Pulse Modulation (Advanced Radar)

Menu Path: MeasSetup > Advanced Radar Measurement Properties > Analysis > Modulation

The Pulse Modulation group lets you choose the types of pulses you want to include within the pulse modulation auto-detection process and report modulation metrics to pulse and statistics tables if detected. You can choose to include any combination of the following modulation types:

• Continuous Wave
• Linear FM
• Triangular FM

• PSK Phase Shift Keying: A broad classification of modulation techniques where the information to be transmitted is contained in the phase of the carrier wave.

  • Barker Phase
  • BPSK
  • QPSK

• Code

  • Frank Code
  • P1 Code
  • P2 Code
  • P3 Code
  • P4 Code
  • Costas Code

• Continuous Wave

  • The pulse modulation is assumed to be continuous wave, where only the amplitude of the signal is modulated on and off, while the frequency remains constant over the pulse-on time.

  • The frequency and phase reference data used is determined by the associated property CW Frequency Offset selection of either Automatic or Manual:

    • CW Frequency Offset = Automatic: The frequency and phase reference data is calculated as the mean frequency value measured over the per pulse frequency and phase measurement analysis range, as determined by the specified Frequency/Phase Analysis Width (%) property CW/Linear FM Frequency Modulation (% of pulse top).
    • CW Frequency Offset = Manual: The frequency and phase reference data is determined by the manually specified CW Frequency Offset (Hz) value.
• Linear FM

  • The pulse modulation is assumed to be linear frequency modulation (LFM), where the frequency of the modulated pulse changes linearly over the pulse-on time.

  • Frequency and phase reference data is calculated as a least squares linear regression best-fit line measured over the per pulse frequency and phase measurement analysis range, as determined by the specified Frequency/Phase Analysis Width (%) property CW/Linear FM (% of pulse top). The associated per pulse Best-Fit FM result metrics are reported in the Pulse Table, Current Record Statistics and Cumulative Statistics.
• Triangular FM

  • The pulse modulation is assumed to consist of two linear frequency modulation (LFM) chirps, of opposite slope polarity, one following the other. (i.e. either up-slope followed by down-slope, or down-slope followed by up-slope)

  • The frequency modulation is assumed to change linearly with a given slope polarity over the first portion of the pulse-on time, until reaching some frequency modulation apex (or point), then the frequency modulation slope polarity is reversed and the frequency changes linearly with opposite slope polarity over the second portion of the pulse-on time.

  • The associated Triangular FM is Symmetrical property determines whether the opposing polarity, frequency modulation slope rates (Hz/us) associated with each of the two LFM chirps, which comprise Triangular FM, are constrained to be symmetrical or not about the detected frequency modulation apex.

    • Triangular FM is Symmetrical = ON: The ideal reference Best-Fit FM Slope rates (Hz/us) of each LFM chirp, located either side of the detected Triangular FM apex, are constrained to be symmetrical (i.e. consist of the same absolute slope rate (Hz/us), but of opposing slope polarity)

    • Triangular FM is Symmetrical = OFF: The ideal reference Best-Fit FM Slope rates (Hz/us) of each LFM chirp, located either side of the detected Triangular FM apex, are not constrained, so may be asymmetrical (i.e. may potentially consist of different absolute slope rates (Hz/us), but still of opposing slope polarity).

  • Frequency and phase reference data is calculated as two least squares linear regression best-fit lines, while taking into account the Triangular FM is Symmetrical property constraint, measured over the per pulse frequency and phase measurement analysis range for each LFM chirp region, as determined by the value of Triangular FM (% of chirp region). The associated per pulse Best-Fit FM result metrics are reported in the Pulse Table, Current Record Statistics and Cumulative Statistics.

• Barker Phase
  • The pulse modulation detector looks for pulses modulated by BPSK Binary phase shift keying - A type of phase modulation using 2 distinct carrier phases to signal ones and zeros. in a pattern of uniform chips.
  • The BPSK phase is normalized so the first chip is at 90 degrees. (This is displayed in the Phase Meas Time trace if you have Compensate Phase Results for Frequency Offset enabled). The chips are assigned values of +1 for 90 degrees and -1 for -90 degrees.
  • BPSK chip count and bit pattern are reported in the Pulse Table along with average chip width (s) and first chip offset (s) reported relative to detected Pulse Top start time.
    
