Hyder Khoja Page 1 1/28/2022 DIGITAL MODULATION TECHNIQUES 1. MODULATION - Modulation is the process of changing some characteristics of a carrier wave in proportion to the signal to be transmitted. - A general equation for a sine wave is: Equation 1. Where is instantaneous amplitude of the sine wave as a function of time. : peak amplitude of the sine wave. : frequency of the sine wave in hertz. : time in seconds. : phase in radians. - Equation one suggests that there are only 3 ways, the sine wave can be changed: a. The amplitude . b. The frequency . c. The phase . - It is also possible to change more than one of these quantities simultaneously. - In digital communications, it is common practice to change both the amplitude and the phase angle to obtain higher data rates. - It should be noted that once a carrier is modulated, it becomes a complete waveform containing more than one frequency components and therefore would require an appropriate channel that can carry all frequency components of this complex modulated signal.
Transcript
Hyder Khoja Page 1 5/6/2023
DIGITAL MODULATION TECHNIQUES
1. MODULATION
- Modulation is the process of changing some characteristics of a carrier wave in proportion to the signal to be transmitted.
- A general equation for a sine wave is:Equation 1.
Where is instantaneous amplitude of the sine wave as a function of time.: peak amplitude of the sine wave.: frequency of the sine wave in hertz.
: time in seconds.: phase in radians.
- Equation one suggests that there are only 3 ways, the sine wave can be changed:a. The amplitude .b. The frequency .c. The phase .
- It is also possible to change more than one of these quantities simultaneously.
- In digital communications, it is common practice to change both the amplitude and the phase angle to obtain higher data rates.
- It should be noted that once a carrier is modulated, it becomes a complete waveform containing more than one frequency components and therefore would require an appropriate channel that can carry all frequency components of this complex modulated signal.
- This gives use to the concept of bandwidth. The signal now occupies a BW and the channel must have sufficient BW.
2. INFORMATION CAPACITY
- Hartley’s Law states that:
Where is the information capacity in bits.: constant that depends upon the modulation scheme and the signal to
noise ratio.: Bandwidth of the system in hertz.
- Note that Hartley’s law is an extremely important law and applies to the operation of all communication systems.
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3. ANALOG MODULATION
- When the modulating signal (the information to be transmitted) is analog in nature, it is called analog modulation. Analog modulation is characterized by continuous changes in the modulated signal.
- Analog modulation is of 3 types as suggested by equation 1:a. Amplitude Modulation (AM): In AM the amplitude of the carrier is varied in
accordance to the instantaneous changes in the amplitude of the modulating signal as shown in the figure below.
b. Frequency Modulation (FM): In FM the frequency of the carrier is changed in proportion to the amplitude of the modulating signal as shown n the figure page 50 H.
c. Phase Modulation (PM): In PM the phase of the carrier is changed in proportion to the instantaneous amplitude of the modulating signal as shown in the figure page 50 H.
4. DIGITAL MODULATION
- When the modulating signal is a digital signal, it is called digital modulation.- Digital modulation results in discrete changes in the modulated signal.- The receiver examines the signal at specified times only and the state of the signal at
each such time is called a symbol.- The exact data rate depends upon the number of signal changes per second.- Bit Rate: Is the number of bits transmitted per second, which is the data rate.- Baud Rate: Is defined as the number of signal changes per second or number of
symbols per seconds that the line experiences or senses the changes in signal states. It
Modulating signal
Carrier
Modulated signal
V
time
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is possible to carry several bits per signal change, giving a higher data rate than the baud rate.
- There is a theoretical limit to the maximum data rate that can be transmitted with a given BW.
- Shannon-Hartley’s Law states that:Equation 2.
Where is the information capacity of the channel in bits/sec: Bandwidth.: number of possible states per symbol.
- Noise also puts limits to the information capacity.- Shannon’s Law states that:
Equation 3.
C can also be expressed as:
Where is the baud rate in symbols per second.: number of symbols.
