Big Dish Telescope: Radio Receivers

The front-end components of the radio receiver system are those at the "front end" of the signal path -- where incoming radio waves are initially received -- and which are often mounted in front of the dish in prime-focus telescopes like ours. These components include feeds and waveguides to receive the signal collected and focused by the reflector, active antenna elements in which the radio waves induce alternating currents, a low-noise radio-frequency amplifier, and, in many cases, a frequency downconverter that reduces the received signal frequency to a lower "intermediate frequency" that is more manageable by subsequent system components. Radio astronomy signals are incredibly faint, so the initial amplifier stage is vitally important for enabling their detection. In modern receiving systems, the front-end components are often combined in a single unit called a low-noise amplifier (LNA), low-noise block-downconverter (LNB), or LNB + feed (LNBF).

Most of the following system characteristics describe available front-end units. A few relate to the size of the reflector dish.

Band (IEEE)	Front-End Unit(s)			Received Spectral Range		Intermediate Freq. (GHz)	Bandwidth (GHz)	Beam Width (FWHM)	Gain (dB)
	Brand	Model	Type	Wavelength (cm)	Frequency (GHz)				Amp.	Directive	Total
X - Ku	Chaparral, Pauxis	Universal Single	LNB	2.35 - 2.56	11.700 - 12.750	1.100 - 2.150	1.050	0.516 - 0.562°	58	50.6 - 51.4	108.6 - 109.4
X				2.56 - 2.80	10.700 - 11.700	0.950 - 1.950	1.000	0.562 - 0.615°		49.8 - 50.6	107.8 - 108.6
S - C	Chaparral, SmartSat	MicroPac	LNBF	7.14 - 8.82	3.400 - 4.200	0.950 - 1.750	0.800	1.57 - 1.94°	65	39.9 - 41.7	104.9 - 106.7
L (line)	NooElec	SAWbird +H1	LNA+ filter	20.82 - 21.80	1.376 - 1.441	--	0.065	4.57 - 4.79°	40	32.0 - 32.4	72.0 - 72.4
L (wide)	GPIO Labs	Ultra+ GNSS	LNA+ filter	17.65 - 27.27	1.100 - 1.700	--	0.600	3.88 - 5.99°	40	30.1 - 33.8	70.1 - 73.8

Notes on the front-end table:

• A band graph shows where these received frequencies fall on the broader electromagnetic radiation spectrum.
• Wavelengths presume electromagnetic radiation in a vacuum. Propagation speed and wavelength are reduced in receiver components, feed lines, etc. (frequencies are unaffected).
• Relevant IEEE band frequency ranges are L=1-2 GHz, S=2-4 GHz, C=4-8 GHz, X=8-12 GHz, and Ku=12-18 GHz.
• The X-Ku LNBs observe one of two sub-bands at a time, controlled by injection of a 22 kHz tone. Although they cover parts of both the X and Ku IEEE bands, these LNBs are often called "X-band" or "Ku-band" units for brevity.
• The S-C LNBFs include scalar rings that help reject ground radiation from outside the dish area "seen" by the feed. They are often called "C-band" units for brevity.
• The narrow-band LNA+filter is a single unit specifically designed for hydrogen 21cm line observations. It does not come with its own antenna or feed, so we plan to make our own. (This is not strictly a front-end component, since it is separated sufficiently from the resonant element to be placed behind the dish, but it performs a similar function as other LNA and LNB units.)
• The broad-band LNA+filter are separate units under consideration for other L-band observations but have not yet been acquired.
• The bandwidth shown here is what the front-end units deliver to later stages of the receiver chain, but it is the capacity of these later stages that dictates how much signal bandwidth can be viewed or recorded at any given time.
• Beam Width is the angular resolution, or smallest detail that can be measured with the telescope, defined as the full width at half maximum (FWHM) of the main beam sensitivity pattern. Here we have assumed optimal dish illumination with a 10 dB edge taper (10% sensitivity at the dish edges), for which the FWHM = 1.15 rad * λ / D, with D = 300 cm being the dish diameter and λ the wavelength. The actual beam FWHM may differ from the 10 dB taper case assumed here and will be measured during commissioning.
• Gain is a measure of signal strength increase, usually defined as a factor (e.g., output power / input power), but often expressed logarithmically in decibel (dB) units, where G_dB = 10 log₁₀ G_factor (or inversely, G_factor = 10 ^{(G_dB / 10)}, so that G_dB = 40 implies G_factor = 10,000). Here we give the amplifier gain of the LNA/LNB stage listed by the manufacturer and the maximum directive gain or directivity of the telescope's main beam. The latter is found as G_dir = 4 π / Ω, where the beam solid angle is Ω = π θ² / (4 ln(2)) for a circular Gaussian beam, and θ is the beam FWHM in radians (for simplicity, we assume a radiation efficiency of 1, with negligible ohmic losses in the antenna and feed). Note that while gain factors multiply together, gains in decibels add instead.
• Sensitivity to specific radio sources is not yet determined. The noise temperatures of our S-C LNBs are listed as 17 K by the manufacturer. We do not plan any active cooling of the front-end receiver electronics.

