SPREAD SPECTRYM

Spread Spectrumimportant encoding method for wireless communicationsanalog & digital data with analog signalspreads data over wide bandwidthmakes jamming and interception hardertwo approaches, both in use:Frequency Hopping : Signal broadcast over seemingly random series of frequenciesDirect Sequence : Each bit is represented by multiple bits in transmitted signal- Chipping Code

Spread Spectrum ConceptInput fed into channel encoderProduces narrow bandwidth analog signal around central frequencySignal modulated using sequence of digits Spreading code/sequenceTypically generated by pseudonoise/pseudorandom number generatorIncreases bandwidth significantly (Effect of modulation is to increase bandwidth of signal to be transmitted)Spreads spectrumReceiver uses same sequence to demodulate signalDemodulated signal fed into channel decoder to recover data

General Model of Spread Spectrum System

Spread Spectrum Advantagesimmunity from noise and multipath distortion- Including jammingcan hide / encrypt signalsOnly receiver who knows spreading code can retrieve signalseveral users can share same higher bandwidth with little interferenceCDM/CDMA Mobile telephonesCode division multiplexing (CDM)Code division multiple access (CDMA)

Pseudorandom NumbersGenerated by a deterministic algorithmnot actually randombut if algorithm good, results pass reasonable tests of randomnessstarting from an initial seedneed to know algorithm and seed to predict sequencehence only receiver can decode signal

Frequency Hopping Spread Spectrum (FHSS)signal is broadcast over seemingly random series of frequenciesReceiver hops between frequencies in sync with transmitterEavesdroppers hear unintelligible blipsJamming on one frequency affects only a few bits

Wireless Networks Spring 2005FHSSSignal is broadcast over seemingly random series of radio frequenciesA number of channels allocated for the FH signalWidth of each channel corresponds to bandwidth of input signalSignal hops from frequency to frequency at fixed intervalsTransmitter operates in one channel at a timeBits are transmitted using some encoding schemeAt each successive interval, a new carrier frequency is selectedChannel sequence dictated by spreading codeReceiver, hopping between frequencies in synchronization with transmitter, picks up messageAdvantagesEavesdroppers hear only unintelligible blipsAttempts to jam signal on one frequency succeed only at knocking out a few bits

Wireless Networks Spring 2005

Basic OperationTypically 2k carriers frequencies forming 2k channelsChannel spacing corresponds with bandwidth of inputEach channel used for fixed interval300 ms in IEEE 802.11Some number of bits transmitted using some encoding schemeMay be fractions of bit (see later)Sequence dictated by spreading code

Frequency Hopping Example

FHSS (Transmitter)

FHSS (Receiver)

Slow and Fast FHSScommonly use multiple FSK (MFSK)Have frequency shifted every Tc secondsDuration of signal element is Ts secondsSlow FHSS has Tc TsFast FHSS has Tc < TsFHSS quite resistant to noise or jammingwith fast FHSS giving better performance in noise (or jamming)

Slow MFSK FHSS

Fast MFSK FHSS

FHSS Performance ConsiderationsTypically large number of frequencies usedImproved resistance to jamming

Direct Sequence Spread Spectrum (DSSS)Each bit is represented by multiple bits using a spreading codeSpreading code spreads signal across wider frequency bandSpread is in direct in proportion to number of bits used10 bit spreading code spreads signal across 10 times bandwidth of 1 bit codeOne method:Combine input with spreading code using XORInput bit 1 inverts spreading code bitInput zero bit doesnt alter spreading code bitData rate equal to original spreading codePerformance similar to FHSS

Wireless Networks Spring 2005Direct Sequence Spread Spectrum (DSSS)Each bit in original signal is represented by multiple bits in the transmitted signalSpreading code spreads signal across a wider frequency band Spread is in direct proportion to number of bits usedOne technique combines digital information stream with the spreading code bit stream using exclusive-OR

Wireless Networks Spring 2005

Direct Sequence Spread Spectrum Example

Direct Sequence Spread Spectrum System

DSSS Example Using BPSK

ApproximateSpectrum of DSSS Signal

Code Division Multiple Access (CDMA)Multiplexing Technique used with spread spectrumStart with data signal rate DCalled bit data rateBreak each bit into k chips according to fixed pattern specific to each userUsers codeNew channel has chip data rate kD chips per secondE.g. k=6, three users (A,B,C) communicating with base receiver RCode for A = Code for B = Code for C =

CDMA Example

CDMA for DSSS

CDMA ExplanationConsider A communicating with baseBase knows As codeAssume communication already synchronizedA wants to send a 1Send chip pattern As codeA wants to send 0Send chip[ pattern Complement of As codeDecoder ignores other sources when using As code to decodeOrthogonal codes

CDMA for DSSSn users each using different orthogonal PN sequenceModulate each users data streamUsing BPSKMultiply by spreading code of user

Seven Channel CDMA Encoding and Decoding

*Chapter 3Frequency-HoppingSystems

*Frequency hopping The periodic changing of the carrier frequency of a transmitted signal. HopsetThe set of M possible carrier frequenciesFrequency hopping patternThe sequence of carrier frequencies. Hopping band Hopping occurs over a frequency band that includes M frequency channels.

*hop durationThe time interval between hopsThe hopping band has bandwidth

*

*If the data modulation is some form of angle modulation then the received signal for the ith hop is

dehoppingThe mixing operation removes the frequency-hopping pattern from the received signal.Frequency hopping enables signals to hop out of frequency channels with interference or slow frequency-selective fading.spectral notchingSome spectral regions with steady interference or a susceptibility to fading may be omitted from the hopset.

*

*Transmission securityThe specific algorithm for generating the control bits is determined by the key and the time-of-day (TOD). The key is a set of bits that are changed infrequently and must be kept secret. The TOD is a set of bits that are derived from the stages of the TOD counter and change with every transition of the TOD clock.The purpose of the TOD is to vary the generator algorithm without constantly changing the key. The generator algorithm is controlled by a time-varying key. The code clock, which regulates the changes of state in the code generator and thereby controls the hop rate, operates at a much higher rate than the TOD clock.

*Dwell intervalA frequency-hopping pulse with a fixed carrier frequency occurs during a portion of the hop interval. dwell timeThe duration of the dwell interval during which the channel symbols are transmitted.

*The hop duration Th is equal to the sum of the dwell time Td and the switching time Tsw. The switching time is equal to the dead time plus the rise and fall times of a pulse.dead time is the duration of the interval when no signal is presentThe nonzero switching time decreases the transmitted symbol duration Ts .If Tso is the symbol duration in the absence of frequency hopping, then The reduction in symbol duration expands the transmitted spectrum and thereby reduces the number of frequency channels within a fixed hopping band.

*Fast frequency hoppingIf there is more than one hop for each information symbol. Slow frequency hopping If one or more information symbols are transmitted in the time interval between frequency hops.Let M denote the hopset size, B denote the bandwidth of frequency channels, and Fs denote the minimum separation between adjacent carriers in a hopset. For full protection against stationary narrowband interference and jamming, it is desirable that so that the frequency channels are nearly spectrally disjoint. A hop then enables the transmitted signal to escape the interference in a frequency channel.

* Symbol errors are independent if the fading is independent in each frequency channel and each symbol is transmitted in a different frequency channel. If each of the interleaved code symbols is transmitted at the same location in each hop dwell interval, then adjacent symbols are separated by Th after the interleaving.The sufficient condition for nearly independent symbol errors is

where Tcoh is the coherence time of the fading channel. Bcoh is the coherence bandwidth of the fading channel.

*For a hopping band with bandwidth W, and a hopset with a uniform carrier separation, If nearly independent symbol errors are to be ensured, the number of frequency channels is constrained by

If B < Bcoh equalization will not be necessary because the channel transfer function is nearly flat over each frequency channel. If B Bcoh equalization may be used to prevent intersymbol interference.

