Committee on Radio Astronomy Frequencies

Summation Methodology:

The summation methodology assumes that all emitters are located on equally spaced concentric rings with the victim receiver in the center of the distribution as shown in figure below. The emitters are bounded by an inner ring and an outer ring. The emitters are evenly spaced from each other on each ring. Since all the emitters on each ring have the same distance to the receiver, the path loss is the same for all the emitters on that ring. The spectral power flux density (SPFD) is then calculated for all the emitters in each ring and the total SPFD is the summation of the SPFD contributed by each ring.

FIGURE 3

The summation methodology

Table 1 shows a list of all parameters used and their units of measurement.

TABLE 1

RI	Inner ring radius	Km
Ro	Outer ring radius	Km
Rj	The jth ring radius in the distribution	Km
q	Sector angle defined by the antenna horizontal beam width	Radians
K	Emitter density	#/km2
T	Total number of emitters in the full annulus
N	Number of emitters in the sector
Nj	Number of emitters in the sector in the jth ring
	Ring separation distance	Km
M	Number of rings used
EIRP	Effective isotropically radiated average power	Watts
G	Transmitter’s gain	dB
L	Path loss between transmitters and receiver	dB
fc	Center frequency of transmitter
BW	Bandwidth of transmitter
SPFD	Spectral power flux density	Watts/m2/MHz

The user defines a density K, and the total number of emitters in the annulus is calculated by: T = K(R_o² - R_I²). The ring separation distance is given by: . The number of rings (M) is given by: M = {(R_o – R_I)/} + 1.

The radius R_j is used to calculate the path loss between each ring and the antenna of the victim receiver. R_j is the inner ring plus the j^th ring separation distance . This leads to:

R_j = R_I + ( j - 1)

for j = 1 to M.

The emitter distribution is based on having the ratio of number of emitters on each ring-to-ring radius to be constant. This leads to:

N_j = 2T {R_I+(j-1)} / {2M R_I+(M-1)M}

The path loss L_j, is defined as: L_j = 4R_j².

The power received at the center comes from combining the above equations to be:

P_R(single) = EIRP(G/L)

And the aggregate power receive at the center is:

The aggregate spectral power flux density is: