Case study: IMT spurious emission and RAS (generic single-interferer worst-case)¶

License¶

HOWTO: Calculate level of interference in radio-astronomical
observations produced from a single IMT device in spurious domain.
Copyright (C) 2015+  Benjamin Winkel (bwinkel@mpifr.de)

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

In [1]:

%matplotlib inline

In [2]:

import numpy as np
import matplotlib.pyplot as plt
from pycraf import conversions as cnv
from pycraf import pathprof, protection, antenna
from astropy import units as u
from astropy import constants as con

WARNING: AstropyDeprecationWarning: astropy.utils.compat.funcsigs is now deprecated - use inspect instead [astropy.utils.compat.funcsigs]

System parameters¶

To protect other services, in almost all bands, IMT has to ensure that spurious emissions of each terminal (base stations and user equipment) are lower the $-$$30~\mathrm{dBm/MHz}$. Therefore, one can easily work out necessary separation distances for the single-interferer worst-case scenario (as a generic study, aka flat-Earth) for the various RA.769 thresholds, continuum, spectral-line, or VLBI. Note that the spurious limit is to be understood as EIRP.

In [3]:

# IMT transmitter; 
P_spurious = -30 * cnv.dBm_MHz

Compatibility / Separation distances¶

We'll produce one plot for each threshold type, that contains curves for various frequencies and Tx heights. No clutter correction is applied in this worst-case scenario!

In [4]:

HEIGHTS = [40, 1.5] * u.m

In [5]:

def path_atten(freq, height, max_dist=200 * u.km, ras_height=50 * u.m):
    
    lon_t, lon_r = 0 * u.deg, 0 * u.deg
    lat_t, lat_r = 50 * u.deg, 50 * u.deg
    h_tg, h_rg = height, ras_height
    G_t, G_r = 0. * cnv.dBi, 0. * cnv.dBi

    temperature = 293.15 * u.K
    pressure = 1013. * u.hPa

    time_percent = 2 * u.percent
    DN, N0 = 38. * cnv.dimless / u.km, 324. * cnv.dimless

    hprof_step = 50 * u.m
    hprof_data = pathprof.height_path_data_generic(
        max_dist, hprof_step, lon_t, lat_t,
        )
    
    results = pathprof.atten_path_fast(
        freq, temperature, pressure,
        h_tg, h_rg, time_percent,
        hprof_data,
        )
    
    return hprof_data['distances'][5:], results['L_b'][5:]

Continuum thresholds¶

In [6]:

tab = protection.ra769_limits()[5:11]

In [7]:

tab

Out[7]:

QTable length=6

frequency	bandwidth	T_A	T_rx	T_rms	P_rms_nu	Plim	Plim_nu	Slim	Slim_nu	Efield	Efield_norm
MHz	MHz	K	K	mK	dB(W / Hz)	dB(W)	dB(W / Hz)	dB(W / m2)	dB(W / (Hz m2))	dB(uV2 / m2)	dB(uV2 / m2)
float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64
408	4	25	60	0.962	-258.8	-202.9	-268.8	-189.2	-255.1	-43.4	-49.3
611	6	20	60	0.730	-260.0	-202.2	-270.0	-185.0	-252.8	-39.2	-47.0
1414	27	12	10	0.095	-268.8	-204.5	-278.8	-180.1	-254.4	-34.3	-48.6
1665	10	12	10	0.156	-266.7	-206.7	-276.7	-180.8	-250.8	-35.0	-45.0
2695	10	12	10	0.156	-266.7	-206.7	-276.7	-176.6	-246.6	-30.9	-40.9
4995	10	12	10	0.156	-266.7	-206.7	-276.7	-171.3	-241.3	-25.5	-35.5

In [8]:

prop_cycle = plt.rcParams['axes.prop_cycle']
colors = prop_cycle.by_key()['color']

plt.close()
fig = plt.figure(figsize=(14, 8))
ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))
for freq, Plim_nu, color in zip(tab['frequency'], tab['Plim_nu'], colors):
    
    for height, ls in zip(HEIGHTS, ['-', '--']):

        dist, atten = path_atten(freq, height)
        
        margin = Plim_nu.to_value(cnv.dBm_MHz) - (
            P_spurious.to_value(cnv.dBm_MHz) - atten.to_value(cnv.dB)
            )
        
        ax.plot(
            dist, margin,
            ls=ls, c=color, label='f={:.0f}, h={:.1f}'.format(freq, height)
            )

ax.legend(
    *ax.get_legend_handles_labels(), 
    loc='lower right', fontsize=8, handlelength=3
    )
ax.axhline(0, c='r')
ax.set_xlim((10, 199))
ax.set_ylim((-49, 29))
ax.set_xlabel('Distance [km]')
ax.set_ylabel('Margin [dB]')
ax.grid()
ax.set_title('IMT vs. RAS separation distances (worst-case spurious domain); Continuum')
plt.show()

Spectral line thresholds¶

In [9]:

tab = protection.ra769_limits(mode='spectroscopy')[[0, 1, 3, 4]]

In [10]:

tab

Out[10]:

QTable length=4

frequency	bandwidth	T_A	T_rx	T_rms	P_rms_nu	Plim	Plim_nu	Slim	Slim_nu	Efield	Efield_norm
MHz	kHz	K	K	mK	dB(W / Hz)	dB(W)	dB(W / Hz)	dB(W / m2)	dB(W / (Hz m2))	dB(uV2 / m2)	dB(uV2 / m2)
float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64
327	10	40	60	22.361	-245.1	-215.1	-255.1	-203.4	-243.4	-57.6	-37.6
1420	20	12	10	3.479	-253.2	-220.2	-263.2	-195.7	-238.7	-49.9	-32.9
1665	20	12	10	3.479	-253.2	-220.2	-263.2	-194.3	-237.3	-48.5	-31.5
4830	50	12	10	2.200	-255.2	-218.2	-265.2	-183.1	-230.0	-37.3	-24.3

In [11]:

prop_cycle = plt.rcParams['axes.prop_cycle']
colors = prop_cycle.by_key()['color']

plt.close()
fig = plt.figure(figsize=(14, 8))
ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))
for freq, Plim_nu, color in zip(tab['frequency'], tab['Plim_nu'], colors):
    
    for height, ls in zip(HEIGHTS, ['-', '--']):

        dist, atten = path_atten(freq, height)
        
        margin = Plim_nu.to_value(cnv.dBm_MHz) - (
            P_spurious.to_value(cnv.dBm_MHz) - atten.to_value(cnv.dB)
            )
        
        ax.plot(
            dist, margin,
            ls=ls, c=color, label='f={:.0f}, h={:.1f}'.format(freq, height)
            )

ax.legend(
    *ax.get_legend_handles_labels(), 
    loc='lower right', fontsize=8, handlelength=3
    )
ax.axhline(0, c='r')
ax.set_xlim((10, 199))
ax.set_ylim((-49, 29))
ax.set_xlabel('Distance [km]')
ax.set_ylabel('Margin [dB]')
ax.grid()
ax.set_title('IMT vs. RAS separation distances (worst-case spurious domain); Spectroscopy')
plt.show()

VLBI thresholds¶

In [12]:

tab = protection.ra769_limits(mode='vlbi')[5:11]

First, we need to augment the table with the power limits.

In [13]:

tab['Plim_nu'] = (
    tab['Slim_nu'].to(u.W / u.m ** 2 / u.Hz) / 4 / np.pi * con.c ** 2 / tab['frequency'] ** 2
    ).to(cnv.dB_W_Hz)

In [14]:

tab

Out[14]:

QTable length=6

frequency	T_A	T_rx	Slim_nu	Plim_nu
MHz	K	K	dB(W / (Hz m2))	dB(W / Hz)
float64	float64	float64	float64	float64
408	25	60	-215.6	-229.3
611	20	60	-212.4	-229.6
1414	12	10	-210.7	-235.2
1665	12	10	-209.3	-235.2
2695	12	10	-205.1	-235.2
4995	12	10	-199.7	-235.2

In [15]:

prop_cycle = plt.rcParams['axes.prop_cycle']
colors = prop_cycle.by_key()['color']

plt.close()
fig = plt.figure(figsize=(14, 8))
ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))
for freq, Plim_nu, color in zip(tab['frequency'], tab['Plim_nu'], colors):
    
    for height, ls in zip(HEIGHTS, ['-', '--']):

        dist, atten = path_atten(freq, height)
        
        margin = Plim_nu.to_value(cnv.dBm_MHz) - (
            P_spurious.to_value(cnv.dBm_MHz) - atten.to_value(cnv.dB)
            )
        
        ax.plot(
            dist, margin,
            ls=ls, c=color, label='f={:.0f}, h={:.1f}'.format(freq, height)
            )

ax.legend(
    *ax.get_legend_handles_labels(), 
    loc='lower right', fontsize=8, handlelength=3
    )
ax.axhline(0, c='r')
ax.set_xlim((1, 49))
ax.set_ylim((-26, 36))
ax.set_xlabel('Distance [km]')
ax.set_ylabel('Margin [dB]')
ax.grid()
ax.set_title('IMT vs. RAS separation distances (worst-case spurious domain); VLBI')
plt.show()

In [ ]: