Spectrum and Modulation Measurement, Signal Analysis

1
Spectrum and Modulation Measurement, Signal
Analysis
INA Academy Workshop Spectrum Management
Series Workshop 3 "Measurements and Techniques"

• Prof. Venceslav Kafedziski
• University "Ss Cyril and Methodius"
• Skopje, Republic of Macedonia

2
Outline

• Introduction
• Review of analog modulation techniques spectra,
  modulation parameters
• Digital modulation techniques signal space
  representation, demodulation, spectra
• Elements of digital spectral analysis DSP, FFT,
  digital spectrum analyzers
• Bandwidth measurement definitions, occupied
  bandwidth measurement, x-dB measurement, effects
  of noise and interference, equipment requirements

3
Introduction

• Spectrum monitoring is amidst major change
  because of introducing new digital modulation
  techniques, and new and sophisticated measurement
  equipment.
• There is an increased use of digital modulation
  in GSM, DAB, DVB-T, WLAN etc. These new
  techniques require measurement a number of new
  parameters.
• There is an increased use of modern digital
  receivers that employ modern DSP for demodulation
  and signal analysis, including spectral analysis.
• New training procedures are required for smooth
  transition towards monitoring new digital
  modulations and employing new digital receivers.

4
Analog modulation

• Analog modulation the message is an analog
  signal and is impressed on a carrier.
• To study analog modulation is still important,
  since
• AM and FM are still in use in radio broadcasting,
  and AM vestigial side band in TV broadcasting
• digital modulation techniques also use AM, FM and
  PM.
• Transition towards digital modulation has already
  happened in mobile telephony.
• Major shift towards introducing digital
  modulation in broadcasting is happening in
  Europe DAB, DVB-T.

5
Analog modulation AM

• Amplitude modulation include AM, AM Double Side
  Band Suppressed Carrier (AM-DSB-SC), AM Single
  Side Band (AM-SSB), AM Vestigial Side Band
  (AM-VSB).
• Spectrum of any AM modulation can be obtained by
  pure translation of the baseband spectrum to
  carrier frequency and filtering.
• AM bandwidth depends on the particular modulation
  technique, and is at most 2B for AM-DSB-SC and AM
  modulation, and at least B for AM-SSB, where B is
  the bandwidth of the message.
• AM-VSB is the best trade-off between bandwidth
  and receiver complexity used in conventional
  television.

6
Analog modulation AM

• AM signal used in AM broadcasting
• u(t)Ac1m mn(t)cos(2pfctfc)
• Parameter m is called modulation depth, and mn(t)
  is the normalized message.
• Total power is computed as PAc2/21m2Pm where
  Pm is the power in the normalized message mn(t).
  
• Percentage power loss in carrier is usually
  large, since m is usually small, and Pm is always
  less than one.

7
AM modulation depth

• AM modulation depth can be measured by measuring
  certain values of the signal envelope.
• 
  

8
Analog modulation FM and PM

• Angle modulation u(t)Accos2pfctf(t), where
  for FM
• and for PM, f(t)kpm(t).
• Bandwidth of FM can be estimated based on Carson
  formula
• where B is the maximum frequency in the message
  signal, and Df is the maximum deviation.
• FM is a modulation technique that expands
  bandwidth in order to improve the output SNR.

9
Stereo FM

• Two signals, LR, and L-R which is modulated
  DSB-SC at 38 kHz, are transmitted, together with
  a pilot tone of 19 kHz.

10
FM broadcast multiplex

• Besides the stereo message FM broadcast may
  contain additional signals such as traffic
  information, RDS (Radio Data Signal) at 57 kHz,
  and/or HSDS (High Speed Data System), for
  instance DARC (Data Radio Channel) at 76 kHz.

11
IQ modulation

• It is possible to increase the efficiency of
  AM-DSB-SC by using two quadrature carriers, and
  transmitting a different signal on each of them.
• The bandwidth efficiency of IQ is equal to the
  efficiency of AM-SSB, i.e. B per message signal.

12
Introduction to digital modulation

• The first step to digital transmission is to
  perform A/D conversion which includes the
  following steps
• taking samples from a continuous (analog) signal
  bandlimited to B by the celebrated sampling
  theorem, perfect reconstruction from samples is
  possible if the sampling rate meets the condition
  fsgtB.
• quantization, which is practically rounding off
  the signal samples to a finite number L of values
  (quantization with L levels).
• conversion of quantized samples to bits the
  number of bits used for transmission of a
  quantized sample is log2q, and, thus, the bit
  rate is equal to Rfslog2L bit/s.

13
A/D conversion

• sampling
• quantizing Dv2mp/L

14
Introduction to digital modulation

• In digital transmission we transmit bits. Shannon
  showed that by keeping the transmission rate R
  bits/second below channel capacity C, errorless
  transmission is possible
• Since channels are analog, bits are transmitted
  by sending waveforms, i.e. analog signals s1(t),
  s2(t),,sM(t). Each waveform carries klog2M bits
  of information.
• When bits are transmitted on analog waveforms, we
  have a digital modulation.

15
Signal space representation

• For unified representation of signals, we use a
  signal space approach, representing signals as
  vectors in an N-dimensional vector space.
• Consider M signals s1(t), s2(t),,sM(t).
• Any signal can be represented as
• where yj(t) are basis functions with energy
  equal to 1 (creating an orthonormal basis), and
  NltM.
• Thus, any signal si(t) can be represented as a
  vector
• si(si,1,si,2,...,si,N).

16
Example of a signal set in a signal space
17
Pulse Amplitude Modulation-PAM

• Baseband PAM digital signal is
• where an can have one of M values sm,1 Am,1,
  m1,2, ... ,M and gT(t) is an arbitrary pulse in
  0,T.
• PAM is one-dimensional signal with basis function
  gT(t)
• Similarly, bandpass PAM signal
• is one-dimensional signal with basis function
  gT(t)cos2pfct.

18
Two dimensional signals

• Consider a bandpass signal modulated by cosine
  and sine wave, called in-phase and quadrature
  components
• The signal s(t) can be represented as
• where is the complex
  information sequence.
  

19
Two dimensional signals

• Basis functions are
• The signal transmitted is sm,1y1(t)sm,2y2(t),
  where sm(sm,1,sm,2) and sm,1AmI, sm,2AmQ,
  m1,2,...,M.
• We can represent signals as vectors in a two
  dimensional space (AmI,AmQ), i1,2, ... ,M.
• All the signal points create a constellation
  diagram.

20
QAM and MPSK

• QAM signal points are positioned on a rectangular
  grid.
• M-ary PSK signal points are on a circle, i.e. all
  the signals have identical energy.

QAM
PSK
21
Demodulation correlation receiver

• Assume that signal sk(t) was sent. There exists
  an additive white Gaussian noise n(t) at the
  receiver input.
• To demodulate, multiply the received signal
  r(t)sk(t)n(t) by basis functions and integrate,
  producing the coordinates rjsk,jnj, where sk,j
  are signal coordinates, and nj are noise
  coordinates, j1,2,...,N.

22
Demodulation matched filter receiver

• There is a matched filter version of the
  receiver.
• Correlators are replaced with matched filters.
• There is yet another version of matched filter
  receiver where filters are matched to signals
  si(t), i1,2, ... ,M, instead to basis functions
  yi(t), i1,2, ... , N.

23
Optimal Detection

• Optimal detector minimizes the probability of
  error, which results in Bayesian decision rule.
• Smallest distance receiver results from the
  assumption of Gaussian noise and the
  orthonormality of the basis functions.
• The detector computes the distance from the
  received vector r(r1,r2, ...,rN) to each signal
  point si, i1,2,...,M, and decides in favor of
  the closest signal point.

24
Power Spectral Density

• Since signals are carrier modulated, power
  spectral density (PSD) is shifted around the
  carrier frequency
• where
• is the PSD of the complex envelope sB(t).
• Sa(f) is the Fourier transform of the
  autocorrelation Ra(n)Eanmam of the complex
  information sequence an.

25
Power Spectral Density

• When the complex symbols an are uncorrelated
• where sa2 is the variance, and ma is the mean of
  the information sequence an.
• When the symbols are uncorrelated, then the PSD
  becomes

26
Power Spectral Density of QAM and M-ary PSK

• If there is a DC component in the information
  sequence, there exist discrete components at n/T
  in the PSD.
• PSD of M-ary PSK and QAM signals depend on the
  pulse shape of gT(t) and on the correlation of
  information sequence. For sa21 and rectangular
  pulse gT(t) with energy 2, we get

27
QPSK and OQPSK

• Offset QPSK (OQPSK) is QPSK where in-phase and
  quadrature components are offset for T, and the
  duration of gT(t) is 2T. This results in phase
  changes of K90 degrees, as opposed to K180 and
  K90 for QPSK.
• This can eliminate phase ambiguity, and can also
  decrease envelope changes.

28
Nyquist Condition

• When the pulse is rectangular, the resulting
  spectrum is infinite. Since all transmission
  systems are bandlimited, there is an inter-symbol
  interference (ISI) at the receiver.
• To avoid ISI, Nyquist condition for the signal
  x(t)gT(t)c(t)gR(t) after the channel c(t) and
  receive filter gR(t) has to be met
• In frequency domain, Nyquist condition translates
  to

29
Nyquist Condition

• So called raised cosine pulses meet Nyquist
  condition

Nyquist pulse in time domain
Nyquist pulse in frequency domain
30
Eye Diagram

• The amount of ISI and noise present in the
  received signal can be viewed on an
  oscilloscope.
• Eye diagram is obtained by displaying the signal
  on the vertical input with the horizontal sweep
  rate at 1/T.
• Eye opening shows how big is ISI and the margin
  against noise. Eye width shows the margin against
  timing errors.

31
M-ary FSK

• M-ary FSK is an M-dimensional modulation with
  signals
• and basis functions
• i1, ,M. Minimum distance between carriers
  that provides orthogonality is 1/2T. Required
  bandwidth is M/2T.
• Signal power does not depend on M, since
  different signals are equal to the basis
  functions, scaled by Es.

32
M-ary FSK

• Vector representation is smoEsym, for m1,2,
  ... ,M.
• Distance between any two signal points is

s1(oEs,0,0) s2(0,oEs,0) s3(0,0,oEs)
33
QAM versus M-ary FSK

• Bit rate for both QAM and M-ary FSK is
• Rb1/T log2M
• Bandwidth for QAM is W1/T, and for M-ary FSK is
  WM/2T.
• Bandwidth efficiency is defined as the ratio
  between bit rate and bandwidth and is measured in
  bit/s/Hz.
• Bandwidth efficiency for QAM is log2Mbit/s/Hz
  and for M-ary FSK is (2log2M)/M bit/s/Hz.
  

34
Power versus bandwidth

• By increasing M in QAM, the average signal power
  has to also increase, since the probability of
  error depends on the distance between signal
  points. By increasing M with M-ary FSK, the
  average power does not increase.
• There is a trade-off between signal power and
  bandwidth necessary for transmission.
• QAM is bandwidth efficient, but power inefficient
  modulation.
• M-ary FSK is power efficient, but bandwidth
  inefficient modulation.

35
Power versus bandwidth

• Comparison of different modulation methods at
  10-5 symbol probability of error is given.
• Bandwidth limited region is for Rb/Wgt1.
• Power limited region is for Rb/Wlt1.
• Signal to noise ratio is equal to energy per bit
  divided by the noise PSD.

36
Continuous Phase Modulation - CPM

• Continuous Phase Modulation (CPM) was introduced
  to avoid abrupt changes in envelope and to save
  bandwidth. To obtain CPM, PAM signal
• where gT(t) is a pulse of duration T, is used
  to frequency modulate a carrier
• The resulting frequency modulated signal is phase
  continuous and, hence, is called CPM.

