Methods for accurate use of finite dynamic range measurement data in radio path loss propagation model calibration
View Patent ↗Methods for accurately predicting radio propagation from signal strength measurements. Dynamic range limitations in the measurement data are explicitly taken into account. The resulting propagation models accurately predict signal strength for calculation of coverage and interference.
1. A method of accurately calculating an unbiased parameter set for application to a radio signal propagation model describing data of limited dynamic range, comprising the steps of:
a) representing a set of N data points of radio signal data collected by a receiver as a truncated data set, wherein said truncated data set is truncated using a set of N lower truncation limits, wherein a lower truncation limit is calculated for each data point according to a sensitivity threshold of the radio signal data determined by said receiver, and wherein said truncated data set is further truncated using an upper truncation limit calculated according to an upper limit of the linear range of said receiver;
b) excluding from said truncated data set all data outside a range defined by said lower and upper truncation limits; and
c) based on said truncated data set, based on said lower and upper truncation limits, and based on a radio signal propagation model, calculating an unbiased parameter set maximizing the accuracy with which said radio signal propagation model describes said data set, wherein the method uses a truncated likelihood function that only includes terms involving observed signals and the truncation limits, but no terms corresponding directly to unobserved signals.
2. The method of claim 1 , wherein said step of calculating comprises maximizing the likelihood of said signal propagation model to calculate radio path signal loss, given said data, said lower truncation limit, and said upper truncation limit.
3. The method of claim 1 , wherein said step of representing comprises representing the signal strength of the radio signal data.
4. The method of claim 1 , wherein said step of representing comprises representing the set of N data points as collected by a cellular phone network.
5. The method of claim 4 , wherein said step of representing comprises representing the signal strength of the radio signal data.
6. The method of claim 1 , wherein said step of calculating is performed using a maximum likelihood (ML) fit.
7. The method of claim 1 , wherein an Ordinary Least Squares (OLS) solution is given by finding a vector β minimizing a quantity:
Σ( y i −x i β) 2 (1)
where a sum is taken over all observations i, y, is a i th measured value, x, is a vector of dependent variables used in calibration, and β is a vector of parameters to be optimized.
8. The method of claim 7 , wherein the dependent variables used in calibration comprise one or more of log distance, diffraction, effective antenna height, and clutter terms.
9. The method of claim 7 , wherein the parameters to be optimized comprise one of more of intercept, slope, diffraction multiplier, and clutter parameters.
10. The method of claim 7 , wherein the OLS problem is reformulated as a maximum likelihood (ML) problem.
11. The method of claim 10 , wherein the log of the likelihood to be maximized is:
L=Σ i log(2πσ) −1/2 −( y i −x i β) 2 /(2σ 2 ) (2)
where σ is an estimate of the dispersion and is an additional parameter to be optimized.
12. The method of claim 11 , wherein the optimized parameters for the truncated problem are obtained by maximizing the log of the likelihood L according to the equation:
L=Σ i log(2πσ) −1/2 −Σ i ( y i −x i β) 2 /(2σ 2 )−Σ i log Φ[( c i −x i ρ)/σ]−Σ i log Φ[( x i β−d i )/σ]. (3)
13. The method of claim 12 , wherein an optimized value of σ is approximately equal to a standard deviation of the measured values y i .
14. The method of claim 4 , wherein the cellular phone network is a Code Division Multiple Access (CDMA) network.
15. The method of claim 14 , wherein the lower truncation limit is a measured value of I o , in decibels of power referenced to one milliwatt plus a minimum value of Ec/I o in decibels that the receiver can reliably measure.
16. The method of claim 4 , wherein the cellular phone network is a Universal Mobile Telecommunications System (UMTS) network.
17. The method of claim 16 , wherein the lower truncation limit is a measured value of I 0 , in decibels of power referenced to one milliwatt plus a minimum value of Ec/I 0 in decibels that the receiver can reliably measure.
18. The method of claim 4 , wherein the cellular phone network is a Global Standard for Mobile Communications (GSM) network.
19. The method of claim 18 , wherein the lower truncation limit is a measured value of I, in decibels of power referenced to one milliwatt plus a minimum value of C/I in decibels that the receiver can reliably measure.