*In military applications, the ability of frequency-hopping systems to avoid interference is potentially neutralized by a repeater jammer (also known as a follower jammer), which is a device that intercepts a signal, processes it, and then transmits jamming at the same center frequency. To be effective against a frequency-hopping system, the jamming energy must reach the victim receiver before it hops to a new set of frequency channels. Thus, the hop rate is the critical factor in protecting a system against a repeater jammer.

*3.2 ModulationsFH/MFSK system Uses MFSK as its data modulation. One of q frequencies is selected as the carrier or center frequency for each transmitted symbol, and the set of q possible frequencies changes with each hop.An FH/MFSK signal has the form

is the average signal power during a dwell interval. is a unit-amplitude rectangular pulse of duration Ts.Nh is the number of symbols per dwell interval.

*

*The effective number of frequency channels is

M : the hopset size.q : frequencies or tones in an MFSK setFor noncoherent orthogonal signals, the MFSK tones must be separated enough that a received signal produces negligible responses in the incorrect subchannels. The frequency separation must be k is a nonzero integer.Ts denotes the symbol duration. To maximize the hopset size when the MFSK subchannels are contiguous, k=1 is selected.

*The bandwidth of a frequency channel for slow frequency hopping with many symbols per dwell interval is

Tb is the duration of a bit.The hopset size is

*Soft-Decision DecodingWe consider an FH/MFSK system that uses a repetition code and the receiver of Figure 3.5(b). Each information symbol, which is transmitted as L code symbols, may be regarded as a codeword or as an uncoded symbol that uses diversity combining. The interference is modeled as wideband Gaussian noise uniformly distributed over part of the hopping band. Slow frequency hopping with a fixed hop rate and ideal interleaving.The optimal metric for the Rayleigh-fading channel and a good metric for the additive-white-Gaussian-noise (AWGN) channel without fading is the Rayleigh metric which is

*

*Linear square-law combining

Rli is the sample value of the envelope-detector output that is associated with code symbol i of candidate information-symbol.L is the number of repetitions or code symbols.This metric has the advantage that no side information, which is specific information about the reliability of symbols, is required for its implementation. A performance analysis of a frequency-hopping system with binary FSK and soft-decision decoding with the Rayleigh metric indicates that the system performs poorly against worst case partial-band jamming [6] primarily because a single jammed frequency can corrupt the metrics.

*Nonlinear square-law combining

Noi is the two-sided power spectral density of the interference and noise over all the MFSK subchannels during code symbol i.Variable-gain metric:

*Suppose that the interference is partial-band jamming.

N1/2: the two-sided power-spectral density: the fraction of the hopping band with interference .It0 : the spectral density that would exist if the interference power were uniformly spread over the entire hopping band. Upper bound on the information-bit error probability:

where

*Suppose that the interference is worst-case partial-band jamming. An upper bound on Pb is obtained by maximizing the right-hand side of (3-27) with respect to . Calculus yields the maximizing value of

Substituting (3-28) into (3-27), we obtain

*let L0 denote the minimizing value of L.

*The upper bound on Pb for worst-case partial-band jamming when L= L0 is given by

This upper bound indicates that Pb decreases exponentially as increases if the appropriate number of repetitions is chosen. Thus, the nonlinear diversity combining with the variable-gain metric sharply limits the performance degradation caused by worst-case partial-band jamming relative to full-band jamming.

*Substituting (3-30) into (3-28), we obtain

This result shows that the appropriate choice of L implies that worst-case jamming must cover three-fourths or more of the hopping band.The task may not be a practical possibility for a jammer.

*Narrowband Jamming SignalsAlthough (3-31) indicates that it is advantageous to use nonbinary signaling (m > 1) when . This advantage is completely undermined when distributed, narrowband jamming signals are a threat.A sophisticated jammer with knowledge of the spectral locations of the MFSK sets can cause increased system degradation by placing one jamming tone or narrowband jamming signal in every MFSK set.