5. DIGITAL MODULATION SCHEMES
- Figure page 324 H shows various digital modulation schemes used in various communication systems.
- Amplitude Shift Keying (ASK): As seen in the figure, in ASK the is turned on and off in response to the digital data. A binary “1” is represented by the presence of the carrier and a “0” by the absence. Bell 202 modem uses ASK for error control.
- Frequency Shift Keying (FSK): In this case the frequency of the carrier is shifted in response to a binary 1 or 0. For example Bell 103/113 modems use FSK to transmit digital data.Originate Mode: = 1170 Hz, “1” = 1270 Hz, “0” = 1070 Hz.Answer Mode: = 2125 Hz, “1” = 2225, “0” = 2025 Hz.
- One method to generate FSK is to frequency modulate a single carrier oscillator using the message signal.
- Gaussian Minimum Shift Keying (GMSK): In GMSK, the “1” and “0” frequencies are separated by half the bit rate.
bit rate, where is the mask frequency and is the space frequency. Thus, the deviation from the center frequency of the carrier will be .
Thus the modulate index will be: .
Thus GMSK uses less BW than conventional FSK.
Example:The GSM cellular radio system uses GMSK in a 200KHz channel, with a channel data rata of 270.833 Kbps. Calculate:a. Frequency shift between mask and space.
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b. If the carrier frequency is 880 MHz, calculate the transmitted frequency.c. The BW efficiency of the system in b/s/Hz.
Solution:a. Frequency shift =
.b. The shift each way for the carrier frequency will be half of
c. BW efficiency = .The word “Gaussian” refers to the shape of the filter that is used before the modulated Gaussian filter reduces the BW of the transmitted signal by allowing to change gradually from mask to space rather than instantaneously as is the case with regular FSK.
- Phase Shift Keying (PSK): In this case the phase of the carrier is charged in accordance with the data while keeping the frequency constant and when only two phases are used, it is called BPSK.PSK requires changing the phase of the carrier with respect to a reference phase.A “0” represent a 0 degree reference phase and “1” represents a carrier shift of 180° as shown below on the constellation diagram.
“I” stands fro In-phase and “Q” stands for Quadrature.For BPSK, one bit causes one phase shift in the carrier phase as one signal change/bit.
- Quadrature Phase Shift Keying (QPSK): QPSK implements the concept of phase shift further. The carrier can be made to under go 4 phase shifts, thus can represent 4 binary bit patterns of data, effectively XXX the data rate as shown below:
- GPRS uses 8-PSK as shown above, effectively tripling the data rate as we are now transmitting 3 bits per signal change. Since it is difficult to maintain a zero degree reference, phase changes are measured with respect to previous phase.The figure below shows how way to generate a di-bit PSK output.
- Quadrature Amplitude Modulation (QAM): The only way to obtain higher data rates with a narrow band channel is to increase the number of bits per signal change.QAM uses a combination of amplitude and phase modulation, for example, the table below shows two messages of amplitude and 4 possible phase shifts to transmit 3 bits per signal change.
- Mathematically there is no limit to the data rate that may be supported by a given baud rate, however, practically it is limited by the presence of noise, when the adjacent states become too small to be detected reliably.
000 000101
110
111
010
011
2V180°
1V180°
1V0°
2V0°
001
2V, 90°
1V, 90°
000001010011100101110111
1V2V1V2V1V2V1V2V
0°0°90°90°180°180°270°270°
Amp Phase
Function Generator
Oscilloscope
1 2I + Q = 45°
I = 0°
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- On the scope, QAM signal has noise appearance as blurred data Page 124 B, Page 332, 333, 335, 337 H, Page 164, 165 Agenxx.
- 16 QAM involves applying the signal with 12 different pahses and 3 different amplitudes for a total of 16 different possible values each encoding 4 bits.16 QAM is used in microwave digital radio, digital video broadcasting - cable, and high speed modes.
6. SPREAD SPECTRUM MODULATION TECHNIQUES
- Spread Spectrum Modulation technique was developed by U.S. military some 50 years ago to prevent or minimize jamming of U.S. radio signals by enemy forces.
