modulation techniques in satellite communications

Slide Number 1Rev -, July 2001

Technical Introduction to Geostationary Satellite Communication Systems Original Prepared by Telesat Canada

3.4



Vol 3: Satellite Communication Principles, Sec 4: Modulation Techniques

Part 1: Analog Techniques

3.4.1.1: Amplitude Modulation

Amplitude ModulationAmplitude modulation is very rarely used in satellite communications. Other modulation techniques as described in other sections provide many benefits over amplitude modulation. One of the major problems with amplitude modulation is its susceptibility to noise.

Unwanted amplitude modulation will cause phase (or frequency) modulation in non-linear devices. The parameter defining this is called AM/PM conversion. This unwanted modulation will exhibit itself as phase or frequency shifts in addition to those from the actual signal. The net effect of the AM/PM conversion is unwanted noise.





3.4.1.2: Frequency Modulation

Frequency ModulationRecall that Frequency Modulation (FM) is the process of shifting the frequency of a bearer carrier by an amount dependant upon the amplitude of the applied information-carrying signal.

FM was created to be amplitude independent, sidestepping the noise-producing effects that undesired amplitude variations have on AM carriers.

The amount that the carrier frequency shifts away from its rest frequency when modulated is called “deviation”.

Since we must be careful not to let the frequency of our carrier stray into the frequency assigned to an adjacent carrier, the amount of deviation—hence the amount of modulation—must be carefully controlled, and is in fact subject to government regulation.






Frequency ModulationFM provides an important tradeoff between the use of bandwidth and the use of power. This is a very important factor in using FM in satellite communications. FM is particularly convenient in single carrier applications because the constant envelope of the FM signal allows the power amplifiers to operate near saturation, therefore maximizing the use of available power.

FM is also used to distribute analog TV broadcasts. The audio signal is usually multiplexed with a video sub-carrier using FDM.

Assignment of the subcarrier frequencies will result in third order intermodulation problems, however careful placement of the subcarriers can significantly reduce this problem. Consequently, the intermodulation products and harmonics they generate primarily determine sub-carrier spacing.



Frequency ModulationThe most popular audio sub-carrier frequencies are as follows:

Sub-carrier plan Freq (MHz) Audio Deviation (kHz) Mod. Index Rxfilter (kHz)

High Level (A) 6.8 100 0.294 400

High Level (B) 6.8 100 0.294 4006.17 100 0.294 4005.41 100 0.294 400

1 High Level &8 Low Level (C) 6.8 100 0.294 400

5.4 50 0.15 1305.58 50 0.15 1305.76 50 0.15 1305.94 50 0.15 1306.12 50 0.15 1306.3 50 0.15 1307.38 50 0.15 1307.56 50 0.15 130






Frequency ModulationAudio deviation of 100 kHz occurs with a 1 kHz signal @ 8 dBm.

Audio deviation of 50 kHz occurs with a 1 kHz signal @ 18 dBm.

The bandwidth requirements for low distortion transmissions include those sidebands that are 40 dB below the unmodulated carrier. All other sidebands below the –40 dB level are ignored.

For voice communication, a higher degree of distortion can be tolerated; therefore, sidebands below –20 dB levels are ignored.






Frequency ModulationBandwidth can be calculated by Carson’s formula:

B = 2fm (1 + m)where: B = bandwidth

fm = modulating frequency

m = modulating index

m = deltaFmax/fm

Advantages & DisadvantagesFM carriers have the following advantages:

• Constant Amplitude• High Signal-to-Noise Ratio• Very mature technology

EQ. 3.4.1a Bandwidth






Frequency ModulationThe main disadvantage is:

• Very large bandwidth requirement

Single Channel per Carrier FM (SCPC/FM)An SCPC/FM network is primarily intended for telephony applications. A single carrier is used to transmit a telephone channel, therefore eliminating expensive multiplexing and de-multiplexing equipment.

This type of system can therefore be used in networks where traffic channel capacity is low. Although SCPC/FM technology is old, it has been coupled to a DAMA processor to provide dynamic selection of uplink frequencies to provide multiple access in star or mesh configurations.






Frequency ModulationSignal-to-noise performance can be calculated as follows:

S/N = C/No – 95.4 + 20 log10 deltafpk

The formula assumes 2.5 dB weighting and 6.3 dB pre-emphasis gain.

The use of companders can reduce the peak deviation and thus reduce the transponder bandwidth requirements.

Analog TelevisionFor a FM link carrying television, a simple general form is given here for the relationship between baseband signal-to-noise ratio (S/N) and the ratio of the carrier power-to-noise power density (C/No) applied to the receiver discriminator.

