Communication Systems
Spread spectrum technique
The spread spectrum system (SSS) is one in which the transmitted signal is spread over a wide frequency band, much wider, than the minimum bandwidth required to transmit the information being sent.
-A system is defined to be a speared spectrum system if it fulfills the following requirements:
1-The signal occupies a bandwidth much in excess of the minimum bandwidth necessary to send the information.
2-Spreading is accomplished by means of a spreading signal, often called a code signal, which is independent of the data.
3-At the receiver, despreading (recovering the original data) is accomplished by the correlation of the received spread signal with a synchronized replica of the spreading signal used to spread the information.
Note
Standard modulation such as FM and PCM also spread the spectrum of an information signal, but they do not qualify as spread spectrum systems since they do not satisfy all the conditions above.
The advantages of spread spectrum systems
-Interference suppression.
-White Gaussian noise is a mathematical model has infinite power spread uniformly over all frequencies. The communication is possible with this interfering noise (white Gaussian noise) of infinite power because only the finite power noise components that are present within the signal bandwidth can interfere with the signal.
-For a typical narrowband signal, this means that only the noise in the signal bandwidth degrade performance.
The idea behind a spread spectrum anti-jam (AJ) system is as follows:
a- consider that many orthogonal signal components are available to a communication link and that only a small subset of these signal coordinates are used at any time.
[Against white Gaussian noise, with infinite power, the use of spreading offers no performance].
b-The noise from interferer (jammer) with a fixed finite power and with uncertainty as to where in the signal space the signal components (coordinates) are located, the jammer’s choices are limited to the
following:-1-jam all the signal components (coordinates) of the system, with equal amount of power in each one, with the result that a little power is available for each component (coordinate).
2-jam a few signal components (coordinates) with increased power in each of the jammed coordinates.
Fig (14.1) compares the effect of spreading in the presence of white noise with spreading in the presence of interferer (jammer). The power spectral density of the signal is denoted G(F) before spreading and Gss(f) after spreading.
Fig(14.1)
-Fig(14.1a) it can be seen that the single sided power spectral density of white noise, is unchanged as a result of expanding the signal bandwidth.
If interferer choice results in a reduction in interferer noise spectral density by because
ss ssW
W
J
W
J
J
00 broadband jammer noise spectral density(14.1)
If interferer choice 2 results in a reduction in the number of signal coordinates, that the jammer can increase its noise spectral density
from where ρ is the portion of interferer (jammer) bandwidth.
2-Energy density reduction.
Since in SSS, the signal is spread over many more signaling components than conventional modulation schemes, the resulting signal power is spread uniformly in the spread domain. Thus the received signal is small, very difficult to detect by anyone except the desired receiver (or intended receiver) systems designed for this special task are known as low probability of detection (LPD) or low probability of intercept (LPI).
3-Fine time resolution
Spread spectrum signals can be used for ranging or determination of position location. Distance can be determined by measuring the time delay between transmitted and received signal. Uncertainly in the delay measurements is inversely proportion proportional to the
bandwidth of the signal pulse as shown in fig (14.2). The uncertainty of the measurement, t, is proportional to the rise time of pulse, is given by
fig(14.1a)
Multiple access
-Multiple access refers to techniques that enable sharing a common communication channel between multiple users.
-There is a difference between multiplexing and multiple access. With multiplexing users requirements (or plans) are fixed, or at most, slowly changing. The user allocation is assigned a priori and the multiplexing (sharing) is usually a process that takes place within the confines of a local site (e.g a circuit board). With multiple access, usually involves the remote multiplexing (sharing)
of a user and users requirements are changed (e.g satellite communications).
-Spread spectrum methods can be used a multiple access technique, in order to multiplex (share) a communication resource among numerous users. The technique, termed code division multiple access (CDMA), since each simultaneous user employ a unique spread spectrum signaling code. One of the by products of this type of multiple access is the ability to provide communication privacy between users with different spreading signals. An unauthorized user cannot easily monitor the communications of the authorized users.
The basis of spread spectrum technology
-The basis of spread spectrum technology is expressed by Shannon theorem in the form of channel capacity
)
3
.
14
...(
...
1
log
2
N
S
W
C
whereC=capacity in bit/sec, N=noise power W=bandwidth in Hz, S=Signal power
This equation shows the relationship between the ability of a channel to transfer error–free information, compared with the signal to noise ratio existing in the channel and the bandwidth used to transmit the information.
