandwidth of the signal:

Frequency hopping: The signal is rapidly switched between different frequencies within the hopping bandwidth pseudo-randomly, and the receiver knows before hand where to find the signal at any given time.

Time hopping: The signal is transmitted in short bursts pseudo-randomly, and the receiver knows beforehand when to expect the burst.

Direct sequence: The digital data is directly coded at a much higher frequency. The code is generated pseudo-randomly, the receiver knows how to generate the same code, and correlates the received signal with that code to extract the data.

Figure 4.1 Shows the Spread Spectrum in the CDMA.

The direct-sequence spread-spectrum signal is generated by multiplying the message signal by a pseudorandom noise signal In most cases, the PN signal is a very high rate, Non Return-to-Zero (NRZ) pseudorandom sequence that chops the modulated message waveform into chips, Hence, the rate of the secondary modulating waveform is called the chip rate, while the rate of the message signal is designated the bit rate. The two modulation processes produce different bandwidths, namely, R for the modulated message signal and W for the relatively wide spread-spectrum waveform. Note that the secondary modulation does not increase the overall power of the message signal but merely spreads it over a wider bandwidth. Figure 4.2 show both the Spreading and the Dispreading techniques.

Figure 4.2 shows both the Spreading and the Dispreading Techniques in (a) the Transmitter Side of System and (b) the Receiver Side of System.

4.2 Codes in CDMA

IS-95 and IS-2000 use two particular codes that are really m-sequences but have special names and uses. These are called long codes and short codes.

4.2.1 Long code

The Long Codes are 2^42 bits (created from a LFSR of 42 registers) long and run at 1.2288 Mb/s. The time it takes to recycle this length of code at this speed is 41.2 days. It is used to both spread the signal and to encrypt it. A cyclically shifted version of the long code is generated by the cell phone during call setup. The shift is called the Long Code Mask and is unique to each phone call. CDMA networks have a security protocol called CAVE that requires a 64-bit authentication key, called A-key and the unique ESN (Electronic Serial Number, assigned to mobile based on the phone number). The network uses both of these to create a random number that is then used to create a mask for the long code used to encrypt and spread each phone call. This number, the long code mask is not fixed but changes each time a connection is created. There is a Public long code and a Private long code. The Public long code is used by the mobile to communicate with the base during the call setup phase. The private long code is one generated for each call then abandoned after the call is completed.

4.2.2 Short code

The short code used in CDMA system is based on a m-sequence (created from a LFSR of 15 registers) of length 2^15 ¿½ 1 = 32,767 codes. These codes are used for synchronization in the forward and reverse links and for cell/base station identification in the forward link The short code repeats every 26.666 milliseconds. The sequences repeat exactly 75 times in every 2 seconds. We want this sequence to be fairly short because during call setup, the mobile is looking for a short code and needs to be able find it fairly quickly. Two seconds is the maximum time that a mobile will need to find a base station, if one is present because in 2 seconds the mobile has checked each of the allowed base stations in its database against the network signal it is receiving. Each base station is assigned one of these codes. Since short code is only one sequence, how do we assign it to all the stations? We cyclically shift it. Each station gets the same sequence but it is shifted. From properties of the m-sequences, the shifted version of a m-sequences has a very small cross correlation and so each shifted code is an independent code. For CDMA this shift is 512 chips for each adjacent station. Different cells and cell sectors all use the same short code, but use different phases or shifts, which is how the mobile differentiates one base station from another. The phase shift is known as the PN Offset. The moment when the Short code wraps around and begins again is called a PN Roll. If I call the word ¿½please¿½ a short code, then I can assign, ¿½leasep¿½ to one user, ¿½easepl¿½ to another and so on. The shift by one letter would be my PN Offset. So if I say your ID is 3, then you would use the code ¿½aseple¿½. A mobile is assigned a short code PN offset by the base station to which it is transmitting. The mobile adds the short code at the specified PN offset to its traffic message, so that the base station in the region knows that the particular message is meant for it and not to the adjacent base station. This is essentially the way the primary base station is identified in a phone call. The base station maintains a list of nearby base stations and during handoff, the mobile is notified of the change in the short code. There are actually two short codes per base station. One for each I and Q channels to be used in the quadrature spreading and despreading of CDMA signals.

