Institute for Telecommunication Sciences / Research / Radio Propagation Software / MPM / Millimeter–wave Propagation Model (MPM)

Millimeter–wave Propagation Model (MPM)

The Millimeter-wave Propagation Model (MPM) calculates the complex refractivity N for atmospheric conditions. The output is expressed in real and imaginary parts of N, or in specific rates of power attenuation and propagation delay.


  • Real Part of Refractivity, N' [ppm]
  • Imaginary Part of Refractivity, N" [ppm]
  • Non-dispersive Refractivity, No [ppm]
  • Attenuation, 0.1820 F N" [dB/km]
  • Dispersive Delay, 3.3356 N' [ps/km]
  • Total Delay, 3.3356 (N' + No) [ps/km]

The input data includes the frequency (F), pressure (P), temperature (T), relative humidity (RH), and rain rate (RR). For 80 < RH < 99.95%, a haze model predicts water droplet density (W) for four climate zones (Rural, Urban, Maritime, Maritime+Strong Wind). The haze growth model is dependent on hygroscopic aerosol reference density (wA), which is specified at 80% RH. At 100% RH, a suspended water droplet density is specified to simulate fog or cloud conditions. Partial vapor pressure, E is calculated from RH and the saturation vapor pressure, Es(T), over liquid water (for T > 0 C) or ice (for T < -40 C). In the temperature range -40 <= T <= 0 C, the user specifies Es over liquid water or ice. This criteria also defines whether water droplets or ice particles contribute to attenuation and delay.


  • Frequency, 1 <= F <= 1000 [GHz]
  • Barometric pressure, 0 <= P <= 1100 [mb]
  • Temperature, -80 <= T <= 50 [C]
  • Relative humidity, 0 <= RH (=100E/Es) <= 100 [%]
  • Rain Rate, 0 <= RR <= 200 [mm/hr]
  • Water-droplet density, 0 <= W <= 10 [g/m3]

MPM93 is based on Dr. Hans Liebe's final publication [1]. MPM Software (which operates in a DOS environment) that aligns with this publication is available in three different versions, which compute frequency, humidity, and pressure profiles. It is necessary to include the following spectroscopic line coefficient data files in the working directory: oxygen.dat and water.dat.

The MPM software is available for download as a "zip" file. The download contains software developed by NTIA. NTIA does not make any warranty of any kind, express, implied or statutory, including, without limitation, the implied warranty of merchantability, fitness for a particular purpose, non-infringement and data accuracy. NTIA does not warrant or make any representations regarding the use of the software or the results thereof, including but not limited to the correctness, accuracy, reliability or usefulness of the software or the results. You can use, copy, modify, and redistribute the NTIA-developed software upon your acceptance of these terms and conditions and upon your express agreement to provide appropriate acknowledgments of NTIA's ownership of and development of the software by keeping this exact text present in any copied or derivative works. By clicking this link to download the software, you acknowledge that you have read the above disclaimer.

ITS publications related to MPM include:

[1] H.J. Liebe, G.A. Hufford, M.G. Cotton, "Propagation modeling of moist air and suspended water/ice particles at frequencies below 1000 GHz," Proc. NATO/AGARD Wave Propagation Panel, 52nd meeting, No. 3/1-10, Mallorca, Spain, 17 - 20 May, 1993.

[2] H.J. Liebe, P.W. Rosenkranz, and G.A. Hufford, "Atmospheric 60-GHz oxygen spectrum: New laboratory measurements and line parameters", Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 48, no. 5/6, pp. 629-643, 1992.

[3] H.J. Liebe, G.A. Hufford, T. Manabe, "A model for the complex permittivity of water at frequencies below 1 THz", International Journal of Infrared and Millimeter Waves, vol. 12, no. 7, pp. 659-675, Jul. 1991.

[4] G.A. Hufford, "A model for the complex permittivity of ice at frequencies below 1 THz", International Journal of Infrared and Millimeter Waves, vol. 12, no. 7, pp. 677-680, Jul. 1991.

[5] H.J. Liebe, G.A. Hufford, and R. DeBolt, "The atmospheric 60-GHz oxygen spectrum: Modeling and laboratory measurements", NTIA Report 91-272, Mar. 1991.

[6] H.J. Liebe,"MPM - An atmospheric mm-wave propagation model", International Journal of Infrared and Millimeter Waves, vol. 10, no. 6, pp. 631-650, June 1989.

[7] G.A. Hufford and H.J. Liebe, "Millimeter-wave propagation in the mesosphere", NTIA Report 89-249, Sept. 1989.

[8] H.J. Liebe, T. Manabe, and G.A. Hufford, "Millimeter-wave attenuation and delay rates due to fog/cloud conditions", IEEE Transactions on Antennas and Propagation, AP-37, no. 12, pp. 1617-1623, Dec. 1989.

[9] H.J. Liebe, G.A. Hufford, "Modeling millimeter-wave propagation effects in the atmosphere", AGARD Conference Proceedings No. 454, March 1990, pp.18-1–18-13, CP-454, Oct. 1989.

[10] H.J. Liebe, "A contribution to modeling atmospheric millimeter-wave properties," Frequenz, vol. 41, no. 1/2, pp. 31-36, Jan./Feb. 1987.

[11] H.J. Liebe and D.H. Layton, "Millimeter-wave properties of the atmosphere", NTIA Report 87-224, Oct. 1987.

[12] H.J. Liebe, "An updated model for millimeter-wave propagation in moist air", Radio Science, vol. 20, no. 5, pp. 1069-1089, May 1985.

For information about MPM, contact Michael G. Cotton.