Letting C be the desired system information rate and changing bases, we find
a)
4
.
14
(
1
log
44
.
1
2
N
S
W
C
Note 1 1 4 1 3 1 2 1 1 log 3 2 N S for N S N S N S N S N S eand for S / N small, say 0.1,
)
5
.
14
(
44
.
1
44
.
1
b)
4
.
14
(
44
.
1
S
C
N
W
C
W
S
N
N
S
W
C
Eq (14.5) shows that for any given noise to signal ratio we can have a low information error rate by increasing the bandwidth used to transfer the information. For example if we want a system to operate in a link in which the interfering noise is 100 time greater than the signal and if C=3k bit/s
10
3
100
3
Spread spectrum techniques
The following techniques are used in spread spectrum systems:-1-Direct sequence (DS)
2-Frequency hopping (FH)
3-Pulsed frequency modulation (chirp) 4-Time hopping (TH)
5-Hybrid forms [DS/FH, FH/TH and DS/FH/TH]
All the techniques mentioned above require a pseudo random noise (PN) code generator for bandwidth spreading. A (PN) generator produces a binary sequence which is apparently random but can be reproduced deterministically by the intended recipients.
Pseudonoise sequences
-A random signal cannot be predicted, its future variations can only be described in a statistical sense. However, pseudorandom signal is not random at all, it is deterministic, periodic signal that is known to both transmitter and receiver.
Why the name Pseudonoise or pseudorandom? Even though the signal is deterministic, it appears to have the statistical properties of sampled white noise. It appears, to an unauthorized listener, to be a truly random signal.
Randomness properties of a pseudorandom signal
-There are three basic properties that can be applied to any periodic binary sequence as a test for appearance of
randomness:-1-Balance property. Good balance requires as a sequence, the number of binary ones differs from the binary zeros by at most one digit
2-Run property. A run is defined as a sequence of a single type of binary digit (or digits). The appearance of the alternate digit in a sequence starts a new run. Among the runs of ones and zeros in each period, it is desirable that about one half the runs of each type are length 1, about one fourth are of length 2, one eight are of length 3 and so on.
3-Correlation property. If a period of the sequence is compared term by term with any cyclic shift of itself, it is best if the number of agreements differs from the number of disagreements by not more than one count.
Let us consider the output sequence of PN generator is 0001001101011111
1)No. of zeros =7, No. of ones =8
2)Consider the zero runs, there are four of them. one half are of length 1 and
one fourth are length 2 one fourth are length 3
Consider the linear shift register illustrated in fig(14.2). It is made up of a four stage register for storage and shifting, a modulo-2 adder, and a feedback path from the adder to the input of the
clock pulses. At each clock pulse the contents of each state in the register is shifted one stage to the right. The shift register sequence is defined to the output of the last stage in this example.
Assume that stage is initially filed with one and the remaining stages are filled with zeros, that is the initial state of the register is 1000. The shift register states will be as
follows:-1
X X2 X3 X4
fig(14.2)
a-Since the last state, 1000 corresponds to the initial state 1000, we see that the register repeats the forgoing sequence after 15 clock pulse.
b-The o/p sequence is obtained by noting the contents of stage at each clock pulse.
c-The output sequence: 00100110101111
-The shift register generator produces sequences that depend on the number of stages, the feedback tap connections and initial conditions. The output sequences can be classified
as:-1-Maximal length, have the property that for an n stage linear feedback shift register the sequence repetition period in clock pulse P is
2-Nonmaximal length, if the sequence length is less than ( )
PN autocorrelation function
-The autocorrelation function of a periodic waveform χ(t), with period is given by
And the average power of a periodic signal χ(t) is given by
-The autocorrelation function of a periodic waveform χ(t), with period in normalized from
Where χ(t) is a periodic pulse waveform representing a PN code, we refer to each fundamental pulse as a PN code symbol or a chip. -For a PN waveform of a unit chip duration and period P chips, the normalized autocorrelation function may be expressed as
(14.7) The normalized autocorrelation function for a maximal sequence , is shown plotted in fig(14.3), for three stages if reference sequence 1110010
Shift Sequence Agreement Disagreement
1 0111001 3 4 2 1011100 3 4 3 0101110 3 4 4 0010111 3 4 5 1001011 3 4 6 1100101 3 4 0 1110010 7 0 +1 1110010 daadadd d=difference a=agreement fig(14.3)
-The block diagram in fig(14.4a) shows a direct sequence (DS) modulator. Direct sequence is the name given to the spectrum spreading technique whereby a carrier wave is modulated with a data signal. χ(t), then the data modulated signal is again modulated with a high speed (wideband) spreading signal g(t).