4.2.3 Walsh codes

In addition to the above two codes, another special code, called Walsh is also used in CDMA. Walsh codes do not have the properties of m-sequences regarding cross correlation.. IS-95 uses 64 Walsh codes and these allow the creation of 64 channels from the base station. In other words, a base station can talk to a maximum of 64 (this number is actually only 54 because some codes are used for pilot and synch channels) mobiles at the same time. CDMA 2000 used 256 of these codes. Walsh codes are created out of Haddamard matrices and Transform. Haddamard is the matrix type from which Walsh created these codes. Walsh codes have just one outstanding quality. In a family of Walsh codes, all codes are orthogonal to each other and are used to create channelization within the 1.25 MHz band. Here are first four Hadamard matrices. The code length is the size of the matrix. Each row is one Walsh code of size N. The first matrix gives us two codes; 00, 01. The second matrix gives: 0000, 0101, 0011, 0110 and so on.

In general each higher level of Hadamard matrix is generated from the previous by the

4.2.4 Hadamard transform

Where is the inverse of HN.

Their main purpose of Walsh codes in CDMA is to provide orthogonality among all the users in a cell. Each user traffic channel is assigned a different Walsh code by the base station. IS-95 has capability to use 64 codes, whereas CDMA 2000 can use up to 256 such codes. Walsh code 0 (which is itself all 0s) is reserved for pilot channels, 1 to 7 for synch and paging channels and rest for traffic channels. They are also used to create an orthogonal modulation on the forward link and are used for modulation and spreading on the reverse channel. Orthogonal means that cross correlation between Walsh codes is zero when aligned. However, the auto-correlation of Walsh-Hadamard code words does not have good characteristics. It can have more than one peak and this makes it difficult for the receiver to detect the beginning of the codeword without an external synchronization. The partial sequence cross correlation can also be non-zero and un-synchronized users can interfere with each other particularly as the multipath environment will differentially delay the sequences. This is why Walsh-Hadamard codes are only used in synchronous CDMA and only by the base station which can maintain orthogonality between signals for its users.

4.3 Channels in CDMA

Figure 4.3: Forward Channel

The communications between the mobile and the base station takes place using specific channels. Figure below shows the architecture of these channels. The forward channel (from base station to mobile) is made up of the following channels:

1- Pilot channel (always uses Walsh code W0) (Beacon Signals)

2- Paging channel(s) (use Walsh codes W1-W7)

3- Sync channel (always uses Walsh code W32)

4- Traffic channels (use Walsh codes W8-W31 and W33-W63)

The reverse channel (from mobile to base station) is made up of the following channels:

1- Access channel

2- Traffic channel

4.3.1 Forward Channel description

A base station can communicate on up to 64 channels. It has one pilot signal, one synch channel and 8 paging channels. The remaining are used for traffic with individual mobiles. All data is sent simultaneously.

Figure 4.4: Forward channel is the transmission of all traffic from the base station within its cell.

4.3.2 Pilot Channel

Let¿½s start with how the base station establishes contact with the mobiles within its cell. It is continually transmitting an all zero signal, which is covered by a Walsh code 0, a all 0¿½s code. So what we have here is a one very long bit of all zeros. For this reason, the pilot channel has very good SNR making it easy for mobiles to find it. This all zero signal is then multiplied by the base stations¿½ short code, which if you recall is the same short code that all base station use, but each with different PN offset. Pilot PN Offsets are always assigned to stations in multiples of 64 chips, giving a total of 512 possible assignments. The 9-bit number that identifies the pilot phase assignment is called the

4.3.3 Pilot Offset.

This signal is real so it only goes out on the I channel, and is up-converted to the carrier frequency which in the US is 845 MHz. On the receive side, the mobile picks up this signal and notes the base station that is transmitting it. Here is a question, if the short code is cyclical, how does the receiver know what the phase offset is. Do not all the signals from all the other nearby base stations look the same? Yes, and the mobile at this point does not know which base station it is talking to, only that it has found the network. To determine of all the possible base station and there can 256 of them, each using a 512 chip shifted short code, the network uses the GPS signal and timing. The zero offset base station aligns its pilot transmission with every even second time tick of GPS. So let¿½s say that your mobile is in the cell belonging to a base station with PN offset ID of 10. That means that is will start its transmission 10 x 512 chip = 5120 chips after every even second time tick. So when the mobile wakes up and looks at it time, it knows exactly where each base station short code should be. Then all it has to do is to do a correlation of the bits it is seeing with each of the 256 possible sequences. Of course, it tries the base station where it was last but if it has been moved then theoretical it will have to go through all 256 correlations to figure out where it is. But it does do it and at the end of the process, it knows exactly which of the base stations it is hearing.