*To assess the impact of this sophisticated multitone jamming on hard decision decoding in the receiver of Figure 3.5(b), It is assumed that thermal noise is absent and that each jamming tone coincides with one MFSK tone in a frequency channel encompassing q MFSK tones.Whether a jamming tone coincides with the transmitted MFSK tone or an incorrect one, there will be no symbol error if the desired-signal power S exceeds the jamming power.If It is the total available jamming power, then the jammer can maximize symbol errors by placing tones with power levels slightly above S whenever possible in approximately J frequency channels such that

*If a transmitted tone enters a jammed frequency channel and then with probability , the jamming tone will not coincide with the transmitted tone and will cause a symbol error after hard-decision decoding.Since J/M is the probability that a frequency channel is jammed, the symbol error probability is

Substitution of (3-8), (3-9), and (3-34) into (3-35) yields

* denotes the energy per bit. denotes the spectral density of the interference power that would exist if it were uniformly spread over the hopping band. This equation exhibits an inverse linear dependence of Ps on It is observed that Ps increases with q which is the opposite of what is observed over the AWGN channel. Thus, binary FSK is advantageous against this sophisticated multitone jamming.

*3.3 Hybrid SystemsFrequency-hopping systems reject interference by avoiding it, whereas direct-sequence systems reject interference by spreading it. Channel codes are more essential for frequency-hopping systems than for direct-sequence systems.Because partial-band interference is a more pervasive threat than high-power pulsed interference. When frequency-hopping and direct-sequence systems are constrained to use the same fixed bandwidth, then direct-sequence systems have an inherent advantage. They can use coherent PSK rather than a noncoherent modulation. Coherent PSK has an approximately 4 dB advantage relative to noncoherent MSK over the AWGN channel and an even larger advantage over fading channels.

*A major advantage of frequency-hopping systems It is possible to hop into noncontiguous frequency channels over a much wider band than can be occupied by a direct-sequence signal. This advantage more than compensates for the relatively inefficient noncoherent demodulation that is usually required for frequency-hopping systems. Excluding frequency channels with steady or frequent interference.The reduced susceptibility to the near-far problem and the relatively rapid acquisition.

*A hybrid frequency-hopping direct-sequence systemA frequency-hopping system that uses direct-sequence spreading during each dwell interval Or, equivalently, a direct-sequence system in which the carrier frequency changes periodically.

*

*Hops occur periodically after a fixed number of sequence chips. Because of the phase changes due to the frequency hopping, noncoherent modulation, such as DPSK, is usually required unless the hop rate is very low. Serial-search acquisition occurs in two stages. To provide alignment of the hopping patterns.The phase of the pseudonoise sequence finishes acquisition rapidly. Because the timing uncertainty has been reduced by the first stage to less than a hop duration.

*A hybrid system curtails partial-band interference in two ways. The hopping allows the avoidance of the interference spectrum part of the time. When the system hops into the interference, the interference is spread and filtered as in a direct-sequence system. Large bandwidth limits the number of available frequency channels, which increases the susceptibility to narrowband interference and the near-far problem. Hybrid systems are seldom used except perhaps in specialized military applications because the additional direct-sequence spreading weakens the major strengths of frequency hopping.

*3.4 ApplicationsAnti-jamming is an important application for spread spectrum modulations.In addition to anti-jamming, we will briefly introduce several other spread spectrum applications in this section. In describing these applications, we focus on DS-SS systems. One should note that other spread spectrum techniques also have similar applications since the main idea behind these applications is the spreading of the spectrum.

*3.4.1 Anti-jammingWe know that we can combat a wide-band Gaussian jammer by spreading the spectrum of the data signal. Here we consider another kind of jammersthe continuous wave (CW) jammers. Suppose the spread spectrum signal is given by

It is jammed by a sinusoidal signal with frequency and power PJ . The received signal is given by

where n(t) represents the AWGN.

*We can easily see that the power spectrum of the received signal r(t) is given by

We consider the matched filter receiver in the equivalent correlator form in Figure 3.11.

Figure 3.11: Matched filter receiver (correlator form) for DS-SS

*At the output of the despreader, the signal z(t) can be expressed as

It can be shown that the power spectrum of the despread signal z(t) is

Now the anti-jamming property of the spread spectrum modulation can be explained by comparing the spectra of the signals before and after despreading in Figure 3.12.