The ideal suppressed carrier binary phase shift keying BPSK modulation results in instantaneous changes either 0 or π radians according to the data. Thus, the data phase modulated can be
fig(14.4)
Where P is the amplitude of the carrier . The transmitted waveform can be expressed by
Where g(t) is an antipodal spreading code (signal) with +1or -1. The modulator based on eq(14.8b) is shown in fig (14.4b).
-If the data input pulse χ(t) is binary value (either +1 or -1), then the initial step in the DS/BPSK modulation can be accomplished by the modulo-2 addition of the binary data sequence with the binary spreading sequence.
-Demodulation of the DS/BPSK is accomplished by correlating or remodulating the received signal with a synchronized replica of the spreading signal g(t- d), where d is the receiver estimate of the
propagation delay from the transmitter to the receiver. In the absence of noise and interference, the output signal from the correlator can be written as
Where the constant A is a system gain parameter and φ is a random phase angle in the range (0,2π). Since g(t)=±1, the product will be unity if , that is, if the code signal at the receiver is exactly synchronized with the code signal at the transmitter. When it is synchronized, the output of the receiver correlator is the despread data modulated signal. The despreading correlator is then followed by a conventional demodulator for recovering the data.
Let us consider an example of DS/BPSK modulation and demodulation as a shown in fig(14.5) following the block diagrams of fig(14.4b and d). The demodulation is a two
steps:-a-Despreading is accomplished by correlating the received signal with a synchronized replica of the code.
b-Data demodulation, is accomplished by a conventional BPSK. -In the example of fig(14.5) we see the code replica in fig(14.5e) as the phase shift (either o or π) that is produced at the receiver by despreading code.
Fig(14.5f) shows the resulting estimate of the carrier phase
after despreading or after has been added to . At this point the original data pattern can be recognized. The final step shown in fig(14.5) can be obtained after BPSK demodulator.
) (t x ) (t g ) ( ) (t g t x ) ( ) (t t x g ) ( ˆ t g ) ( ˆ t x ) (t x fig(14.5)
Processing gain and jamming margin
A fundamental subject in spread spectrum systems is how much protection spreading can provide against interfering signals with finite power. The process gain of a processor is defined as the difference between the output (S/N) ratio of the processor and the input (S/N) of the processor.
-Spread spectrum develops its process gain in a sequential signal bandwidth spreading and despreading operation. The process gain of a spread spectrum processor can be defined as
Where is the spread spectrum bandwidth (the total bandwidth used by the spreading technique) R is the data rate.
-For direct sequence systems, is approximately the code chip rate and the processing gain can be expressed as
This process gain does not mean that the processor can perform satisfactorily when faced with an interfering signal having a power level larger than the desired signal by the amount of the available process gain. For this reason, jamming Margin ( ) is used to express the capability of the spread spectrum system under interference conditions. can be expressed as
Frequency Hopping system (FH)
-In a frequency hopping system spread spectrum, the frequency of the modulating signal shift by a PN code. The frequency shifting is performed by a frequency mixer (converter).
are used to determine which one of M frequencies is to be transmitted. The position of the M-ary signal set is shifted pseudorandomly by the frequency synthesizer over a hopping bandwidth . A typical FH/MFSK system block diagram is shown in fig(14.6). In a conventional MFSK system, the data symbol modulates a fixed frequency carrier, in an FH/MFSK the data symbol modulates a carrier whose frequency is pseudorandomly determined. In either case, a single tone is
transmitted:--The FH system in fig(14.6) contains two step modulation process-data modulation and frequency hopping modulation.
-Also FH system can be implemented as a single step whereby the frequency synthesizer produces a transmission tone based on the simultaneous the desired PN code and the data.
-At each frequency hop time, a PN generator feeds the frequency synthesizer a frequency word (as a sequence of chips), which selects one of symbol–set positions.