    Below is a summary of all supported valid Barker Code results, note that the +/- sign of reported Barker Code result metric indicates the actual bit order of the detected bit pattern (always normalized to +1 (+90deg) value for first chip):
    
    

  Barker Code	Chip Count	Bits (Hex)	Bits ( 1 = +, 0 = - )
  2	2	0x1	10
  3	3	0x3	110
  41	4	0xD	1101
  42	4	0xE	1110
  5	5	0x17	11101
  7	7	0x27	1110010
  11	11	0x247	11100010010
  13	13	0x159F	1111100110101
  -2	2	0x1	10
  -3	3	0x1	100
  -41	4	0xB	1011
  -42	4	0x8	0111
  -5	5	0x1D	10111
  -7	7	0x0D	1011000
  -11	11	0x0ED	10110111000
  -13	13	0x1F35	1010110011111

  • If the BPSK modulation bit pattern is detected as a valid Barker sequence, the Barker Code number is reported in the Table (as per examples above).
  • If the BPSK modulation bit pattern is detected as an invalid Barker sequence, the Barker Code number is reported as *** (NaN) result value, but the Chip Count and Bits associated with the detected BPSK modulation are still reported.
  • Note that when Pulse Modulation checkboxes for both Barker Phase and Continuous Wave are enabled simultaneously for auto-detection, only BPSK modulated pulses containing valid Barker Code detections (as listed within above table) will be automatically detected as BPSK.
  • Frequency and phase reference data, and associated error trace results are calculated and measured over the per pulse frequency and phase measurement analysis range, as determined by the specified Frequency/Phase Analysis Width (%) property Barker Phase (% of chip). The associated per pulse Barker result metrics are reported in the Pulse Table, Current Record Statistics and Cumulative Statistics.
• BPSK

  • The pulse modulation detector looks for pulses modulated by BPSK in a pattern of uniform chips.

  • The BPSK phase is normalized so the first chip is at 90 degrees. (This is displayed in the Phase Meas Time trace if you have Compensate Phase Results for Frequency Offset enabled). The chips are assigned values of +1 for 90 degrees and -1 for -90 degrees.

  • BPSK chip count and bit pattern are reported in the Pulse Table along with average chip width (s) and first chip offset (s) reported relative to detected Pulse Top start time.

• QPSK Quadrature phase shift keying

  • The pulse modulation detector looks for pulses modulated by QPSK.

  • The QPSK phase is normalized so the first chip is at 45 degrees, and the subsequent chips are at 135 degrees, 225 degrees, and 315 degrees. (This is displayed in the Phase Meas Time trace if you have Compensate Phase Results for Frequency Offset enabled).

  • QPSK chip count and bit pattern are reported in the Pulse Table along with average chip width (s) and first chip offset (s) reported relative to detected Pulse Top start time.

• Frank Code

  • The pulse modulation detector looks for pulses modulated by Frank Code, which is a polyphase code modulation format used for pulse compression.

  • It uses harmonically related phases which are based on certain fundamental phase increments. The Frank Code has N² elements and is defined as: Φi,j = (2π/N)(i-1)(j-1)

• P1 Code

  • The pulse modulation detector looks for pulses modulated by P1 Code.

  • The P1 code is a modified version of the Frank code where the DC frequency term is in the middle of the pulse instead of at the beginning.

  • The default P1 code Code Order is N = 4. The P1 code has N² elements and is defined as: Φi,j = (pi/N)(N+1-2j)(N(j-1) + (i-1)), where i and j range from 1 to N.

• P2 Code

  • The pulse modulation detector looks for pulses modulated by P2 Code.

  • The P2 code is a modified version of the Frank code where the DC frequency term is in the middle of the pulse instead of at the beginning. The P2 code is only valid for even code orders (N = 2, 4, 6, 8...)

  • The default P2 code Code Order is N = 4. The P1 code has N² elements and is defined as: Φi,j = (pi/2N)(N+1-2i) (N+1-2j), where i and j range from 1 to N.

• P3 Code

  • The pulse modulation detector looks for pulses modulated by P3 Code.