EQ. 3.4.1b S/N Performance






Frequency ModulationS/N = C/No + 10 log [ 3/2delta f2

pk/f3v] + PW – IM +CF

Delta fpk= peak deviation of video signal

fv = top baseband frequency (NTSC=4.2MHz, PAL=5MHz)

IM = demodulator implementation margin (0.8 to 1 dB)

CF = rms to peak-to-peak luminance signal conversion factor (6 dB)

PW = emphasis plus weighting factor (NTSC=12.8 dB, PAL=6 dB)

Frequency Division Multiplexed FM (FDM/FM)In a FDM/FM system a number of channels are arranged side-by-side in the baseband; therefore, many narrow bandwidth channels can be accommodated by a single bandwidth transmission system. The FDM baseband is fed from the multiplex equipment to the FM modulator, giving rise to FDM/FM.

EQ. 3.4.1c Analog






Frequency ModulationAudio channels are stacked one above each other at 4 kHz intervals. Stacking is done by the double-sideband suppressed carrier (DSBSC) method.

Therefore each voice channel is first amplitude modulated on the appropriate carrier then the upper sideband is filtered out.

All the lower sidebands are summed to provide the baseband signal ready for FM modulation.






Frequency ModulationThe bandwidth of the baseband signal in relation to channel capacity is highlighted below:

Audio Channel Capacity Baseband Signal fmax (kHz)

12 6024 10836 15648 20460 25272 30096 408132 552192 804252 1052312 1300372 1548432 1796492 2044552 2292612 2540792 3284972 40281092 48921200 53401332 58841872 8120






Frequency ModulationIt is a common practice to use “white noise” loading to simulate the audio channel capacity within the allotted baseband signal (fmax).

Equivalent loading was established by CCIR and given by the following equations:

L = (-15 + 10 log10 N) dBm0When N > 240 audio channels

L = (-1 + 4 log10 N) dBm0When N = 12 to 240 audio channels

EQ. 3.4.1d Equivalent Loading (N>240)

EQ. 3.4.1e Equivalent Loading (N=12)






Frequency ModulationThe relationship between S/N in the baseband and C/N in the IF spectrum is given by the following formula:

S/Nw = C/Nif + 20 log10 (fp/fmax) + 10 log10 (Bif/2b) + P + W + Cfp = peak test-tone deviation at 0 dBm0(Hz)

Fmax = highest voice channel frequency (Hz)

2b = channel bandwidth (Hz)

Bif = receiver IF bandwidth (Hz)

P = psophometric weighing improvement factor (2 dB)

W = top channel emphasis improvement factor (4 dB)

C = companding advantage if used (17 dB)

C/Nif received IF carrier-to-noise ratio (dB)

EQ. 3.4.1f S/N & C/N Relationship






3.4.2 Digital Techniques




Part 2: Digital Techniques

3.4.2.1: Analog to Digital Conversion

Analog to Digital ConversionPulse Code Modulation (PCM) is a conglomerate term used to describe several essentially separate functions:

• Sampling of an analog signal• Quantizing the sample amplitudes• Encoding to generate a digital signal representing the quantized

analog samples

PCM is used because transmission quality is almost independent of distance, particularly when the concept of digital switching is taken into account.

For telephony, an error ratio of 1 X 10-4 is generally regarded as being acceptable and as not having any significant effect on speech. Furthermore, it is possible to implement long transmission paths without infringing this limit.



Analog to Digital ConversionSamplingThe theory of sampling shows that if a waveform has a spectrum that is limited to a finite range of frequencies it is not necessary to know its value at every instant in time in order to completely specify it.

In simple terms, Nyquist’s sampling theorem states:

“If a continuous function f(t) contains no frequencies greater than f Hertz, the function may be completely described by the magnitudes of its ordinates at intervals not less than 1/2f seconds”.

This means that if the spectrum of a signal has an upper frequency limit of f Hertz and the sampling frequency is at least 2f then the sampling process loses no information.






Analog to Digital ConversionIn telephony applications the audio signal is band limited by a low-pass filter with a nominal upper limit of 3400 Hz. Consequently, a sampling frequency of 8000 Hz is generally used in the telephone industry.

QuantizingSince the amplitude samples derived from the original signal are to be represented by binary numbers, it is necessary to limit the number of permissible values. This means, in practice, that bounds are set within which any amplitude will have a single binary number allocated to it by the encoder.

For an n-digit system there will be 2n quantized values. Therefore an 8 digit application (28 = 256) with a set of 256 quanta will have 128 positive decision values and 128 negative decision values. The bound of each quantum is a decision value.






Analog to Digital ConversionTherefore, a maximum error of up to half a quantum between the actual signal and the quantized value will result.

Since the PCM receiver can only interpret the received binary number as the corresponding quantized value, a discrepancy will occur between the original magnitude of the sample and its reconstructed value.

These discrepancies appear as a noise signal superimposed on the received speech, and this is known as quantization distortion.

EncodingThe encoder is that part of the PCM system that generates binary signals representing the quantized values of the samples.