- Today, in its advanced form, it is being widely implemented in CDMA systems as well as 802.11 wireless LAN.
- Not only that, some v variation of CDMA is expected to be deployed in all future 3G systems including GSM/NA-TDMA wireless networks.
- The SS modulation technique consists of spreading a narrowband signal over a very large BW, so that only a small portion of the signal is transmitted at a time. Thus only a small portion of the signal is transmitted at a time.
- Thus only a small portion of the signal is affected by the presence of interference and noise, and it also improves security by making eavesdropping virtually impossible.
TYPICAL QPSK TRANSMITTER
- 90° phase Shift ± BPFQPSKoutput~
Sin(wct)Binarybits
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- This is very similar to having a 12-lane highway. If an accident occurs in one lane, the traffic can still move along the other 11 lanes.
- BW spreading is accomplished before the transmission through the use of a code that is independent of the transmitted data.
- The same code is used to demodulate the data at the receiving end.- The figure below shows spreading of the data signal by the code signal ,
creating a modulated message :
- There are basically 2 frequency spread techniques:a. The Frequency Hopping Spread Spectrum (FHSS).b. Direct Sequence Spread Spectrum (DSSS).
6.1. Frequency Hopping Spread Spectrum (FHSS)
- FHSS uses a range of frequencies to send a signal rather than just one frequency.- A pseudorandom sequence is used to change the radio signal frequency across a
broad frequency band in a fashion that appears to be random to an unintended receiver.
- However, the intended receiver is preprogrammed to de-hop the received band of frequencies to recover the original signal.
- The technique consists of transmitting a short burst of the signal at one frequency, then another short burst at another frequency and so on, until the entire signal has been sent, as shown in the figure below:
c(t)
Transmitter
Digital signal
s(t)
Spread signalm(t)
f
Power
f
Power
Hopping Paddles
Transmitter
Digital signal
De-Hopping
Receiver
Digital signal
Spread signal
f
Power
f
Power
f
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- The received signal is de-hopped at the receiver using a frequency synthesizer controlled by a pseudo random sequence generator synchronized to the transmitter’s pseudo random sequence generator.
- Multiple users can transmit simultaneously as long as they are using a different hopping sequence, or if they are using the same hopping sequence at different times.
- Consider the figure shown (Page 41 Ciampa).
6.2. Direct Sequence Spread Spectrum (DSSS)
- In DSSS, the radio signal is multiplied by a pseudorandom sequence whose bandwidth is much greater than of the signal itself.
- Effectively, DSSS transmits a lot more bits than the data bits, thereby spreads the signal.
- Errors or interference, or fading will affect only a small portion of the original signal.
- Thus all subscribers can use the entire allocated frequency spectrum as long as they are using a different modulating code.
- CDMA uses DSSS technique.- In DSSS, a pseudo random sequence directly phase modulates a data modulated
carrier as shown in the figure below:- The pseudo random code is called a chipping code.
- Consider the figure in the hand out, Page 44 Ciampa.- 3 bits are being transmitted 1,0,1.- However DSS substitutes these 3 original bits with (mixed with the chipping
code) 1001, 0110, 1001.- Notice that for 1 it transmits 1001, and for a 0 it transmits 0110.- Most chipping odes are actually 11 bits long.- Next it combines the chipping code with the data bit as follows:
a. For a data bit of “1”, it adds 1 to each bit of the chipping code.
Hopping Paddles
Transmitter
Digital signal
De-Hopping
Receiver
Digital signalSpread signal
f
Power
f
Power
f
Spreading Dispreading
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b. For a data bit of “0”, it adds “0” to each bit of the chipping code, as shown below:
1 0 0 1 0 1 1 01 1 1 1 0 0 0 0
0 1 1 0 0 1 1 0
- This is what is actually sent.- For consecutive “1” bits an extra “0” bit is placed between them in the chipping
code so that it becomes 100101001 which is transmitted as 011010110.- It is instructive to note that to an unintended receiver, the sequence appears
random or as noise spikes because of the low power and will be rejected, but an intended receiver, properly programmed and synchronized with the transmitter, will properly decode the received signal.