Figure 4.5: The Mobile Looks for the Code that Aligns with GPS Timing.

It picks off the code received at this time, does a correlation with stored data and knows which base station it has found

4.3.4 Synch Channel

The Synch channel information includes the pilot offset of the pilot the mobile has acquired. This information allows the mobile to know where to search for the pilots in the neighbor list. It also includes system time, the time of day, based on Global Positioning Satellite (GPS) time. The system time is used to synchronize system functions. For instance, the PN generators on the reverse link use zero offset relative to the even numbered seconds in GPS time. However, the mobiles only know system time at the base stations plus an uncertainty due to the propagation delay from its base station to the mobile's location. The state of the long code generator at system time is also sent to the mobile in the Synchronization message. This allows the mobile to initialize and run its long code generator very closely in time synchronism with the long code generators in the base stations. The Synchronization message also notifies the mobile of the paging channel data rate, which may be either 4800 or 9600 bits/sec. The data rate of this channel is always 1200 bps.

4.3.5 Paging Channel

Now the mobile flashes the name of the network on its screen and is ready to receive and make calls. Your paging channel may now be full of data. It may include a ring tone or a ¿½voicemail received¿½ message. The data on the paging channel sent by the base station, includes mobile Electronic Serial Identification Number (ESIN), and is covered by a long code. How does the mobile figure out what this long code is? At the paging level, the system uses a public long code. This is because it is not talking to a specific mobile, it is paging and needs to reach all mobiles. When the correct mobile responds, a new private long code will be assigned at that time before the call will be connected. The mobile while scanning the paging channel recognizes its phone number and responds by ringing. When you pick up the call, an access message goes back to the base station. The mobile using Qualcomm CDMA generatse a 18-bit code. The mobile sends this authentication sequence to the base station during the sync part of the messaging protocol. The base station checks the authentication code before allowing call setup. It then issues a random number to the mobile, which the mobile uses in the CAVE algorithm to generate a call specific long code mask. At the same time, the base station, will also do exactly that. The two now have the same long code with which to cover the messages.

4.3.6 Traffic Channel

The base station can transmit traffic data to as many as 54 mobiles at the same time. It keeps these channels separate by using Walsh codes. This is a code division multiplexing rather than a frequency based channelization. Walsh codes are used only by the base station and in this fashion; it is a synchronous CDMA on the forward link, whereas on the return link it is asynchronous CDMA, because there is no attempted separation between the various users. But the use of m-sequences for spreading, the quality of orthogonality although not perfect is very good. The traffic channel construct starts with baseband data at 4.8 kbps. It is then convolutionally encoded at rate of ¿½, so the data rate now doubles to 9.6 kbps. Symbol repetition is used to get the data rate up to 19.2 kbps. All information rates are submultiples of this rate. Data is then interleaved. The interleaving does not change the data rate, only that the bits are reordered to provide protection against burst errors. Now at this point, we multiply the resulting data sequences with the long code, which starts at the point determined by the private random number generated by both the base station and the mobile jointly. This start point is call-based and changes every time. Mobiles do not have a fixed long code assigned to them. Reverse CDMA Channel can have up to 242 -1 logical channels or the total number of calls that can be served are 17179869184.

Now the data is multiplied by a specific Walsh codes which is the nth call that the base station is involved in. Mobile already knows this number from the paging channel. The base station then combines all its traffic channels (each covered by a different Walsh code) and all paging channels (just 8) and the one pilot channel and one synch channel adds them up, does serial to parallel conversion to I and Q channels. Each is then covered by a I and a Q short code and is QPSK modulated up to carrier frequencies and then transmitted in the cell.

4.3.7 Reverse Channels

In IS-95, there are just two channels on which the mobile transmits, and even that never simultaneously. It is either on the access channel or it is transmitting traffic. The channel structure is similar but simpler to the forward channel, with the addition of 64-ary modulation.