37
CPFSK, MSK and GMSK

• When gT(t) is a rectangular pulse of amplitude
  1/2T and duration T, CPM is called CPFSK.
• Minimum shift keying (MSK) is a special form of
  CPFSK in which the modulation index is h1/2. It
  can be also viewed as OQPSK with cosine pulse
  shape.
• Gaussian MSK (GMSK) is used in DECT and GSM. The
  pulse is a convolution of Gaussian pulse and
  rectangular pulse, i.e. is described by
  difference of two Q functions. Parameter BT is
  used to characterize GMSK, where B is the
  equivalent pulse bandwidth.
• CPM and CPFSK are modulations with memory.

38
Partial response CPM

• Partial response CPM is obtained when an
  arbitrary pulse gT(t) which extends beyond the
  time interval 0lttltT, is used.
• The primary reason for this is to further reduce
  the bandwidth of the transmitted signal.
• When the duration of the pulse extends over
  0lttltLT, where Lgt1, additional memory is
  introduced in the CPM signal, and the number of
  states increases.
• Notation LRC is used if gT(t) is a raised cosine
  pulse of duration LT.

39
PSD of MSK and OQPSK

• MSK can be viewed as OQPSK with sinusoidal
  shaping.
• The sidelobes of MSK fall off faster than those
  of OQPSK, but its main lobe is 50 wider than
  that of OQPSK.

40
PSD of GMSK and CPM

• (a) PSD of GMSK compared to PSD of MSK.
• (b) PSD of LRC CPM compared to PSD of MSK.

(b)
(a)
41
OFDM

• OFDM has attracted lot of interest recently for
  use on frequency selective channels, i.e.
  channels that introduce intersymbol interference.
• Applications include ADSL, DAB, DVB-T, WLAN
  802.11a.
• Digital TV broadcasting will replace the analog
  systems in coming years
• TV production environment has become digital
• improved picture quality (transmission of HDTV
  signal)
• saves frequency spectrum (4 digital channels
  versus 1 analog channel in 8 MHz slot)

42
OFDM

• The idea of FDM is to subdivide the available
  channel bandwidth in N sub-channels, such that
  each sub-channel is nearly ideal.
• Then, each sub-channel is modulated with a
  separate symbol sequence and the N obtained
  signals are frequency multiplexed.

43
OFDM

• OFDM uses the idea that more efficient use of
  bandwidth can be obtained if the spectra of the
  individual sub-channels are permitted to overlap,
  with specific orthogonality constraints imposed
  to facilitate separation of the sub-channels at
  the receiver.

44
OFDM

• An input sequence with a symbol rate 1/T is
  subdivided into N parallel information sequences
  with rate 1/NT. Each sequence modulates one of N
  subcarriers, with frequency fk of the subcarrier.
  
• Symbol interval is TuNT, and subcarrier spacing
  is 1/Tu. Inside interval Tu, signals overlap, but
  are orthogonal.

45
OFDM

• The discrete time implementation of OFDM
  modulator is by inverse FFT on block of symbols.
• The collection of N received samples is FFT
  transformed to obtain N received symbols.

46
OFDM

• N complex QAM symbols are IDFT transformed at
  transmitter
• The received block of samples is DFT transformed
• The effect of channel is as if Xk were multiplied
  by the channel transfer function at the same
  frequencies and adding AWGN to obtain N complex
  symbols
• RkCkXkNk

47
PSD of OFDM

• PSD of OFDM is obtained by summing the PSD's of
  all the carriers.
• Increasing N, PSD decreases more rapidly (Figure
  (a)).
• The use of windows can also shape the spectrum
  raised cosine windows with roll-off factor a in
  Figure (b).

(a)
(b)
48
Signal analysis

• Radio monitoring is changing, due to introducing
  new digital signals, and transmitting additional
  information in the existing, more conventional
  signals.
• Signal analysis is the art of extracting every
  possible bit of information from a signal, in our
  case a radio signal.
• Includes modulation characteristics (symbol
  rate, frequency shift, linear/nonlinear
  modulation, kind of modulation, constellation),
  time characteristics (burst waveforms), spectrum
  characteristics (narrow/wide band, single carrier
  or multicarrier), traffic measurements,
  extraction of information from the demodulated
  data stream including hidden information.

49
DTFT

• Fourier transform of a signal x(t) is computed as
  
• If the signal is a discrete sequence x(nTs), the
  Discrete Time Fourier Transform (DTFT) is
  computed as
• where Ts is the sampling period. The DTFT is a
  periodic function with a period fs1/Ts.

50
DFT

• Assume that we have N samples of discrete time
  signal x(nTs), with Ts the sampling period.
  Signal is time limited to NTs. Denote this
  sequence by x(n), n0, ... ,N-1.
• We define Discrete Fourier Transform
• Since X(k) is a discrete function, time signal
  becomes a periodic function with period NTs.
• Inverse DFT is defined as

51
Comparison of FT, DTFT, FS, DFT

• Fourier transform of a continuous and aperiodic
  signal
• DTFT of a sampled and aperiodic signal
• Fourier series of a continuous and periodic
  signal
• DFT of a sampled and periodic signal

52
DFT resolution

• Note that the DFT is a sampled version of DTFT
  when a block of samples is observed. When N
  increases to infinity, it coincides with the
  DTFT.
• The DFT resolution can be increased by increasing
  the number of samples (block length) used for
  computation.
• Since real signals are non-stationary, long
  blocks of samples should not be used. Using short
  blocks of samples is called Short Term Fourier
  Transform (STFT).
• There is a trade-off between increased spectral
  resolution and the requirement of using short
  blocks of samples for non-stationary signals.

53
DFT spectral leakage

• Since N samples of the signal are used to compute
  the DFT, this corresponds to multiplying the
  signal with a rectangular window of duration N
  samples (NTs seconds).
• Multiplication in time domain is convolution in
  frequency domain, so the spectrum of the signal
  is convolved with sin(pfNTs)/pfNTs function. This
  causes spectral leakage.
• The window spectrum from f0 to the first null is
  called main lobe.
• The window spectrum between any two consecutive
  nulls is called side lobe.

54
DFT windows

• In order to decrease spectral leakage, various
  time windows are used. The requirements from a
  window are to have low first sidelobe and the
  power in the sidelobes to decrease as fast as
  possible.
• Windows that produce low side lobes, produce wide
  main lobe. This is a trade-off between resolution
  (the width of the main lobe) and spectral leakage
  (the amplitude of the side lobes).
• Rectangular window has the narrowest main lobe,
  but the largest side lobes Blackman window has
  the widest main lobe, but the lowest side lobes.

55
DFT windows

• (a) Rectangular window
• (b) Hamming window
• (c) Blackman window

(b)
(a)
(c)
56
FFT

• FFT is just an algorithm for fast computation of
  DFT, when the block length is a power of 2.
• This criterion can be met in one of three ways
  sampling a sequence in a way that block length is
  a power of 2, interpolating the sampled sequence
  to obtain a length that is a power of 2, or,
  putting zeros at the end and beginning of the
  sampled sequence (zero padding).
• There are different algorithms for computing FFT.
  The complexity is proportional to Nlog2N, as
  opposed to N2 for DFT.

57
Equipment for spectrum analysis

• Digital technologies, such as analog to digital
  converters (ADCs) and DSP have become more common
  in spectrum analyzers, gradually moving from data
  display functions toward the analyzers' inputs.
• In modern analyzers, this digital technology is
  concentrated in the stages following the final
  IF, i.e. resolution bandwidth (RBW) filtering.
• Modern spectrum analyzers use an all digital IF
  section. Using DSP instead of series of analog
  gain and filtering stages eliminates or vastly
  reduces many sources of error including IF gain
  uncertainty, RBW switching error, RBW filter
  bandwidth uncertainty, etc.

58
FFT versus swept spectrum analyzers

• Modern spectrum analyzers use both swept and FFT
  analysis techniques for spectrum measurements.
• In a swept spectrum analyzer the amplitude
  accuracy of the RBW filters can be quite high
  because they are all centered at the same
  frequency.
• In the case of FFTs, the flatness of the IF
  preceding A/D process is a factor in determining
  accuracy.
• The primary advantage of FFT analysis is
  measurement speed in measurements that require a
  narrow RBW and a relatively wide frequency span.
  FFT processing can be viewed as the operation of
  many RBW filters in parallel.

