## Corrected Signal-to-Noise Ratio Distribution by George Lane

[This document is part of the help files integrated into the ITS HFBC software package.]

As noted in an earlier article in this newsletter [Lane and Davis, 1994], a suspected error was found in the signal-to-noise ratio (SNR) distribution calculation used in IONCAP [Teters, et al., 1983]. A. D. Spaulding, formerly at ITS, pointed out to the author that the same error occurs in ITS-78 [Barghausen, et al., 1969] and HFMUFES-4 [Haydon, et al., 1976]. Under tasking from the United States Information Agency's International Broadcasting Bureau, Don Lucas [1995] has located the error and has made corrections for VOACAP. The corrected method estimates the SNR distribution in a manner consistent with ITSA-1 [Lucas and Haydon, 1966]. Subsequently, Greg Hand at ITS has made similar corrections to ICEPAC. This particular error never existed in the ITU-R (formerly CCIR) models of Report 894 or Recommendation 533.

The error was found to cause up to 6 dB under-prediction of the lower decile of the SNR distribution with the majority of the cases falling in the range of 2 to 4 dB. The output parameters; RELIABILITY, REQUIRED POWER GAIN, and the decile ranges of the signal-to-noise ratio, SNR LW and SNR UP, are affected by this error. In rare cases the error can change the most reliable mode and its associated characteristics: ANGLE, VIRTUAL HEIGHT and DELAY TIME. This article describes the nature of the error and the corrective actions made to VOACAP.

The SNR distribution is the critical calculation in estimating the performance of HF radio systems. Communications quality is dependent upon the SNR available in the detector stage of the receiver. Hence, reliability is then expressed as the fraction of time that the actual SNR exceeds the minimum level associated with the quality of communications required by the user. In HF prediction programs the signal and the noise distributions are computed separately and then combined to obtain the joint SNR distribution.

The signal power delivered to the HF receiver via the ionospheric channel is computed using the transmitter power plus the transmit and receiver antenna gain less the transmission loss. In most prediction programs, one is provided with the monthly median signal power or if the receive antenna is ignored, the field strength. The signal level has a diurnal, seasonal and sunspot number dependence. It also has variability that is because of the changing ionospheric conditions from one day to the next during the month.

Lucas and Haydon [1966] proposed an empirical correction factor, termed excess system loss, which adjusted the signal power median to the least error with respect to the only available data base at the time. This table also contained the upper and lower standard deviation around the expected excess system loss. The ITSA-1 prediction program [Lucas and Haydon, 1966] used this expected deviation to develop the distribution of the hourly signal levels around the median value for the days of the month. A similar but slightly different approach was used in ITS-78 and in HFMUFES. In IONCAP, Lloyd, et al. [1978] developed a frequency dependent signal level for each ionospheric mode (i.e. hop). Frequency dependence is based on above-the-MUF loss, deviative absorption terms and E-layer obscuration losses, as well as the expected excess system loss table from ITSA-1 but now called "Distribution of Transmission Loss." The frequency dependence is also computed for the lower and upper decile ranges of the expected day-to-day variations. This computation is done for up to twenty different ionospheric modes (three hops per layer * three layers * high and low ray plus high and low rays from the Es layer). The median monthly signal power distribution is given by the individual summation for the three parameters; namely, the median, lower decile and upper decile. In the IONCAP output, the decile range values are given as SIG LW and SIG UP, respectively. This range in the signal power is from a few dB up to a limit of 25 dB for poor propagation conditions.

The estimated radio noise level, consisting of the combination of atmospheric, man-made and galactic sources, has a monthly median value with a diurnal and seasonal dependence, as well as a short-term time variance. In IONCAP the noise power distribution is found by summing the three components in watts in order to obtain the median, lower decile and upper decile values. VOACAP uses a more correct method of combining the noise power distributions [Spaulding and Stewart, 1987] which produces a split Gauss distribution defined by a median, lower decile and upper decile.