- This spread spectrum technique has great advantage in terms of anti-interference characteristics, security and improved capacity.
- CDMA uses WALSH codes that has orthogonal properties (non-over lopping).- In the next section we will study WALSH code.
Now let us take a deep look at DSSS process:
- For DSSS, each bit in the original signal is represented by multiple bits in the transitted signal, using a spreading code called pseudorandom sequence code (PNC) or orthogonal code such as Walsh code.
- A 10 bit spreading code spreads the signal across a frequency band that is 10 times greater than a 1 bit spreading code.
- The technique used is to combine the digital data stream with the PNC using an X-OR function as shown in the figure (figure 76 page 167 W.S.). Notice that in this figure, the spreading code bit is clocked at 4 times the data bit rate.
- At the receiver, the same PNC is used with a X-OR function to recover the original data bits.
6.3. DSS Using BPSK
- Recall that in BPSK data bits are represented by a “+1” and “-1” instead of binary “1” or “0”.
- These data bits produce a phase shift in the carrier frequency.- There are 2 ways to implement this scheme:
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a. First multiply (X-OR) data bits with the PNC and then perform BPSK. This was done in fig 7.6 above.
b. The second implementation would be to first perform BPSK on the data stream and then combine the result of BPSK with the PNC. This is shown in fig 7.8 page 169 W.S. Notice that in this figure “+1” and “-1” have been used (instead of “1” and “0”) to represent both: the data bits and the code bits.
7. Code Division Multiple Access (CDMA)
Note: The following material has been derived from “Wireless Communication Networks by William Stalling”, and QUALCOMM Inc.
- In CDMA all users use the same carrier frequency but each user is assigned a separate code.
- Thus there is no limit to the number of users as long as they use different “non-interfering” codes to transmit and receive.
(3 dimensional picture illustrating CDMA)
- CDMA is a multiplexing scheme that uses spread spectrum technique.- Each user is assigned a separate spreading code called chipping code. A k bit code is
called a k chips code.- The receiver knows the chipping code for each user and must be synchronized with
the transmitter to decode the data bits.- Let us consider an example of 3 different users, with 3 different codes assigned (fig
7.10 W.S.).- Notice that we start with the signal data rate of D bits/sec for each user and multiply
it with a k chip code. The result is a bit stream of kD bits/sec. In the figure k = 6.- All 3 users are communicating with the same base station receiver.- The user A data bits are 1101.- The figure shows how the BS receiver recovers user A’s data bits when synchronized
with A’s transmission, which rejects B and C transmission.- Chipping code for A,B,C are:
- For data bits “1” the chipping code is sent as it is.- For a data bit “0”, the complement of the chipping code is sent to the receiver. For
user A we have:
7.1. Decoding at the receiver
- The receiver simply performs the following function:
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Where d represents the received data bits and c represents the chipping code for the user. The receiver is trying to decode as shown.
- For user A:For data bits “1”:
For data bits “0”:
- It is instructive to note that if the chipping code is selected properly, the receiver will always decode +6 for “1” and –6 for “0” regardless of the actual sequence of data bits. Any other value represents error or noise or someone else’s information.
- You can verify, that for B and C data bits , if we try to decode with A’s code, the result will be “0”.
- Table 7.1 (W.S.) shows the result of the calculation.- It is interesting to observe the results of case (d) and (e).- Note that in case (d) B and C are transmitting simultaneously and the receiver is
attempting to decode B’s transmission. The result of multiplication and addition is not zero. What does it mean? It means that there is a small contribution from C to B’s transmission.
- In practice, CDMA receiver can filter out the contributions from unwanted users as they appear as low-level noise.
- Two codes that produce “0” after multiplication and addition are called orthogonal codes or non-overlapping codes.
- WALSH codes are the most common orthogonal codes used in CDMA applications.