59
FFT versus swept spectrum analyzers

• Sweep time for an FFT analyzer increases linearly
  as RBW is reduced, rather than as the inverse
  square of the RBW (as it would for a single swept
  RBW filter).
• For wider bandwidths the FFT computational
  overload becomes more significant and begins to
  exceed the gains from parallel processing. As a
  consequence, FFT analysis can actually be
  substantially slower than swept techniques in
  analyzing wide frequency spans.

60
FFT versus swept spectrum analyzers

• (a) resolution bandwidth (RBW) in swept analyzers
  is narrow
• (b) conceptual comparison of measurement speeds
  for swept and FFT analysis
• (c) practical measurement speeds for an existing
  spectrum analyzer

(b)
(a)
(c)
61
Swept spectrum analyzers

• For the measurement of narrowband emissions, a
  spectrum analyzer having a high degree of
  resolution is desirable. A typical instrument has
  a maximum resolution of 10 Hz and provides a
  swept range adjustable from 1 kHz to 100 kHz,
  together with a sweep rate adjustable from 1 to
  30 sweeps per second.
• For the analysis of wideband emissions, available
  instruments cover frequency range up to 44 GHz
  with a sweep width continuously variable up to
  100 MHz (at the higher frequencies). The sweep
  rate is adjustable from 1 to 60 sweeps per
  second.

62
Digital receivers

• Receivers are also becoming all digital. That
  means that following the A/D conversion at IF,
  they process samples instead of analog waveforms.
  Demodulation is performed by DSP.
• DSP techniques used in modern digital receivers
  digital down conversion, digital filtering
  (including FIR and IIR filtering), downsampling.
• It is much easier to realize digital filter than
  analog filter. Digital filters use mathematical
  algorithms, as opposed to analog filters, that
  are directly attributable to the physics of the
  devices implementing them.

63
Digital receivers

• First step is conversion of the RF signal to IF
  signal.
• Second step is the IF digitizing using A/D
  converter.
• Then the DSP performs filtering and demodulation.
• A/D converter performs analog signal
  reconstruction.

64
Digital receivers

• The performance of digital receivers does not
  vary with regard to time and temperature.
• Digital receivers have improved flexibility, and
  can accommodate complex modulation formats,
  including digital modulation formats.
• Additional IF bandwidth, demodulation modes or
  other functions can be made in a DSP based
  circuit by a software change.
• Modern digital monitoring receivers include a
  display with a control unit, typically a PC with
  computer software.
• The receiver also has a remote interface,
  including LAN.

65
Bandwidth definitions

• baseband bandwidth The width of the band of
  frequencies occupied by one signal, or a number
  of multiplexed signals, which is intended to be
  conveyed by a line or a radio transmission
  system.
• necessary bandwidth For a given class of
  emission, the width of the frequency band which
  is just sufficient to ensure the transmission of
  information at the rate and with the quality
  required under specified conditions.
• out-of-band emission Emission on a frequency or
  frequencies immediately outside the necessary
  bandwidth which results from the modulation
  process, but excluding spurious emissions.

66
Bandwidth definitions

• out-of-band spectrum (of an emission) The part of
  the power density spectrum of an emission, which
  is outside the necessary bandwidth and which
  results from the modulation process, with the
  exception of spurious emissions.
• spurious emission Emission on a frequency or
  frequencies which are outside the necessary
  bandwidth and the level of which may be reduced
  without affecting the corresponding transmission
  of information. Spurious emissions include
  harmonic emissions, parasitic emissions,
  intermodulation products and frequency conversion
  products, but exclude out-of-band emissions.

67
Bandwidth definitions

• unwanted emissions Consist of spurious emissions
  and out-of-band emissions.
• out-of-band power (of an emission) The total
  power emitted at the frequencies of the
  out-of-band spectrum.
• occupied bandwidth The width of a frequency band
  such that, below the lower and above the upper
  frequency limits, the mean powers emitted are
  each equal to a specified percentage b/2 of the
  total mean power of a given emission. Unless
  otherwise specified by the Radiocommunication
  Assembly for the appropriate class of emission,
  b/20.5.