  • The P3 code is a modified version of the Frank code where the DC frequency term is in the middle of the pulse instead of at the beginning. The code order (N) is the number of values in the phase pattern. The number of items in the Frank, P1, and P2 codes patterns is N².

  • The default P3 code Code Order is N = 16.

  • The P3 code has N elements and is defined as: Φi,j = (pi/N)(I -1)², where I ranges from 1 to N

• P4 Code

  • The pulse modulation detector looks for pulses modulated by P4 Code.

  • The P4 code is a modified version of the Frank code where the DC frequency term is in the middle of the pulse instead of at the beginning. The code order (N) is the number of values in the phase pattern. The number of items in the Frank, P1, and P2 codes patterns is N².

  • The default P4 code Code Order is N = 16.

  • The P4 code has N elements and is defined as: Φi,j = (pi/N)(i -1)(i-1-N), where I ranges from 1 to N.

• Costas Code

  • The pulse modulation detector looks for pulses modulated by Costas Code, which is a burst of contiguous uncoded pulse waveforms, each with a different frequency selected from a finite set of coherently processed, equally spaced frequencies.

• Enable extended bits (BPSK/QPSK) enables BPSK/QPSK long demodulation when BPSK and/or QPSK is selected. The demodulated results are shown in the Pulse Demod Bits Result Table.
  Default: disabled
  

• Enable Custom BPSK -- When enabled, enter a custom phase shift angle for BPSK modulation. Normally, BPSK modulation has a 180 degree phase shift from symbol to symbol. In some signals, BPSK phase shift may be less than 180 degrees. This parameter allows you enter a non-standard BPSK phase shift angle so the BPSK modulation can be detected and analyzed.
  Default: disabled; 180 degrees

  Range: 30 to 180 degrees
  

Pulse Modulation Metrics

The pulse modulation detected by the 89600 VSA Software is reported within the Pulse Table results as the Modulation result metric. This determines how the frequency and phase reference trace data is calculated for each detected pulse. This in turn affects the reported frequency and phase versus time reference and error trace results.

In addition, the combination of user-enabled Pulse Modulation checkboxes of Continuous Wave, Linear FM, Triangular FM, Barker PhaseBPSK, QPSK, Frank Code and the P1 - P4 Codes affects which modulation type associated performance metrics are reported within the Pulse Table, Current Record Statistics, and Cumulative Statistics tables, as described below.

Trace results affected include:

• FM Reference, FM Error
• Phase Reference, Phase Error

Performance metric results affected include:

• Freq Error RMS (Hz)
• Freq Error Peak (Hz)
• Freq Error Peak Loc (s)
• Phase Error RMS (Hz)
• Phase Error Peak (Hz)
• Phase Error Peak Loc (s)

The following Best-Fit FM performance error metric results are only reported when the detected Pulse Modulation is Linear FM or Triangular FM:

• Best-Fit FM Mean (Hz)
• Best-Fit FM Start (Hz)
• Best-Fit FM Stop (Hz)
• Best-Fit FM Pk-Pk Dev (Hz)
• Best-Fit FM Slope (Hz/us)
• Best-Fit FM INL (%)

The following Best-Fit FM performance error metric results are only reported when the detected Pulse Modulation is Triangular FM:

• Best-Fit FM Start 2nd (Hz) (triangular FM only, second chirp)
• Best-Fit FM Slope 2nd (Hz/us) (triangular FM only, second chirp)
• Best-Fit FM INL 2nd (%) (triangular FM only, second chirp)
• Best-Fit Apex Freq (Hz) (triangular FM only, describes Frequency location of the Triangular FM frequency modulation peak, derived from crossover point of the two individual LFM chirp’s Best-Fit reference lines)
• Best-Fit Apex Time (%) (triangular FM only, describes Time location (reported relative to Pulse Top center time), of the Triangular FM frequency modulation peak, derived from crossover point of the two individual LFM chirp’s Best-Fit reference lines)
• Best-Fit FM Stop 2nd (Hz) (triangular FM only, second chirp)

The following metric results are only reported when the detected Pulse Modulation is Barker Phase, BPSK, QPSK, Frank Code, or P1 - P4 Code.

• Modulation Code
• Chip Count
• Chip Width (s)
• Chip Offset (s)