Figure 4.6: Reverse Channel - from mobile to base station communication 64-ary modulation

This block takes a group of six incoming bits (which makes 26 = 64 different bit sequences of 6 bits) and assigns a particular Walsh code to each. We know that each Walsh code sequence is orthogonal to all the others so in this way, a form of spreading has been forced on the arbitrarily created symbols of 6 bits. And this spreading also forces the symbols to be orthogonal. It is not really a modulation but is more of a spreading function because we still have not up converted this signal to the carrier frequency. After this, a randomization function is employed to make sure we do not get too many 0¿½s or 1¿½s in a row. This is because certain Walsh codes have a lot of consecutive 0¿½s. Next comes multiplication with the long code starting at a particular private start point. Then comes serial to parallel conversion, and application of baseband filtering which can be a Gaussian or a root cosine shaping. Then the Q channel (or I, it makes no difference) is delayed by half a symbol, as shown below. The reason this is done is to turn this into an offset QPSK modulated signal. The offset modulated signal has a lower non-linearity susceptibility and is better suitable to being transmitted by a class C amplifier such as may be used in a CDMA cell phone. From there, each I and Q channel is multiplied by the Rf carrier, (a sine and a cosine of frequency fc) and off the signal goes to the base station. On the demodulation side, the most notable item is the Rake receiver. Due to the presence of multipath, Rake receivers which allow maximal combining of delayed and attenuated signal, make the whole thing work within reasonable power requirements. Without Rake receivers, your cell phone would not be as small as it is.

4.3.8 CDMA Codes Summary

Table 4.1: CDMA Codes

Type of sequence How many Length Special properties Forward link function Reverse link function

Walsh codes 64 64 chips Mutually Orthogonal Logical channel (user) identification and spreading Orthogonal modulation

Short PN Sequences 2 215 Orthogonal with itself at any time shift value except 0 Base station identity(distinguish cells and sectors) Synchronization and quadrature spreading.

Long PN Sequences 1 242-1 Near-orthogonal if shifted Data scrambling (encryption) Distinguish users and spreading.

4.4 PN-Code Generation

Codes in CDMA technology is one of the main issues of concern in the study of digital communications as considered. Although understanding the importance of efficient bandwidth and power for any signal, which are considered as a primary communication resources, there are situations where it is necessary to sacrifice this efficiency in order to meet certain other design objectives. For example, a system may be need to provide a form of secure communication in a hostile environment in so that the transmitted signal is not easily detected or recognized by unwanted listeners. This needs is satisfied by a class of signaling techniques, which are known as spread-spectrum modulation. s

The main advantage of spread-spectrum communication system is its ability to reject interference, whether unintentional interference by another user at the same time in an attempt to transmit through the channel, or intentional interference from a hostile transmitters to jamming the channel.

The definition of spread-spectrum modulation may be divides in two parts:

I. Spread spectrum is a means of transmission in which the data sequence occupies a bandwidth in excess of the minimum bandwidth necessary to send it. q

II. The spectrum spreading is accomplished before transmission through the use of a code that is independent of the data sequence. The same code is used in the receiver (operating in synchronism with the transmitter) to dispread the received signal so that the original data sequence may be recovered. a

Although standard modulation techniques such as frequency modulation and pulse-code modulation do satisfy part I of this definition, they are not spread-spectrum technique because they do not satisfy part II of the definition. s

Spread-spectrum modulation was originally developed for military application where resistance to jamming (interference) is of major concern. However, there are civilian applications that also benefit from the unique characteristics of spread-spectrum modulation. For example, it can be used to provide multipath rejection in a ground-based mobile radio environment. Yet another application is in multiple-access communications in which a number of independent users are required to share a common channel without an external synchronizing mechanism; here, for example, we may mention a ground-based radio environment involving mobile vehicles that must communicate with a central station. a

In this chapter, we discuss principles of spread-spectrum modulation, with emphasis on direct-sequence and frequency-hopping techniques. In a direct-sequence spread spectrum technique, two stages of modulation are used. First, the incoming data sequence is used to modulate a wideband code. This code transforms the narrowband data sequence: into a noise like wideband signal. The resulting wideband signal undergoes a second modulation using a phase-shift keying technique. In a frequency-hop spread-spectrum technique, on the other hand, the spectrum of a data-modulated carrier is widened by changing the carrier frequency in a pseudo-random manner. For their operation, both of these techniques rely on the availability of a noise like spreading code called a pseudo-random or pseudo-noise sequence. Since such a sequence is basic to the operation of spread-spectrum modulation, it is logical that we begin our study by describing the generation and properties of pseudo-noise sequences.