The frequency hopping bandwidth , and the minimum frequency spacing between hop positions ∆f, determine the minimum of chips necessary in the frequency word. Thus
-Note
-The receiver for FH system reverses the signal processing steps of the transmitter. The received signal is first FH demodulated (dehopping) by mixing it with the same sequence of pseudorandomly selected frequency tones that was used for hopping. Then the dehopped signal is applied to a conventional bank of M noncoherent energy detectors to select the most likely symbol.
fig(14.6)
-The processing gain in FH is larger than DS because the SS technology permits FH bandwidth larger than implementable DS
bandwidth ( ).
-Since FH techniques operate over such wide bandwidths, it is difficult to maintain phase coherence from hop to hop. Therefore, noncoherent demodulation is used for HF.
-Let us consider the FH example illustrated in fig(14.7). The input data consist of a binary sequence with data rate R=150 bit/s. The
The symbol rate is
The symbol duration (T)= =20 msec The frequency is hopped once per symbol
The hopping rate=50 hop/sec
Fig(14.7) shows the time-bandwidth plane of the communication resource.
The tone separation
Which corresponds to the minimum required tone spacing for the orthogonal signaling.
fig(14.7)
-In a conventional 8-ary MFSK scheme, a single tone (offset from , the fixed center frequency of the data band). The only difference in this FH/MFSK example is that the center frequency of the data band is not fixed, the center frequency is changed according PN code as indicated in the dashed line.
Robustness of FH
Robustness characterizes a signals ability to withstand impairments from the channel, such as noise, jamming, fading and so on. A signal configured with multiple replicate copies, each transmitted on a different frequency, has a greater likelihood of survival than does a single such signal with equal total power and frequency (i.e one single frequency). The greater the diversity (multiple transmissions, at different frequencies, spread in time), the more robust the signal against random interference. The following example should clarify the concept. Consider a message consisting of three symbols: . If a diversity technique is used with repeating the message N times. Let us choose N=4. Then, the repeated symbols called chips can be written
Each chip is transmitted at a different hopping frequency (the center of the data bandwidth is changed for each chip). The resulting transmissions at frequencies yield a more robust signal than without such diversity as shown in fig(14.8).
fig(14.8) Fast hopping versus slow hopping
-For frequency hopping systems, the term chip is used to characterize the shortest continuous waveform in the system. FH system is classified
as:-1-Slow frequency hopping (SFH), in which the symbol rate is an integer multiple of the hop rate. That is several symbols are transmitted on each frequency hop.
2-Fast frequency hopping (FFH), in which the hop rate . That is, the carrier frequency will change or hop several times during the transmission of one symbol.
1 f 2 f 3 f 4 f 1 f fig(14.9)
Processing gain for FH
The processing gain for FH can be expressed by the general equation for processing gain as
Time hopping(TH)
Time hopping is pulse modulation with PN code sequence is used to key the transmitter on and off as shown in fig(14.10). Transmitter on and off times are there for pseudorandom, like the code, which give an average transmit duty cycle of as much as 50%.
1 2 P n T
fig(14.10)
-TH has found major application in combination with frequency hopping. The fine difference separating time frequency and plain frequency hopping is that in FH systems the transmitted frequency is changed at each code bit time, whereas a TH/FH system may change frequency only at one/zero transitions in the PN code (or change both frequency and time of transitions). Fig(14.11) shows a time hopping system.
fig(14.11)
-TH is used for ranging and multiple access applications.
Pulsed FM (chirp) systems
-One type of spread spectrum modulation that does not necessarily employ coding but does use a wider bandwidth than that absolutely required so that it can realize processing gain is chirp modulation.
-Chirp modulation has found its main application in radar but it also applicable to data communications.
-Chirp transmission are characterized by pulse RF signals whose frequency varies in some known way during each pulse period. The advantage of these transmission for radar is that significant power reduction is possible.
-The receiver used for chirp signals is a matched filter, matched to the angular rate of change of the transmitter frequency-swept signal.