The median SNR is found by subtracting the median noise power (dBW) from the median signal power (dBW). When the individual samples within the distributions are unknown, a well-accepted approximation is to use the root sum square of the signal and noise decile ranges to find the upper and lower decile ranges of the joint distribution, such that:

SNR10 = (SNR) + SQRT(SIGUP**2 + NLW**2) SNR90 = (SNR) - SQRT(SIGLW**2 + NUP**2) Where: SNR = Monthly median signal-to-noise ratio in dB SNR10 = Signal-to-noise ratio exceeded 10% of the days SNR90 = Signal-to-noise ratio exceeded 90% of the days S DBW = Monthly median signal power (dBW) at the receiver input SIGUP = dB above the median signal power exceeded 10% of time SIGLW = dB below the median signal power exceeded 90% of time N DBW = Monthly median noise power(dBW/Hz) at receiver input NUP = dB above median noise power exceeded 10% of the days NLW = dB below median noise power exceeded 90% of the daysThe error introduced in ICEPAC, VOACAP, IONCAP, HFMUFES and ITS-78 was that the terms NUP and NLW were reversed in the above equations. This resulted in a "tighter" distribution and an artificially higher reliability prediction. In the original IONCAP program, the "most reliable mode" printed for each frequency column in the output for Methods 20 (for paths less than 10,000 km) and 22 (forced short path method) is defined as the mode having the highest reliability of all the modes present. If two or more modes have reliabilities whose difference is not greater than 5 percent then four other tie breaking criteria may be brought into play.

The correction to VOACAP may change the mode reliabilities in the short path method (Method 22) such that a different mode can be tagged as the "most reliable mode." When this occurs, the mode indicator (hop number and ionospheric layer) will change as will the virtual height, takeoff angle and delay time. Generally, the required power gain and reliability will not change or change by only a small amount. A benchmark analysis of 52,400 frequency-hours using the short path method for typical shortwave broadcast operations showed that less than 1 percent of the predictions had a change in the most reliable mode or the hop number . The long path method uses a different criteria for determining the entry layer for the ionospheric channel than does the short path method. The change in the reliability calculation did not cause any changes to occur in the long path entry and exit layer selection.

The changes made to VOACAP by Don Lucas can make the RPWRG increase by as much as 6 dB. Primarily, changes of this magnitude will be found on short paths requiring the use of nighttime frequencies in the 2 to 4 MHz range. For most other situations the increase in required power gain will be less than 3 dB. The upper and lower decile ranges of the atmospheric radio noise are nearly equal for frequencies above about 10 MHz. Under these conditions and when the man-made radio noise is low with respect to the atmospheric radio noise, no change in the predicted SNR distribution occurs.

During times when the man-made radio noise is controlling, usually during the local daytime at the receive site or when the receive site is in an urban or industrial area, the change in RPWRG can vary from a few tenths of a dB to upwards of 4 dB. These findings with regard to RPWRG are similar for either the short path (Method 22) or the long path (Method 21).

In summary, the correction to the SNR distribution in VOACAP results in a change in the RPWRG of more than 1 dB in 25 to 40% of the usable frequency-hours for paths of more than 3000 km. More differences are found in high sunspot years than low. Also more differences occur for low latitudes than high latitudes. The most significant changes occur for frequencies of less than 10 MHz on circuits with path lengths of less than 3,000 km. The largest difference expected is 6 dB for 2 to 3 MHz on very short paths.

References:Barghausen, A. F., J. W. Finney, L. L. Proctor and L. D. Schultz, Predicting Long-Term Operational Parameters of High-Frequency Sky-Wave Telecommunication Systems, ESSA Technical Report ERL 110- ITS 78, May 1969.

Haydon, G. W., M. Leftin and R. Rosich, Predicting the Performance of High Frequency Sky-Wave Telecommunication Systems (The Use of the HFMUFES 4 Program), Office of Telecommunications Report OT 76-102, September 1976.

Lane, G. and R. F. Davis, Reliability --- The Broken Bell Curve, HFMAP Newsletter, Vol. 1, No. 3, p. 5 - 6, Fall 1994.

Lloyd, J. L., G. W. Haydon, D. L. Lucas and L. R. Teters, Estimating the Performance of Telecommunication Systems Using the Ionospheric Transmission Channel; Volume I: Techniques for Analyzing Ionospheric Effects Upon HF Systems {DRAFT}, US Army CEEIA Technical Report EMEO-PED-79-7, September 1978.

Lucas, D. L., Lucas Consulting Letter Report, January 17, 1995.

Lucas, D.L. and G. W. Haydon, Predicting Statistical Performance Indexes for High Frequency Ionospheric Telecommunications Systems, ESSA Technical Report IER 1-ITSA 1, August 1966.

Spaulding, A.D. and F. G. Stewart, An Updated Noise Model for Use in IONCAP, National Telecommunications and Information Administration (NTIA) Report 87-212, January 1987. Teters, L.R., J. L. Lloyd, G. W. Haydon and D. L. Lucas, Estimating the Performance of Telecommunication Systems Using the Ionospheric Transmission Channel; {Volume II} Ionospheric Communications Analysis and Prediction Program User's Manual, Institute For Telecommunication Sciences NTIA Report 83-127, July 1983.