*

Figure 3.12: Spectra of signals before and after despreading

*Before despreading, the jammer power is concentrated at frequency and the signal power is spread across a wide frequency band ([-2/Tc, 2/Tc]). The despreader spreads the jammer power into a wide frequency band ([-2/Tc, 2/Tc]) while concentrates the signal power into a much narrower band ([-2/T, 2/T]). The integrator acts like a low-pass filter to collect power of the despread signal over the frequency band ([-2/T, 2/T]).

*As a result, almost all of the signal power is collected, but only 1/Nth of the jammer power is collected. The effective power of the jammer is reduced by a factor of N. This is the reason why N is called the spreading gain.

*3.4.2 Low probability of detectionAnother military-oriented application for spread spectrum is low probability of detection (LPD), which means that it is hard for an unintentional receiver to detect the presence of the signal. The idea behind this can be readily seen from Figure 3.12. When the processing gain is large enough, the spread spectrum signal hides below the white noise level. Without knowledge of the signature sequences, an unintentional receiver cannot despread the received signal.

*Therefore, it is hard for the unintentional receiver to detect the presence of the spread spectrum. We are not going to treat the subject of LPD any further than the intuition just given. A more detailed treatment can be found in [1, Ch. 10].

*2.4.3 Multipath combiningAnother advantage of spreading the spectrum is frequency diversity, which is a desirable property when the channel is fading. Fading is caused by destructive interference between time-delayed replica of the transmitted signal arise from different transmission paths (multipaths). The wider the transmitted spectrum, the finer are we able to resolve multipaths at the receiver.

*Loosely speaking, we can resolve multipaths with path-delay differences larger than 1/W seconds when the transmission bandwidth is W Hz. Therefore, spreading the spectrum helps to resolve multipaths and, hence, combats fading.The best way to explain multipath fading is to go through the following simple example. Suppose the transmitter sends a bit with the value +1 in the BPSK format, i.e., the transmitted signal envelope is pT (t), where T is the symbol duration.

*Assume that there are two transmission paths leading from the transmitter to the receiver. The first path is the direct line-of-sight path which arrives at a delay of 0 seconds and has a unity gain. The second path is a reflected path which arrives at a delay of 2Tc seconds and has a gain of -0.8, where Tc = T/10 is the chip duration of the DS-SS system we are going to introduce in a moment.

*The overall received signal can be written as

where n(t) is AWGN. To demodulate the received signal, we employ the matched filter receiver, which is matched to the direct line-of-sight signal, i.e., h(t) = pT (T - t). The output of the matched filter is plotted in Figure 3.13. We can see from the figure that the contribution from the second path partially cancels that from the first path.

*

Figure 3.13: Matched filter output for the two-path channel without spreading

*We sample the matched filter output at time t = T. The signal contribution in the sample is 0.36T and the noise contribution is a zero-mean Gaussian random variable with variance N0T. Compared to the case where only the direct line-of-sight path is present, the signal energy is reduced by 87%, while the noise energy is the same. Therefore, the bit error probability is greatly increased.

*Now, let us spread the spectrum by the spreading signal

whereDS-SS system is

Again, we consider using the matched filter receiver, which is matched to a(t). The output of the matched filter is shown in Figure 3.14. We can clearly see from the figure that the contributions from the two paths are separated since the resolution of the spread system is ten times finer than that of the unspread system.

*

Figure 3.14: Matched filter output for the two-path channel with spreading

*If we sample at t = T, we get a signal contribution of T, which is the same as what we would get if there was only a single path. Hence, unlike what we saw in the unspread system, multipath fading does not have a detrimental effect on the error probability. In fact, we will show in Chapter 4 that we can do better by taking one more sample at t = T + 2Tc to collect the energy of the second path. If we know the channel gain of the second path, we can combine the paths coherently.Otherwise we can perform equal-gain noncoherent combining. This ability of the spread spectrum modulation to collect energies from different paths is called multipath combining.

*3.5 References[1] R. L. Peterson, R. E. Ziemer, and D. E. Borth, Introduction to Spread Spectrum Communications, Prentice Hall, Inc., 1995.[2] M. B. Pursley, Performance evaluation for phase-coded spread-spectrum multiple-access communication Part I: System analysis, IEEE Trans. Commun., vol. 25, no. 8, pp. 795799, Aug. 1977.[3] R. A. Scholtz, Multiple access with time-hopping impulse modulation, Proc. MILCOM 93, pp. 11-14, Boston, MA, Oct. 1993.[4] N. Yee, J. M. G. Linnartz, and G. Fettweis, Multi-carrier CDMA in indoor wireless radio networks, IEICE Trans. Commun., vol. E77-B, no. 7, pp. 900904, Jul. 1994.[5] S. Kondo and L. B. Milstein, Performance of multicarrier DS CDMA systems, IEEE Trans. Commun., vol. 44, no. 2, pp. 238246, Feb. 1996.[6] R. L. Pickholtz, L. B. Milstein, and D. L. Schilling, Spread spectrum for mobile communications, IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 313321, May 1991.[7] D. Torrieri, Principles of spread spectrum communications theory, Springer 2005.

*Lecture slides prepared by Dr Lawrie Brown (UNSW@ADFA) for Data and Computer Communications, 8/e, by William Stallings, Chapter 9 Spread Spectrum.

*Spread spectrum is an increasingly important form of encoding for wireless communications. It it can be used to transmit either analog or digital data, using an analog signal.The basic idea of spread spectrum is to modulate the signal so as to increase significantly the bandwidth (spread the spectrum) of the signal to be transmitted. It was initially developed for military and intelligence requirements. The use of spread spectrum makes jamming and interception more difficult and provides improved reception. The first type of spread spectrum developed is known as frequency hopping. A more recent type of spread spectrum is direct sequence. Both of these techniques are used in various wireless communications standards and products.*Stallings DCC8e Figure 9.1 highlights the key characteristics of any spread spectrum system. Input is fed into a channel encoder that produces an analog signal with a relatively narrow bandwidth around some center frequency. This signal is further modulated using a sequence of digits known as a spreading code or spreading sequence. Typically, but not always, the spreading code is generated by a pseudonoise, or pseudorandom number, generator. The effect of this modulation is to increase significantly the bandwidth (spread the spectrum) of the signal to be transmitted. On the receiving end, the same digit sequence is used to demodulate the spread spectrum signal. Finally, the signal is fed into a channel decoder to recover the data.

*Several advantages can be gained from this apparent waste of spectrum by this approach: The signals gains immunity from various kinds of noise and multipath distortion. The earliest applications of spread spectrum were military, where it was used for its immunity to jamming. It can also be used for hiding and encrypting signals. Only a recipient who knows the spreading code can recover the encoded information. Several users can independently use the same higher bandwidth with very little interference. This property is used in cellular telephony applications, with a technique know as code division multiplexing (CDM) or code division multiple access (CDMA).

*A comment about pseudorandom numbers is in order. These numbers are generated by an algorithm using some initial value called the seed. The algorithm is deterministic and therefore produces sequences of numbers that are not statistically random. However, if the algorithm is good, the resulting sequences will pass many reasonable tests of randomness. Such numbers are often referred to as pseudorandom numbers. The important point is that unless you know the algorithm and the seed, it is impractical to predict the sequence. Hence, only a receiver that shares this information with a transmitter will be able to decode the signal successfully.*With frequency-hopping spread spectrum (FHSS), the signal is broadcast over a seemingly random series of radio frequencies, hopping from frequency to frequency at fixed intervals. A receiver, hopping between frequencies in synchronization with the transmitter, picks up the message. Would-be eavesdroppers hear only unintelligible blips. Attempts to jam the signal on one frequency succeed only at knocking out a few bits of it.

