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# [FAQ] Computing Maximum Range, Velocity and Resolution mmWave System

This FAQ was written to answer a common request: Computing the Max Range, Range Resolution, Max Velocity, Velocity Resolution for a mmWave Chirp Configuration.

This FAQ provides the theoretical equations and shows how to compute them in an example

• Maximum Range
• Range Resolution
• Maximum unambiguous Velocity
• Velocity Resolution

Following are the equations to compute these parameters. For more information on the derivation of these equations the reader is invited to review this training

• Maximum Range
• Rmax = (EFs x c)/(2 x S)
• EFs = Effective Fs = 0.9Fs
• S: slope of the chirp

• Range Resolution
• Rres = c/2B = (EFs x c)/(2*S*ADC_Samples)
• EFs = Effective Fs = 0.9Fs
• S: slope of the chirp

• Maximum Unambiguous Velocity
• Vmax = Lambda / (4 * ETc)
• Lambda: Wavelength
• ETc: Effective Tc = (Idle_Time + rampEndTime) * nb_Tx (for MIMO configuration)
• Velocity Resolution
• Vres = Lambda / (2 * Active frame time)
• Active frame time AFT = Tc * #Tx * #chirps/Tx (for MIMO configuration)

Example for following chirp configuration

profileCfg 1 77 7 3 39 0 0 50 1 128 3600 0 0 36

chirpCfg 2 2 1 0 0 0 0 1
chirpCfg 3 3 1 0 0 0 0 2
chirpCfg 4 4 1 0 0 0 0 4

frameCfg 0 2 128 0 100 1 0

Following are the computed values:

• Maximum Range
• Rmax = (0.9*3600e3*3e8 m/s)/(2*50 e12 /s) = 9.72m

• Range Resolution
• Rres = Rmax/128 = 0.076m

• Maximum unambiguous Velocity
• Lambda (Wavelength) (77Ghz) = (3e8 m/s) / 77e9 /s) = 0.3/77m = 0.003896

• Tc = Idle_Time + rampEndTime  = (7+39) usec = 46usec

• Effective chirp time, taking MIMO into account:
• ETc = 3*Tc = 138usec
• Vmax = 3.896e-3m/(4x138e-6)s = 7.05 m/s

• Velocity Resolution
• Active frame time AFT = 51x3x128usec = 19584usec = 19.584ms
• Vres2 = 3.896e-3m/(2x19.584e-3)s = 0.1 m/s