4.4.1 Pseudo- Noise Sequences:

A pseudo-noise (PN) sequence is a periodic binary sequence with a noise like waveform that is usually generated by means of a feedback shift register, a general block diagram of which is shown in Figure 4.7. A feedback shift register consists of an ordinary shift register made up of m flip-flops (two-state memory stages) and a logic circuit that are interconnected to form a multi loop feedback circuit. The flip-flops in the shift register are regulated by a single timing clock. At each pulse (tick) of the clock, the state of each flip-flop is shifted to the next one down the line. With each clock pulse the logic circuit computes a Boolean function of the states of the flip-flops. The result is then feedback as the input to the first flip-flop, thereby preventing the shift register from emptying. The PN sequence so generated is determined by the length m of the shift register, its initial state, and the feedback logic.

Let sj(k) denote the state of the kth flip-flop after the kth clock pulse; this state may be represented by symbol 0 or 1. The state of the shift register after the kth clock pulse is then defined by the set {s1(k), s2(k), . . . , sm(k)), where k 0. For the initial state, k is zero. From the definition of a shift register, we have


where s0(k) is the input applied to the first flip-flop after the kth clock pulse. According to the configuration described in Figure 4.7, s0(k) is a Boolean function of the individual states s1(k), s2(k),. . ., sm(k). For a specified length m, this Boolean function uniquely determines the subsequent sequence of states and therefore the PN sequence produced at the output of the final flip-flop in the shift register. With a total number of m flip-flops, the number of possible states of the shift register is at most 2m. It follows therefore that the PN sequence generated by a feedback shift register must eventually become periodic with a period of at most 2m.

A feedback shift register is said to be linear when the feedback logic consists entirely of rnodulo-2 adders. In such a case, the zero state (e.g., the state for which all the flip-flops are in state 0) is not permitted. We say so because for a zero state, the input s0(k) produced by the feedback logic would be 0, the shift register would then continue to remain in the zero state, and the output would therefore consist entirely of Os. Consequently, the period of a PN sequence produced by a linear feedback shift register with m flip-flops cannot exceed 2m - 1. When the period is exactly 2m - 1, the PN sequence is called a maximal- length-sequence or simply m-sequence.

Example 4.1: Consider the linear feedback shift register shown in Figure 4.8, involving three flip-flops. The input s0 applied to the first flip-flop is equal to the modulo-2 sum of s1 and s3. It is assumed that the initial state of the shift register is 100 (reading the contents of the three flip-flops from left to right). Then, the succession of states will be as follows: 100, 110, 111, 011, 101, 010, 001, 100,¿½¿½

The output sequence (the last position of each state of the shift register) is therefore

00111010 ¿½

which repeats itself with period 23 - 1 = 7.

Note that the choice of 100 as the initial state is arbitrary. Any of the other six permissible states could serve equally well as an initial state. The resulting output sequence would then simply experience a cyclic shift.

Properties of Maximal Length Sequences

Maximal-length sequences have many of the properties possessed by a truly random binary sequence. A random binary sequence is a sequence in which the presence of binary symbol 1 or 0 is equally probable. Some properties of maximal-length sequences are follows:

1. In each period of a maximal-length sequence, the number of 1's is always one more than the number of 0's. This property is called the balance property.

2. Among the runs of 1's and of 0's in each period of a maximal-length sequence, on half the runs of each kind are of length one, one-fourth are of length two, one-eighth of length three, and so on as long as these fractions represent meaningful numbers runs. This property is called the run property. By a ¿½run¿½ we mean a subsequence of identical symbols (1's or 0's) within one period of the sequence. The length of t subsequence is the length of the run. For a maximal-length sequence generated by linear feedback shift register of length m, the total number of runs is (N + 1)/2, where N=2m-1.

3. The autocorrelation function of a maximal-length sequence is periodic and binary-valued. This property is called the correlation property.