-The transmitted signal can be generated by using VCO and matched filter used in the receiver as dispersive delay line (DDL). Fig(14. 12) shows typical waveform and block diagram for chirp system. t t B B / 2 where
-The chirp matched filter compresses a frequency sweep, usually linear, which provides an improvement in output signal (voltage) to noise ratio equal to , Where the compression ratio
Where transmitted pulse duration
t t B fig(14.12a)
Synchronization for SSS
For both DS and FH spread spectrum systems, a receiver must employ a synchronized replica of the spreading or code signal to demodulate the received signal successfully. The process of synchronizing the locally generated spreading signal with the received SS signal is usually accomplished in two
steps:-a-Acquistion, consists of bringing the two spreading signals into coarse alignment with one another.
b-Tracking, takes over and continuously maintains the best possible waveform fine alignment by means of a feedback loop.
-The acquisition problem is one of searching a limited region of time and frequency uncertainty in order to synchronize the received spread spectrum signal with the locally generated spreading signal. Acquisition process can be classified
as:-a)coherent. B)noncoherent.
-Since the dispreading process typically takes place before carrier synchronization, and therefore the carrier phase is unknown at this point, most acquisition process utilized noncoherent detection.
-When determining the limits of the uncertainty in time and frequency, the following items must be
considered:-1-uncertainty in the distance between the transmitter and receiver translates into uncertainty in the amount of propagation delay.
2-Uncertainty of the receiver relative velocity with respect to the transmitter translates into uncertainty in the value of Doppler frequency offset of the incoming signal.
3-Relative oscillator instabilities between the transmitter and the receiver result in frequency offset between the two signals.
Correlator structures method for acquisition
-A common feature of all acquisition methods is that the receiver signal and the locally generated signal are first correlated to produce a measure of similarity between the two. This measure is then compared with a threshold to decide if the two signals are in synchronism. If they are in synchronism, the tracking loop takes over. If they are not in synchronism, the acquisition procedure
provides for a phase or frequency change in the locally generated uncertainty region, and another correlation process is started again. 1-Direct sequence parallel search acquisitions.
Fig(14.12) shows DS parallel search acquisitions. The locally generated code g(t) is available with delays that are spaced one-half chip ( ) apart. If the time uncertainty between the local code and the received code is chips, and a complete parallel search of the entire time uncertainty region is to be accomplished in a single search time, 2 correlators are used. Each carrelator simultaneously examines a sequence of λ chips, after which the 2 correlator outputs are compared. The locally generated code, corresponding to the correlator with the largest output is chosen.
Fig(14.13) shows a simple parallel search acquisition. Assume that a sequence of N frequencies from the hop sequence is chosen as a synchronization pattern (without data modulation). The N noncoherent matched filters each consists of a mixer followed by a bandpass filter (BPF) and a square law envelope detector(an envelope detector followed by a square law device). If the frequency hopping sequence is delays are inserted into the matched filters so that when the correct frequency hopping sequence appear, the system produces a large out, indicating detection of the synchronization. Acquisition can be accomplished rapidly because all possible code offsets are examined simultaneously.
Since the required number of correlator or matched filters are large, fully acquisition techniques are not usually used.
Serial search acquisition techniques are used instead of parallel acquisition technique.
3-Direct sequence serial search acquisition.
-A popular technique for the acquisition of spread spectrum signals is to use a single correlator or matched filter to serially search for the correct phase of the DS code signal or the correct hopping pattern of the FH signal.
-In a stepped serial acquisition scheme for a DS systems, the timing of the local PN code is set, and the locally generated PN signal is correlated with the incoming PN signal. At fixed examination intervals of , where. , the output signal is compared to a preset threshold. If the output is below the threshold, the phase of the locally generated code signal is incremented by a fraction(usually one half) of a chip and the correlation is reexamined. When the threshold is exceeded, the PN code is assumed to have been acquired, the phase incrementing process of the local code is stopped, and the code tracking procedure will be initiated.
fig(14.14)
4-FH serial search acquisition.
Fig(14.15) shows, the PN code generator controls the frequency hopper. Acquisition is accomplished when the local hopping is aligned with that of the received signal, in a similar procedure to DS.
fig(14.15)
Tracking
-Once acquisition or coarse synchronization is completed, tracking or fine synchronization takes place.
as:-1. Coherent tracking loops: The carrier frequency and phase are known exactly so that the loop can operate on a baseband signal.
2. Noncoherent tracking loops: The carrier frequency is not known exactly (due to Doppler effects, for example), nor is the phase.
-In most instances, since the carrier frequency and phase are not known exactly, a noncoherent code loop is used to tract the received PN code.