*Stallings DCC8e Figure 9.2 shows an example of a frequency-hopping signal. A number of channels are allocated for the FH signal. Typically, there are 2k carrier frequencies forming 2k channels. The spacing between carrier frequencies and hence the width of each channel usually corresponds to the bandwidth of the input signal. The transmitter operates in one channel at a time for a fixed interval; for example, the IEEE 802.11 standard uses a 300-ms interval. During that interval, some number of bits (possibly a fraction of a bit, as discussed subsequently) is transmitted using some encoding scheme. A spreading code dictates the sequence of channels used. Both transmitter and receiver use the same code to tune into a sequence of channels in synchronization.

*A common modulation technique used in conjunction with FHSS is multiple FSK (MFSK), which uses M = 2L different frequencies to encode the digital input L bits at a time (see Chapter 5). For FHSS, the MFSK signal is translated to a new frequency every Tc seconds by modulating the MFSK signal with the FHSS carrier signal. The effect is to translate the MFSK signal into the appropriate FHSS channel. For a data rate of R, the duration of a bit is T = 1/R seconds and the duration of a signal element is Ts = LT seconds. If Tc is greater than or equal to Ts, the spreading modulation is referred to as slow-frequency-hop spread spectrum; otherwise it is known as fast-frequency-hop spread spectrum.Typically, a large number of frequencies is used in FHSS so that bandwidth of the FHSS signal is much larger than that of the original MFSK signal. One benefit of this is that a large value of k results in a system that is quite resistant to jamming. If frequency hopping is used, the jammer must jam all 2k frequencies. With a fixed power, this reduces the jamming power in any one frequency band to Sj/2k. In general, fast FHSS provides improved performance compared to slow FHSS in the face of noise or jamming, as will discuss shortly.*Stallings DCC8e Figure 9.4 shows an example of slow FHSS, using the MFSK example from Stallings DCC8e Figure 5.9. Here we have M = 4, which means that four different frequencies are used to encode the data input 2 bits at a time. Each signal element is a discrete frequency tone, and the total MFSK bandwidth is Wd = Mfd. We use an FHSS scheme with k = 2. That is, there are 4 = 2k different channels, each of width Wd. The total FHSS bandwidth is Ws = 2kWd. Each 2 bits of the PN sequence is used to select one of the four channels. That channel is held for a duration of two signal elements, or four bits (Tc = 2Ts = 4T).*Stallings DCC8e Figure 9.5 shows an example of fast FHSS, using the same MFSK example. Again, M = 4 and k = 2. In this case, however, each signal element is represented by two frequency tones. Again, Wd = Mfd and Ws = 2kWd. In this example Ts = 2Tc = 2T. In general, fast FHSS provides improved performance compared to slow FHSS in the face of noise or jamming. For example, if three or more frequencies (chips) are used for each signal element, the receiver can decide which signal element was sent on the basis of a majority of the chips being correct.*With direct sequence spread spectrum (DSSS), each bit in the original signal is represented by multiple bits in the transmitted signal, using a spreading code. The spreading code spreads the signal across a wider frequency band in direct proportion to the number of bits used. Therefore, a 10-bit spreading code spreads the signal across a frequency band that is 10 times greater than a 1-bit spreading code.*One technique with direct sequence spread spectrum is to combine the digital information stream with the spreading code bit stream using an exclusive-OR (XOR). Stallings DCC8e Figure 9.6 shows an example. Note that an information bit of one inverts the spreading code bits in the combination, while an information bit of zero causes the spreading code bits to be transmitted without inversion. The combination bit stream has the data rate of the original spreading code sequence, so it has a wider bandwidth than the information stream. In this example, the spreading code bit stream is clocked at four times the information rate.