The period of a maximum-length sequence is defined by

N = 2m -1 (4.2)

where m is the length of the shift register. Let binary symbols 0 and 1 of the sequence be denoted by the levels -1 and +1, respectively. Let c(t) denote the resulting waveform of the maximal-length sequence, as illustrated in Figure 4.3a for N=7. The period of the waveform c(t) is (based on terminology used in subsequent sections)

Tb = NTc (4.3)

where Tc is the duration assigned to symbol 1 or 0 in the maximal-length sequence. By definition, the autocorrelation function of a periodic signal c(t) of period Tb is

Rc (?) = (4.4)

Figure 4.9: (a) Waveform of Maximal-length Sequence for m=3 or Period N=7.

(b) Autocorrelation Function. (C) Power Spectral Density. All Three Parts

Refer to the Output of the Feedback Shift Register of Figure 2.

where the lag ? lies in the interval (-Tb/2, Tb/2); Applying the formula (4.4) to a maximal-length sequence represented by c(t), we get


for the remainder of the period

This result is plotted in Figure 4.3b for the case of m = 3 or N =7.

From Fourier transform theory we know that periodicity in the time domain transformed into uniform sampling in the frequency domain. 1 his interplay between the time and frequency domains is borne our by the power spectral density the maximal- length wave c(t). Specifically, taking the Fourier transform of Equation (4.5), we get the sampled spectrum


Which is plotted in Figure 7.3c for m = 3 or N = 7.

For a period of the maximal-length sequence, the autocorrelation function Rc(?) somewhat similar to that of a random binary wave.

The waveforms of both sequences have the same envelope, sinc2(fT), for their power spectral densities. The fundamental difference between them is that whereas the random binary sequence has a continuous spectral density characteristic, the corresponding characteristic of a maximal length sequence consists of delta functions spaced 1/NTc Hz apart.

As the shift-register length m, or equivalently, the period N of the maximal-length sequence is increased, the maximal-length sequence becomes increasingly similar to the random binary sequence. Indeed, in the limit, the two sequences become identical when N is made infinitely large. However, the price paid for making N large is an increasing storage requirement, which imposes a practical limit on how large N can actually be made.

Choosing A Maximal- Length Sequence

Now that we understand the properties of a maximal-length sequence and the fact that we can generate it using a linear feedback shift register, the key question that we need to address is: How do we find the feedback logic for a desired period N? the answer to this :

Table 4.2: Maximal-length Sequences of Shift-register lengths 2-8


Length, m Feedback Taps

2* [2,1]

3 [3,1]

4 [4,1]

5* [5,2], [5,4,3,2], [5,4,2,1]

6 [6,1], [6,5,2,1], [6,5,3,2]

7* [7,1], [7,3], [7,3,2,1], [7,4,3,2], [7,6,4,2], [7,6,3,1], [7,6,5,2], [7,6,5,4,2,1], [7,5,4,3,2,1]

8 [8,4,3,2], [8,6,5,3], [8,6,5,2], [8,5,3,1], [8,6,5,1], [8,7,6,1], [8,7,6,5,2,1], [8,6,4,3,2,1]

The task of finding the required feedback logic is made particularly easy for us by virtue of the extensive tables of the necessary feedback connections for varying shift- register lengths that have been compiled in the literature. In Table 4.2, we present the sets of maximal (feedback) taps pertaining to shift-register lengths m = 2, 3, . . . , 8. Note that as m increases, the number of alternative schemes (codes) is enlarged. Also, for every set of feedback connections shown in this table, there is an ¿½image¿½ set that generates an identical maximal-length code, reversed in time sequence.

The particular sets identified with an asterisk in Table 4.2 correspond to Messene prime length sequences, for which the period N is a prime number.

Example 4.2: Consider a maximal-length sequence requiring the use of a linear feedback-shift register of length m = 5. For feedback taps, we select the set [5,2] from Table 4.2. The corresponding configuration of the code generator is shown in Figure 4.4a. Assuming that the initial state is 10000, the evolution of one period of the maximal-length sequence generated by this scheme is shown in Table 4.3a, where we see that the generator returns to the initial 10000 after 31 iterations; that is, the period is 31, which agrees with the value obtained from Equation (4.2).

Suppose next we select another set of feedback taps from Table 4.2, namely, [5,4,2, 1]. The corresponding code generator is thus as shown in Figure 4.4b. For the initial state 10000, we now find that the evolution of the maximal-length sequence is as shown in Table 4.3b. Here again, the generator returns to the initial state 10000 after 31 iterations, and so it should. But the maximal-length sequence generated is different from that shown in Table 4.3a.