1)Full time early–late tracking loop [often referred to as a delay locked loop (DLL)].
-A basic noncoherent DLL loops for a direct sequence spread spectrum system using binary phase shift keying (BPSK) is shown in fig(14.16). The data and the code g(t) each modulate the carrier using BPSK, and as before in the absence of noise and interference, the received waveform can expressed as
(14.14)
Where A is a system gain parameter and is a random phase angle in the range (.0.2π). The locally generated code of the tracking loop is offset in phase from the incoming g(t) by a time , where [ is the chip duration of PN code]. The loop provides fine synchronization by first generating two PN code sequences
filters are designed to pass the data and to average the product of g(t) and the two PN sequences .
fig(14.14)
-The square law envelop detector eliminates the data since . The output of each envelope detector is given by
Where is the autocorrelation of the PN waveform.
-The feedback signal instructs the VCO either to increase or decrease its frequency, then forcing τ to either increase or decrease. -When τ, is a small number, , yielding the despread signal Z(t), which is applied to the input of a conventional data demodulator.
-The main problem with the DDL is that the early and late arms must be precisely gain balanced or else the feedback signal will be offset and will not zero signal when the error is zero. This
problem is solved by using a time shared tracking loop in place of the full time locked loop.
-The main advantages are that only one correlator need be used in the design of the loop.
2)Tua–dither tracking loop.
-A problem with some control loops is that if things are going well and the loop is tracking accurately, the control signal is essentially zero. When the control signal is zero, the loop can get confused and do mistakable things. One type of time shared tracking loop, called the tau-dither loop (TDL), shown in fig(14.17).
-Intentionally injecting a small error in the tracking correction, so that the loop kind vibrates around the correct answer. This vibration is typically small, so that the loss in performance is minimal. This design has the advantage that only one correlator is needed to provide the code tracking function and the despreading function. -As Shown in fig (14.17), the PN code generator is driven by a clock signal whose phase is dithered back and forth with a square wave switching function, this eliminates the necessity of ensuring identical transfer functions of the early and late paths. The S/N performance of the TDL is only about 1.1dB worse than that of the DLL.
fig(14.17)
SS Commercial applications
1-Code division multiple access
-
Fig(14.18) shows the communication resource(CR) plane being partitioned by the use of a hybrid combination of FDMA and TDMA known as code division multiple access (DMA).CDMA is an application of spread spectrum (SS) techniques. Since SS techniques can be classified into two major categories, direct sequence SS and frequency hopping FHSS, thus CDMA can be also classified into two major parts.
Code division multiplexing fig(14.18)
a-FH-CDMA
At each time slot whose duration is usually short, the frequency band are divided (i.e band assignments) in FH-CDMA as shown in the fig(14.18). In fig(14.18), during time slot 1, signal 1, occupies band 1, signal 2 occupies band 2 and the signal 3 occupies band 3. During time slot 2, signal 1 hops to band 3, signal 2 hops to band 1, and so on. The CR can thus fully utilized, but the participants, having their frequency bands reassigned at each time slot. Each user employs a specific pseudnoise (PN) code orthogonal control their frequency bands and time slot.
-The block diagram in fig(14.19) shows CDMA frequency hopping. At each frequency hop time the PN generaor feeds a code sequence to a device called frequency hopper. The frequency synthesizer is used to generate one of the allowable hop frequencies according PN code. MFSK modulation is used with FH, the data symbol
At Acos ] cos[n t t A hops frequency l fundamenta step frequency MFSK k 2 fig(14.19) b-DS-CDMA
In DS-CDMA, each of N user groups is given its own code,
wherei=1,2,3,…N. The user codes are approximately orthogonal, so that the cross correlation of two different codes is near zero. Fig(14.20) shows a DS/CDMA. The first lock shows the data modulation of a carrier . The output of the data modulator belonging to a user from group 1 is
(this is a general form independent modulation) The next block, the data modulated signal is multiplied by the spreading signal belonging to user group 1, and the resulting signal is transmitted over the channel. Simultaneously, users from group 2 through N multiply their signals by their own code functions. Frequently, each ode function is kept secret, and its use is restricted to the community of authorized users. The signal
present at the receiver is the linear combination of the received signals from N users
The first stage of the receiver multiples the incoming signals by [for user 1]. The output of the multiplier will yield the signal
-If the code functions are chosen with orthogonal properties, the desired signals can be extracted perfectly in the absence of noise since and the undesired signals are easily rejected, since
fig(14.20)
Multipath channels
-fig (14.21) shows a communication link with two discrete paths. The multipath wave is delayed by some time τ, compared with the direct wave.