68
Bandwidth definitions

• x-dB bandwidth The width of a frequency band such
  that beyond its lower and upper limits any
  discrete spectrum component of continuous
  spectral power density is at least x-dB lower
  than a predetermined 0 dB reference level.
• assigned frequency band The frequency band within
  which the emission of a station is authorized
  the width of the band equals the necessary
  bandwidth plus twice the absolute value of
  frequency tolerance.

69
Measurement of occupied bandwidth

• Digital signal processing techniques can be used
  to calculate the occupied bandwidth from the PSD.
• First, the noise floor of the PSD is estimated.
  The PSD values are set to zero if the power is
  less than Y dB above the noise floor. For most
  signals Y6dB is adopted.
• The total signal power, P, is computed by summing
  the values of the PSD bins containing the signal
  energy. The integral of the PSD is computed and
  the data are interpolated to find the lower and
  upper frequencies, f1 and f2, where the
  integrated power equals Pb/2. The occupied
  bandwidth is f2f1. This is the power-ratio
  method.

70
Measurement of occupied bandwidth

• Emission is considered optimum when its occupied
  bandwidth coincides with the necessary bandwidth
  for the class of emission concerned.

71
Measurement of occupied bandwidth

• A relationship between the errors in the occupied
  bandwidth and the errors in the power comparison
  is obtained from the spectrum envelope
  approximation
• where S(fm) is the power on a given frequency,
  g0.33Nfm and N is a number of dB by which the
  spectrum envelope is reduced within an octave of
  band widening.
• For N12-20 dB/octave, power comparison at
  accuracy of about 15-20 ensures an occupied
  bandwidth measurement accuracy of 3 to 7.

72
Method using a spectrum analyzer

• PSD evaluated by spectrum analysis is used. The
  relevant power values are determined by summing
  the powers of the individual spectral components.
  
• When the PSD is continuous, PSD samples with
  equidistant separation are used.
• A spectrum analyzer with a digitally controlled
  synthesizer scans the spectrum in frequency
  steps, and a digital memory sends the measured
  values to a computer, which in turn performs the
  calculations.
• Since a conventional spectrum analyzer performs a
  sequential measurement, it is advisable to make a
  number of scans.

73
Method relying on FFT

• FFT based power-ratio measuring methods require
  little or no knowledge about the detailed
  parameters of the modulation and are able to
  interpret the part of the signal spectrum that
  emerges out of the noise floor.
• effect of windowing a window must be selected
  that generates an overall low side lobe power
  content, so as to operate in conditions as close
  as possible to the definition, which requires
  rectangular filters.
• FFT resolution 99 power method does not depend
  much on the resolution chosen to compute the FFT.
  It gives very accurate results as soon as more
  that a 100 to 200 bins cover the occupied
  bandwidth of the signal.

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Method relying on FFT

• effect of the duration of signal sample the
  observation window must be long enough to cover
  the entire signal. Simulation tests with
  stationary signals show that reliable results are
  obtained for about 1000 symbols (for digital
  modulation).
• effect of noise under noisy conditions, it is
  essential to filter the signal emerging from
  noise the importance of filtering increases when
  the SNR is low. If the observed bandwidth
  significantly exceeds the occupied bandwidth, the
  99 bandwidth of the signalnoise will be
  measured instead that of the signal alone.

75
x-dB method

• The x-dB method computes bandwidth by taking
  frequencies where the PSD drops for x-dB compared
  to reference 0 dB level
• Method with single band-pass filter sweeping
  narrow-band filter, i.e. spectrum analyzer. The
  x-dB bandwidth is considered to include discrete
  components attenuated less than 26 dB below the
  peak value of the emissions.
• If the signal contains numerous low-level
  components, the result might be different from
  power-ratio result. Also, it is not possible to
  have both high resolution and rapid sweep rates.