*To see how this technique works out in practice, assume that a BPSK modulation scheme is to be used. Rather than represent binary data with 1 and 0, it is more convenient for our purposes to use +1 and 1 to represent the two binary digits. To produce the DSSS signal, we multiply the BPSK signal by c(t), which is the PN sequence taking on values of +1 and 1:s(t) = A d(t)c(t) cos(2fct): Equation (9.5)At the receiver, the incoming signal is multiplied again by c(t). But c(t) c(t) = 1 and therefore the original signal is recovered. Equation (9.5) can be interpreted in two ways, leading to two different implementations. The first interpretation is to first multiply d(t) and c(t) together and then perform the BPSK modulation. That is the interpretation we have been discussing. Alternatively, we can first perform the BPSK modulation on the data stream d(t) to generate the data signal sd(t). This signal can then be multiplied by c(t). An implementation using the second interpretation is shown in Stallings DCC8e Figure 9.7 above.*Stallings DCC8e Figure 9.8 is an example of the approach discussed on the previous slide.*The spectrum spreading achieved by the direct sequence technique is easily determined (Stallings DCC8e Figure 9.9 above). In our example, the information signal has a bit width of T, which is equivalent to a data rate of 1/T. In that case, the spectrum of the signal, depending on the encoding technique, is roughly 2/T. Similarly, the spectrum of the PN signal is 2/Tc. Figure 9.9c shows the resulting spectrum spreading. The amount of spreading that is achieved is a direct result of the data rate of the PN stream.As with FHSS, we can get some insight into the performance of DSSS by looking at its effectiveness against jamming. Let us assume a simple jamming signal at the center frequency of the DSSS system. Can show the carrier power Sj is spread over a bandwidth of approximately 2/Tc. However, the BPSK demodulator (Figure 9.7) following the DSSS despreader includes a bandpass filter matched to the BPSK data, with bandwidth of 2/T. Thus, most of the jamming power is filtered. The jamming power has been reduced by a factor of (Tc /T) through the use of spread spectrum. The result is similar to the result for FHSS.*As an illustration we consider a simple example with k = 6. It is simplest to characterize a chipping code as a sequence of 1s and 1s. Figure 9.10 shows the codes for three users, A, B, and C, each of which is communicating with the same base station receiver, R. Thus, the code for user A is cA = . Similarly, user B has code cB = , and user C has cC = . We now consider the case of user A communicating with the base station. The base station is assumed to know As code. For simplicity, we assume that communication is already synchronized so that the base station knows when to look for codes. If A wants to send a 1 bit, A transmits its code as a chip pattern . If a 0 bit is to be sent, A transmits the complement (1s and 1s reversed) of its code, .At the base station the receiver decodes the chip patterns. If the decoder is linear and if A and B transmit signals sA and sB, respectively, at the same time, then SA(sA + sB) = SA(sA) + SA(sB) = SA(sA) since the decoder ignores B when it is using As code. The codes of A and B that have the property that SA(cB) = SB(cA) = 0 are called orthogonal. Using the decoder, Su, the receiver can sort out transmission from u even when there may be other users broadcasting in the same cell. In practice, the CDMA receiver can filter out the contribution from unwanted users or they appear as low-level noise. However, if there are many users competing for the channel with the user the receiver is trying to listen to, or if the signal power of one or more competing signals is too high, perhaps because it is very near the receiver (the near/far problem), the system breaks down.*Let us now look at CDMA from the viewpoint of a DSSS system using BPSK. Stallings DCC8eFigure 9.11 depicts a configuration in which there are n users, each transmitting using a different, orthogonal, PN sequence (compare Figure 9.7). For each user, the data stream to be transmitted, di(t), is BPSK modulated to produce a signal with a bandwidth of Ws and then multiplied by the spreading code for that user, ci(t). All of the signals, plus noise, are received at the receiver's antenna. Suppose that the receiver is attempting to recover the data of user 1. The incoming signal is multiplied by the spreading code of user 1 and then demodulated. The effect of this is to narrow the bandwidth of that portion of the incoming signal corresponding to user 1 to the original bandwidth of the unspread signal, which is proportional to the data rate. Incoming signals from other users are not despread by the spreading code from user 1 and hence retain their bandwidth of Ws. Thus the unwanted signal energy remains spread over a large bandwidth and the wanted signal is concentrated in a narrow bandwidth. The bandpass filter at the demodulator can therefore recover the desired signal.***************************************************1-(0.36)^2=0.87****