Back-end components of the receiver system are those toward the "back end" of the signal path, also usually located in back of the dish, or even at some distance from it. They accept the amplified and often down-converted signal from the front-end components, sent over a coaxial cable, and perform whatever additional operations on the signal are required. These operations would include additional amplification, demodulation, digitization, and display or recording of the resulting output signal. In many modern systems, all these functions are handled by a software-defined radio (SDR), which can be either a standalone unit or one connected to a computer running specialized software. Our system uses the latter. There are many options for this. Back-end configurations we have tested to date include the following.

Brand	Model	Frequency Range (MHz)	Maximum Bandwidth (MHz)	Bit Depth	Software	Platform	Computer
RTL-SDR Blog	RTL2832U V3	0.5 - 1750	2.4	8	LabVIEW	Raspbian	Raspberry Pi + Macbook
					SDR #	Windows	PC laptop
Airspy	R2	24 - 1750	10	12	SDR #	Windows	PC laptop
SDRplay	RSPdx	0.001 - 2000	10	8 - 14	SDRuno	Windows	PC laptop

Notes on the back-end table:

• The models shown here are a small subset of available SDRs (e.g., see Wikipedia list). Subject to cost and other constraints, we may consider other models providing greater bandwidth or other capabilities.
• The frequency range is applied to whatever input signal is passed down from the front-end receiver stages. This could be either an intermediate frequency after down-conversion or the original received frequency if no conversion is applied (for example, in L-band).
  • The Airspy R2 does not cover frequencies as low as the other SDRs, but this is not important for GHz radio astronomy (its coverage can be lowered with the Spyverter frequency up-converter if desired).
• The maximum or instantaneous bandwidth is the largest frequency range that the system can process and display in real time via fast Fourier transforms of the incoming waveform. Smaller bandwidths can be selected to reduce CPU loading. This bandwidth is the "window" into the larger band made available by the front-end receiver stages (see above) and can be "tuned" around within that range.
• The bit depth is the number of bits used by the analog-to-digital converter (ADC) to encode the analog signal. Greater bit depth enables more faithful representation and better dynamic range to distinguish between strong and faint signals. (For example, 8 bits allows 2⁸ = 256 different levels of signal strength to be captured.) The RSPdx SDR has greater bit depth for narrower bandwidth settings.
• A LabVIEW interface to the RTL2832U SDR was developed to run on a Raspberry Pi 3B board computer that could be controlled over a wireless TCP connection by a Macbook Pro laptop. Off-the-shelf software (SDR #, SDRuno) is currently being used for the more sophisticated SDR models while other options are explored (e.g., GNU Radio).
• Spectral channel sampling across the instantaneous band is being investigated. In principle, the number of channels' worth of information available to be recorded per second should be approximately the instantaneous bandwidth divided by the number of bytes per channel (1 byte = 8 bits). However, the details of how this is handled depend on the SDR software.

• A 22 kHz tone generator is needed to select the upper sub-band in the Ku-band LNB (see above). This is under current investigation.
• A radio-frequency (RF) signal generator is also very useful for testing receiving system components, not unlike a calibration lamp for an optical telescope. An inexpensive unit off eBay tunable between 0.14 and 4.4 GHz enabled direct bench and field tests of both L- and C-band receivers, and its 3rd harmonic allowed testing Ku-band reception.
• For rudimentary tests of SDR functionality, FM broadcast stations can also be received using, e.g., whip antennas shipped with the RTL2832U SDR kit, although almost any conductor will do for a strong enough station. Indeed, if RF shielding is inadequate, the RTL-SDR FM Trap Filter is sometimes necessary to block such stations from contaminating the IF signal path.