Analog to Digital ConversionIt is possible to modify the relationship between the input signal and the decision values of the encoder to improve the quantizing distortion characteristics with respect to low level input amplitudes.

One companding method is to compress the audio signal before being input into a linear encoder and expand the audio signal at the output of the linear decoder. This primitive technique does improve the overall S/N ratio, but is no longer in use today.

A prominent companding method is to input the audio signal into a non-linear encoder. Conversely, a non-linear decoder will output the audio signal.






Analog to Digital ConversionEncoding LawsTwo other companding methods come in the form of non-uniform encoding laws: the Mu-law ("-law") and the -Law.

The relationship between a uniform coder and an equivalent non-uniform coder, both having the same dynamic range at the analog input, is commonly known as the companding advantage, expressed as:

20 log10 N/n dBN = number of decision values of the uniform codern = number of decision values of the non-uniform coder

Consequently, the S/Q ratio of a companded audio signal, measured in dB, will significantly improve relative to a non-companded audio signal.




EQ. 3.4.2.1a Companding Advantage



Analog to Digital ConversionThe table below highlights the companding advantage provided by -law, -law companders compared to a linear encoder. The CCITT limits are highlighted for reference.

Audio input -law S/Q -law S/Q Linear S/Q CCITT S/Q limit-55 24 17 12-50 27 23 17-45 31 27 22-40 34 32 4 27-35 36 36 14 32-30 37 38 18 33-25 38 39 24 34-20 39 39 28 34-15 39 39 34 34-10 39 39 38 34-5 38 37 44 32-3 30 31 40 27






Analog to Digital Conversion-LAW Theory

Compression and decompression of sound files (companding) by -law is a form of logarithmic quantization or companding. It is based on the observation that many signals are statistically more likely to be near a low signal level than a high signal level.

A way of modifying this unevenness is to gradually move the low level signals into the upper energy bands. This is achieved by applying a logarithmic rule to the input signal, which modifies all inputs to fit a suitably curved transfer function.






Analog to Digital ConversionThe -law compression function is as follows:

Y = loge (1 + x)/loge (1 + )

Where x = is the input signal,Y = is the calculated compressed output signal

For =1 the function is relatively flat. The function gradually increases its curvature as is increased. The value used commonly in telecommunications is 255.

EQ. 3.4.2.1b -Law Compression






Analog to Digital Conversion-LAW Theory

This method of compression and decompression is similar to -law except there are two transformation laws placed on the input signal depending upon the value of the input signal.

Initial transformation is a linear section which starts from zero to a limit of 1/A . Following this is a curved transformation similar to the -law.






Analog to Digital ConversionThe -law compression functions are as follows:

Y = 1 + loge (Ax)/1 + loge A

(for input signals with value from 0 to 1/A)

Y = Ax/1 + loge A(for input signals with value > 1/A)

The A value used commonly in telecommunications is 87.6

EQ. 3.4.2.1c -Law Compression

EQ. 3.4.2.1d -Law Compression






Figure 3.4.2.1 Quantization N

oise (Error)






Analog to Digital ConversionDifferential Pulse Code Modulation (DPCM)In a typical PCM-encoded speech waveform there are often successive samples taken in which there is little difference between the amplitude of the two samples. Therefore many redundant PCM codes are transmitted.

Differential Pulse Code Modulation (DPCM) is designed specifically to take advantage of the sample to sample redundancy in typical speech waveforms. With DPCM, the difference in amplitude of two successive samples is transmitted rather than the actual sample. Since the range of sample differences is typically less than the range of individual samples, fewer bits are required for DPCM then conventional PCM. Therefore, for telephony applications, a 64 kbps PCM signal is compressed to 32 kbps.






Analog to Digital ConversionAdaptive Differential Pulse Code Modulation (ADPCM)

ADPCM is a family of speech compression and decompression algorithms. ADPCM produces a lower bit rate by recording only the difference between samples and dynamically adjusting the coding scale to accommodate large and small signal differences. In telephony applications ADPCM will compress a 64 kbps PCM signal to 32 kbps without affecting the quality of service, therefore, maintaining a TOLL quality standard.








3.4.2.2: Frequency Shift Keying (FSK)

Frequency Shift Keying (FSK)FSK is a digital frequency modulation technique in which the modulating signal shifts the output frequency between predetermined values. Therefore two different carrier frequencies are used to represent a binary “1” state and “0” state.

As we saw in the FM versus AM advantage, FSK avoids most of the problems associate with Amplitude Shift Keying (ASK) because it can ignore amplitude noise spikes.