Clearly, the code generator of Figure 4.10a has an advantage over that of Figure 4.10b, as it requires fewer feedback connections.

Table 4.3a: Evolution of the Maximal-length Sequence Generated by the Feedback shift register of Figure 4a.

Feedback symbol State of shift register

Output symbol

1 0 0 0 0

0 0 1 0 0 0 0

1 1 0 1 0 0 0

0 0 1 0 1 0 0

1 1 0 1 0 1 0

1 1 1 0 1 0 1

1 1 1 1 0 1 0

0 0 1 1 1 0 1

1 1 0 1 1 1 0

1 1 1 0 1 1 1

0 0 1 1 0 1 1

0 0 0 1 1 0 1

0 0 0 0 1 1 0

1 1 0 0 0 1 1

1 1 1 0 0 0 1

1 1 1 1 0 0 0

1 1 1 1 1 0 0

1 1 1 1 1 1 0

0 0 1 1 1 1 1

0 0 0 1 1 1 1

1 1 0 0 1 1 1

1 1 1 0 0 1 1

0 0 1 1 0 0 1

1 1 0 1 1 0 0

0 0 1 0 1 1 0

0 0 0 1 0 1 1

1 1 0 0 1 0 1

0 0 1 0 0 1 0

0 0 0 1 0 0 1

0 0 0 0 1 0 0

0 0 0 0 0 1 0

1 1 0 0 0 0 1

Code : 0000101011101100011111001101001

Table 4.3b: Evolution of the Maximal-length Sequence Generated by the Feedback shift register of Figure 4b.

Feedback symbol State of shift register

Output symbol

1 0 0 0 0

1 1 1 0 0 0 0

0 0 1 1 0 0 0

1 1 0 1 1 0 0

0 0 1 0 1 1 0

1 1 0 1 0 1 1

0 0 1 0 1 0 1

0 0 0 1 0 1 0

1 1 0 0 1 0 1

0 0 1 0 0 1 0

0 0 0 1 0 0 1

0 0 0 0 1 0 0

1 1 0 0 0 1 0

0 0 1 0 0 0 1

1 1 0 1 0 0 0

1 1 1 0 1 0 0

1 1 1 1 0 1 0

1 1 1 1 1 0 1

1 1 1 1 1 1 0

0 0 1 1 1 1 1

1 1 0 1 1 1 1

1 1 1 0 1 1 1

0 0 1 1 0 1 1

0 0 0 1 1 0 1

1 1 0 0 1 1 0

1 1 1 0 0 1 1

1 1 1 1 0 0 1

0 0 1 1 1 0 0

0 0 0 1 1 1 0

0 0 0 0 1 1 1

0 0 0 0 0 1 1

1 1 0 0 0 0 1

Code :0000110101001000101111101100111

4.5 A Notion of Spread Spectrum

An important attribute of spread-spectrum modulation is that it can provide protection against externally generated interfering (jamming) signals with finite power. The jamming signal may consist of a fairly powerful broadband noise or multitone waveform that is directed at the receiver for the purpose of disrupting communications. Protection against jamming waveforms is provided by purposely making the information-bearing signal Occupy a bandwidth far in excess of the minimum bandwidth necessary to transmit it. This has the effect of making the transmitted signal assume a noise like appearance so as to blend into the background. The transmitted signal is thus enabled to propagate through the channel undetected by anyone who may be listening. We may therefore think of spread spectrum as a method of ¿½camouflaging¿½ the information-bearing signal.

One method of widening the bandwidth of an information-bearing (data) sequence involves the use of modulation. Let {bk} denote a binary data sequence, and {ck} denote a pseudo-noise (PN) sequence. Let the waveforms b(t) and c(t) denote their respective polar non return-to-zero representations in terms of two levels equal in amplitude and Opposite in polarity, namely, ¿½1. We will refer to b(t) as the information-bearing (data) signal, and to c(t) as the PN signal. The desired modulation is achieved by applying the data signal b(t) and the PN signal c(t) to a product modulator or multiplier, as in Figure ¿½.Sa. We know from Fourier transform theory that multiplication of two signals produces a signal whose spectrum equals the convolution of the spectra of the two component signals. Thus, if the message signal b(t) is narrowband and the PN signal c(t) is wideband, the product (modulated) signal m(t) will have a spectrum that is nearly the same as the wideband PN signal. In other words, in the context of our present application, the PN sequence performs the role of a spreading code.