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x-dB method

• The problem with this approach is how to
  determine the reference level, especially in
  cases where the PSD at carrier frequency is not
  maximum for instance FM modulation might result
  in large reduction of the carrier therefore, the
  reference level is measured by choosing a
  receiver bandwidth that covers the whole signal.
• Another problem is how to specify x for different
  classes of emission usually adopted values are
  x20 dB and x26 dB.
• In the case of CDMA or OFDM, where there is a
  large band of relatively flat PSD, x-dB method
  might give incorrect results.

77
x-dB method

• the ITU-R recommends that "until occupied
  bandwidth measurement methods have been developed
  making full allowance for the specific character
  of the activities of monitoring stations, these
  stations should continue to use the x-dB method
  as specified to perform the measurement at -26 dB
  and apply a correction factor for the appropriate
  class of emission, to determine the occupied
  bandwidth". Also, "administrations and other
  entities of the ITU-R should be encouraged to
  study, including by testing, the extension of the
  x-dB method to other classes of emission and
  development of appropriate correction factors for
  x-26dB".

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Effects of interference

• The ratio of the total power of a signal to the
  total power of interfering emissions is W/U.
• The ratio of the power of the interfering
  emissions remaining outside the occupied
  bandwidth to the total power of interfering
  emissions is k.

79
Effects of interference

• If k is equal to the ratio of the out-of-band
  radiated power of the emission to be measured to
  its total power, the interference does not affect
  the measured value.
• When k0, the interfering emissions are entirely
  within the band and the apparent bandwidth
  becomes narrower.
• When k1, the interfering emissions are entirely
  outside the band, and the apparent bandwidth
  becomes wider.
• In practice, the effects of interference are
  complicated. In the actual measurement, it is
  sufficient to consider k1.
• A value of the ratio W/U gt30 dB restricts the
  measuring error of the power ratio to lt0.1 of
  the total power.

80
Effects of noise

• The effects of random noise on the measured value
  of bandwidth are the same as those of
  interference, replacing k by kn (Wb/WBO), W/U by
  S/N (Pt/PN). Cases kn0 or kn1 do not exist
  with random noise.
• As signal to noise ratio S/N becomes smaller,
  the apparent out-of-band radiated power increases
  and the apparent occupied bandwidth extends.
• To confine the measuring error of the power ratio
  to less than 0.1, the value of S/N for the
  emission to be measured should be greater than
  about 25 dB, for values of k less than about 1/3,
  which is considered appropriate for monitoring.

81
Effects of noise
82
Requirements for equipment

• The frequency characteristic of the passband
  should be flat within K0.5dB over the range of
  the spectrum of the emission to be measured, and
  the loss in stop-band should be at least 30 dB,
  with a steep slope in the transition band.
• The frequency selectivity should be such as to
  discriminate against out-of-band noise and
  interference whilst not introducing a loss of
  more than 2 dB at the edges of the passband
  relative to the level at the middle of passband.
  
• The equipment should exhibit good linearity for
  an input variation of at least 60 dB, in order to
  cope with possible variations of the field
  intensity of the emission.

83
Conclusion

• Digital modulation is becoming predominant
  modulation, such as OFDM for audio and video
  broadcasting (DAB, DVB-T), GMSK and spread
  spectrum for mobile systems, spread spectrum and
  OFDM for WLAN.
• Digital modulations require measurements of a
  number of new parameters, compared to analog
  modulation.
• Modern receivers use A/D converters and modern
  DSP techniques for signal analysis and
  demodulation.
• It is necessary for the monitoring personnel to
  be trained to perform measurements on the newly
  introduced digital modulation techniques, using
  modern DSP receivers.

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Literature

• Communications Systems Engineering, J. G. Proakis
  and M. Salehi, Prentice Hall, 2002.
• The Mobile Communications Handbook, J. D. Gibson,
  editor, CRC Press, 1996.
• Digital Signal Analysis, S. D. Stearns and D. R.
  Hush, Prentice Hall, 1990.
• International Telecommunication Union Spectrum
  Monitoring Handbook, ITU, 2002.
• Swept and FFT Analysis, Product Note, Agilent
  Technologies.