7.2. Generation of Orthogonal WALSH Code.
- Orthogonal codes are generated by:1) Starting with a seed of 0.2) Repeating the zero horizontally and vertically.3) Complementing the “0” diagonally.4) This process is continued with the newly generated block until the desired
codes with the proper length are generated.5) Sequences created in this way are called Walsh codes.6) The process is shown below.
- Qualcomm developed CDMA.- Figure shows 64 bit Walsh codes.
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7.3. Implementing the Spread Spectrum Hardware
- As mentioned earlier, the spreading sequence (the code c(t)) is a sequence of binary digits shared by both the transmitter and the receiver.
- Spreading consists of multiplying (X-ORing) the input data by the spreading sequence, where the bit rate of the spreading sequence is much higher than the input data rate.
- When the signal is received, the spreading is removed by multiplying (X-ORing) again with the same spreading code, exactly synchronized with the received signal.
- CDMA uses both pseudorandom and orthogonal codes.- A pseudorandom generator produces a periodic sequence that eventually repeats
but that appears to be random.- The period of a sequence is the length of the sequence before it starts repeating.- PN sequences 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, a good algorithm will produce sequences that will pass many tests of randomness.
7.4. Correlation
- Correlation is a measure of similarity between any two arbitrary signals.- It is defined as follows: if a period of the sequence is compared term by term with
any cycle shift of itself, the number of terms that are the same differs from those that are different by at most 1. Meaning, there is only 1 common term in the entire shift.
- Figure 7.13 W.S. shows one such 4 bit sequence. Notice that after the complete shift.
- This seemingly complex mathematical procedure requires extremely simple hardware.
- Spreading codes are generated using flip-flops (shift registers) and EX-OR gates.- Here is the procedure:
a. The shift register contains n bits.b. There are 1 to (n-1) EX-OR gates.
d1(t)TX RX
Cos(2πfct) c(t)
EX-ORd1(t)
Cos(2πfct)c(t)
EX-OR
Data bits modulated with the carrier.
Demodulated with fc
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c. The presence or absence of an EX-OR gate corresponds to the presence of a term in the generator polynomial G(x) = A0+A1x+A2x2+…+An-1xn-1+xn, excluding the xn term.
- Referring back to figure 7.13, and table 7.2.- Table 7.2 shows the output sequence generated by the circuit of figure 7.13(a) for
different initial states of the shift register.- Table 7.3 (W.S) tests a generator polynomial that produces an m-sequence for the
shift register of various sizes.- IS-95 uses 2 short PN codes and one long PN code.
a. Two short codes: 215-1 = 32.768.b. One long code: 242-1 = 4400 billion.
- A very important property of PN code is that “time shifted versions of the same PN code sequence have very little correlation with each other”.
- The channalization of users in the reverse link (mobile to BS) is accomplished by assigning each station a different time shifted version of the long code, thus making them uncorrelated with each other.
- This allows BS receivers to distinguish transmission from different mobile.- Let us take an example of a simple 7 bit code using the technique described
earlier.- Consider the figure shown.
- For simplicity, this circuit is drawn as shown below in many technical literatures.
- This circuit produces the sequence 1001011 when the initial state 001 from left to right. The truth table after each shift is shown below.
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- PN codes are m-sequences or maximum length codes.- In general, if there are N flip-flops, the length of the PN code is 2N-1. For
example: in the above example, N=3, so the length of the PN sequence = 23-1=7.- The system keeps generating the sequence 1001011,1001011,1001011 with
continuous clocking.
7.5. Masking
- Masking provides shift in time for PN codes.- Different masks will provide different time shifts.- In CDMA (IS-95) standard, ESN (Electronic Serial Number) are used as masks
for users on the traffic code channels.- Figure below shows Qualcomm masking scheme (page 56, 57 K).- There figures show how a mask generates the same original signal code but
shifted in time.- The 3 digit mask in this diagram determines the offset of the sequence.- Long code offsets are used to separate channels in the reverse link.- The offsets in the short code are to uniquely identify the forward channels of