By multiplying the information-bearing signal b(t) by the PN signal c(t), each information bit is ¿½chopped¿½ up into a number of small time increments, as illustrated in the waveforms of Figure 4.12. These small time increments are commonly referred to as chips.

For baseband transmission, the product signal m(t) represents the transmitted signal. We may thus express the transmitted signal as :

r(t) = m(t) + i(t)= c(t)b(t) + i (t) (4.8)

The received signal r(t) consists of the transmitted signal m(t) plus an additive interference denoted by i(t), as shown in the channel model of Figure 4.11b. Hence, to recover the original message signal b(t), the received signal r(t) is applied to a demodulator that consists of a multiplier followed by an integrator, and a decision device, as in Figure 4.11c. The multiplier is supplied with a locally generated PN sequence that is an exact replica of that used in the transmitter. Moreover, we assume that the receiver operates in perfect synchronism with the transmitter, which means that the PN sequence in the receiver is lined up exactly with that in the transmitter. The multiplier output in the receiver is therefore given by

Z (t) = c (t) r (t) = c2(t)b(t) + c(t)I(t) (4.9)

Equation (4.9) shows that the data signal b(t) is multiplied twice by the PN signal c(t), whereas the unwanted signal i(t) is multiplied only once. The PN signal c(t) alternates between the levels -1 and +1, and the alternation is destroyed when it is squared; hence,

C2 (t) = 1 for all t (4.10)

Accordingly, we may simplify Equation (4.9) as

Z (t) = b(t) + c(t) I(t) (4.11)

We thus see from Equation (4.11) that the data signal b(t) is reproduced at the multiplier output in the receiver, except for the effect of the interference represented by the additive term c(t)i(t). Multiplication of the interference i(t) by the locally generated PN signal c(t) means that the spreading code will affect the interference just as it did the original signal at the transmitter. We now observe that the data component b(t) is narrowband, whereas the spurious component c(t)i(t) is wideband. Hence, by applying the multiplier output to a baseband (low-pass) filter with a bandwidth just large enough to accommodate the recovery of the data signal b(t), most of the power in the spurious component c(t)i(t) is filtered out. The effect of the interference i(t) is thus significantly reduced at the receiver output.

In the receiver shown in Figure 4.11c, the low-pass filtering action is actually performed by the integrator that evaluates the area under the signal produced at the multiplier output. The integration is carried Out for the bit interval 0 ? t ? Tb, providing the sample value v. Finally, a decision is made by the receiver: If v is greater than the threshold of zero, the receiver says that binary symbol 1 of the original data sequence was sent in the interval 0 ? t ? Tb, and if v is less than zero, the receiver says that symbol 0 was sent; if v is exactly zero the receiver makes a random guess in favor of 1 or 0.

In summary, the use of a spreading code (with pseudo-random properties) in the transmitter produces a wideband transmitted signal that appears noise like to a receiver that has no knowledge of the spreading code. From the discussion presented in Section 4.4, we recall that (for a prescribed data rate) the longer we make the period of the spreading code, the closer will the transmitted signal be to a truly random binary wave, and the harder it is to detect. Naturally, the price we have to pay for the improved protection against interference is increased transmission bandwidth, system complexity, and processing delay. However, when our primary concern is the security of transmission, these are not unreasonable costs to pay.

¿½ Synchronization

For its proper operation, a spread-spectrum communication system requires that the locally generated PN sequence used in the receiver to dispread the received signal be synchronized to the PN sequence used to spread the transmitted signal in the transmitter. A solution to the synchronization problem consists of two parts: acquisition and tracking. In acquisition, or coarse synchronization, the two PN codes are aligned to within a fraction of the chip in as short a time as possible. Once the incoming PN code has been acquired, tracking, or fine synchronization, takes place. Typically, PN acquisition proceeds in two steps. First, the received signal is multiplied by a locally generated PN code to produce a measure of correlation between it and the PN code used in the transmitter. Next, an appropriate decision-rule and search strategy is used to process the measure of correlation so obtained to determine whether the two codes are in synchronism and what to do if they are not. As for tracking, it is accomplished using phase-lock techniques very similar to those used for the local generation of coherent carrier references. The principal difference between them lies in the way in which phase discrimination is implemented.