In a DS, if we assume that the receiver is synchronized to the time delay and RF phase of the direct path, the received signal can be expressed as
Where x(t) is the data signal, g(t) is the code signal, n(t) is a zero mean Gaussian noise process, and τ is the differential time delay between the two paths. The angle is a random phase and α is the attenuation of the multipath signal relative to the direct path. The output of the correlator can be written as
Where =1. Also for , g(t)g( )≈0. Therefore, if is less than the differential time delay between the multipath and direct path signals, we can write
Where is a zero mean Gaussian noise. We see that the SSS effectively eliminates the multipath interference by virtue of its code correlation receiver.
fig(14.21)
Note
If FH is used against the multipath problem, using another mechanism to the improvement by rapid frequency change.
Advantages of CDMA
1-Privacy, When the code for a particular user group is only distributed among authorized users, the CDMA process provides privacy, since the transmission cannot easily be intercepted by unauthorized users without the code.
2-Fading channels: If A particular portions of the spectrum is characterized by fading signals in that frequency rage are attenuated. In a FH/CDMA, only during the time a user hops into the affected portion of the spectrum will user experience
degradation. However, in a DS/CDMA only a part from the spreaded bandwidth is affected.
3-Jam resistance according the processing gain .
4-Flexibility: All users can share the full spectrum of the resources (frequency and time) asynchronously, that is the transition times of the different users symbols do not have to coincide.
Ex14.1
A hopping bandwidth of 400 MHz and a frequency step size of 100 Hz are specified. What is the minimum number of PN chips that are required for each frequency word?
Slution
Number of tones contained in Minimum number of chips
Ex14.2
Consider the DS BPSK spread spectrum transmitter. Let the input sequence 100110001, arriving at a rate of 75 bit/s, where the leftmost bit is the earliest bit. Let g(t) be generated by the shift register with initial state of 1111 and a cock rate of 225Hz.
a-Sketch the final transmitted sequence x(t)g(t).
b-What is the bandwidth of the transmitted (spread) signal. c-What is the processing gain?
d-Suppose that the estimated delay is too large by one chip time. Sketch the despread chip sequence?
solution
x(t)=100110001 with data rate=75 bits g(t) =111100010011010 with clock rate=225 Hz
Let b-Bandwidth of c-processing gain d-x(t)g(t) 000100010100101111100010100 g(t) advanced by 1chip 01110001001101011110001001 O/P sum 01101001110100010001001110
Ex14.3
terminals information at 9.6 kbit/s with a direct sequence spread spectrum BPSK modulated signal. Calculate the minimum chip rate of the PN code in order to maintain a bit error probability of
solution
from table of error function x=3.09
4.77=
W=4.77x23x9.6 kbit/s=1.05 MHz
minimum chip rate
where
bit energy,
bit duration
S=received signal power, R=data rate
where =averages signal power to average noise power =Noise power spectral density
W=bandwidth of the system
Ex14.4
Consider an FH/MFSK system .Let the PN generator be defined by a 20 stage linear feedback shift register with a maximal length sequence. Each state of the register dictates a new center frequency within the hopping band. The minimum step size between center frequencies is 200Hz. The register clock rate is 2KHz. Assume that 8-ary FSK modulation is used and that the data rate is 1.2kbit/s. a-What is the hopping bandwidth.
b-What is the chip rate.
c-How many chips are there in each data symbol. d-What is the processing gain.
solution
Hopping bandwidth=
Wss=number of states×minimum step between frequencies
b-chip rate =hop rate=2000chip/s c-chip/symbol:
A feedback shift register PN generator produces a 31 bit PN sequence at a clock rate of 10MHz. What are the equation and graphical form of the autocorrelation function and power spectral density of the sequence? Assume that pulses have values of ±1v.
Solution
The 31 bit sequence has autocorrelation function with a maximum value at
Decreasing linearly to -1/31 at for T equal to a chip interval
[total agreements –total disagreements in one full period of the sequence with a τ position cyclic shift]
) 1 2 ( 31 P