Frequency Shift Keying (FSK)

Figure 3.4.2.2 Frequency Shift Keying



3.4.2.2: Frequency Shift Keying (FSK)





3.4.2.3: Phase Shift Keying (PSK)

Phase Shift Keying (PSK)The selection of a particular modulation technique depends on the specific system configuration. The parameters of importance are as follows:

• Power efficiency (lowest error rate for a given received Eb/No)• Bandwidth efficiency (lowest required bandwidth for a given data

rate)• Cost of hardware and availability• Interference susceptibility• Constant amplitude RF signal

PSK offers excellent performance and makes multi-phase modulation available. PSK is the method most commonly used in digital satellite communication systems.



Phase Shift Keying (PSK)Binary Phase Shift Keying (BPSK)BPSK is a modulation process whereby the input data bits shift the phase of the carrier to two discrete states as:

Y(t) = A cos (Wct + i pi)

Where i = 0, 1 and –T/2 < t < T/2

Wc = carrier frequency, radian/second

The vector representation of BPSK is shown on the next slide. From bit interval to bit interval the phasor instantaneously changes from one state to the other.

EQ. 3.4.2.3a BPSK






Figure 3.4.2.3a BPSK






Phase Shift Keying (PSK)

BPSK RF Carrier

This is a plot of the spectrum of a BPSK signal with a data rate of 100 kbps and a carrier (modulated) frequency of 400 kHz.

Figure 3.4.2.3b BPSK RF Carrier






Phase Shift Keying (PSK)A common filter used is the root-raised cosine filter. The name of this filter is derived from the description of the spectral (frequency) shape that it provides. Essentially the filter replaces the square pulses with one shaped like that in this plot.

Figure 3.4.2.3c BPSK RF Carrier






Phase Shift Keying (PSK)

Since there are no sharp edges or quick transitions in the modulated signal, its frequency spectrum will be much more contained in a band around the carrier center frequency, as shown below.

Figure 3.4.2.3d BPSK RF Carrier






Phase Shift Keying (PSK)Quadrature Phase Shift Keying (QPSK)A QPSK modulator takes two input data bits at a time, I and Q, and produces a carrier whose phase is one of four values. By using two bits at a time the modulator achieves a signaling rate reduction of one-half. The QPSK modulator can be considered as two BPSK modulators in phase quadrature whose outputs are added together.

Figure 3.4.2.3e QP

SK






Figure 3.4.2.3f QPSK






Phase Shift Keying (PSK)Multi-Phase Shift Keying (M-PSK)BPSK and QPSK are subsets of M-PSK, wherein the output can assume one of M discrete phase states. In any M-PSK, M = 2n, where “M” is the number of allowable phase states and “n” is the number of input bits taken each time by the modulator (every symbol period).

Therefore, the signaling rate for a given information bit can be reduced in any M-ARY system by a factor of n. Since the maximum rate of symbols through a channel is proportional to its bandwidth, the reduced rate allows the use of narrower channels. In conclusion, M-ARY systems are more bandwidth efficient.






Phase Shift Keying (PSK)8-level Phase Shift Keying (8PSK)Eight-level Phase Shift Keying is a technique for carrying digital signals over analog systems. It is used in digital radio and television broadcasting. 8PSK has eight phase angles, and it can therefore provide 3-bits per symbol, with one symbol per Hertz of bandwidth.

In practice, however, by the time forward error correction is added, it only provides about 2-bits per Hertz.






Quadrature Amplitude Modulation (QAM)QAM is a modulation scheme in which two sinusoidal carriers, one exactly 90 degrees out of phase with respect to the other, are used to transmit data over a given physical channel. These two carriers, being 90 deg out of phase, are called quadrature, hence the name Quadrature Amplitude Modulation.

Since the two orthogonal carriers occupy the same frequency band and differ by a 90-degree phase shift, each can be modulated independently, transmitted over the same frequency band, and separated by demodulation at the receiver.

By combining amplitude and phase modulation of a carrier signal, the number of states can increase, consequently more bits per every state change can be transmitted.



3.4.2.4: Quadrature Amplitude Modulation (QAM)



In the constellation pattern shown here, the dots at 0, 90, 180, and 270 degrees all have two possible amplitudes resulting in eight different states. With eight unique states, it is possible to transmit 3 bits in every state.




0 deg

270 deg

180 deg

90 deg

Figure 3.4.2.3g QAM

Quadrature Amplitude Modulation (QAM)



Quadrature Amplitude Modulation (QAM)The table below highlights the bit pattern generated by QAM modulation.

Amplitude Phase (deg) Bit Pattern1 (blue) 0 0002 (red) 0 0011 (blue) 90 0102 (red) 90 0111 (blue) 180 1002 (red) 180 1011 (blue) 270 1102 (red) 270 111

3 bits are transmitted for every state change, or baud rate.

As a footnote, for a given available bandwidth, QAM enables data transmission at twice the rate of standard pulse amplitude modulation (PAM) without any degradation in the bit error rate (BER). QAM and its derivatives are used in both mobile radio and satellite communication systems.




modulation techniques in satellite communications

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