Radio Telescope on the far side of the moon

Location and operation of the radio telescope

The radio telescope is to be installed on the far side of the moon since at this place it will be shielded from most of the man-made noise which is essential when "listening to signals from deep space".
Since the radio telescope should operate in a way similar to the telescope in Arecibo, Puerto Rico, it will use the same 300m diameter dish in order to make measurements of the spectrum between 1 and 4 GHz. The transmission of the measurement data back to earth will be digital since we want to make use of the advantages of digital transmission such as error correction etc.
For the transmission of the data it will make use of a communication system (with a 6m dish antenna) that is discussed in more detail here.
For power supply we will use solar cells and batteries as back-up for times when the solar cells are shielded from sun light.

Sampling and quantization of spectrum

Hence we need to sample and quantize the spectrum to get a digital signal. In total we have a bandwidth of 3 GHz which means we would require a sampling frequency of at least 6GHz.

Since there is no A/D converter available that provides a sufficient sampling rate we will have to use multiple A/D converters with a lower sampling rate and combine the data. A challenge in this approach is that the A/D converters need to be precisely synchronized in order to not introduce any errors into the measured signal.
Another parameter is the number of quantization bits we want to use. A general rule of thumb says that we get a SNR of 6*N dB where N is the number of quantization bits.
Typical numbers of quantization bits range from 4-16bit. In order to get a high SNR we would like to choose a high number of quantization bits (to get a small quantization error), however increasing the number of quantization bits also increases the required data rate and hence also the required bandwidth and/or receive SNR in order to reliably receive the transmitted signal.
Furthermore high-speed A/D converters tend to have a lower number of quantization bits, so there is another tradeooff: If we want to have a high number of quantization bits we need to use lower speed A/D converters and hence to sample the complete spectral bandwidth of 3 GHz we need to use many low-speed A/D converters which could make the synchronization more difficult.

Solution 1

As a compromise we could use for example 6x 1GHz A/D converters with 8bit which would give a quantization SNR of 48dB and would result in a total data rate of R_b = 48 Gbps. We will use this result later on in the design of the relay system.
To check if 8bit quantization provides sufficient SNR, we need to calculate

• the noise power of the telescope
• the maximum signal power

Calculation of noise power:

Using T_sys = 20K, bandwidth B=3GHz and k = 1.3807*10^-23 J/K, we can calculate P_N = k*T_sys*B = 8.2842*10^-13W.

Calculation of maximum signal power:

A typical value of power density E for the brightest source in radio astronomy is 10,000 Janskys = 10^-22 W / (Hz*m²). (from [3]) To calculate the maximum signal power we can use the following formula:
P_S = E * B * Pi * (d/2)² * η = 1.9085*10^-8W.
The maximum required SNR is then 10*log₁₀(P_S / P_N) = 43.62dB.
Hence we can conclude that quantization with 8bit (SNR = 48dB) yields sufficient SNR.
However since a 8bit A/D converter never provides an SNR equivalent to 8bits but rather 7.0-7.5bit, we will reduce the data to a 7bit representation to reduce the required data rate and save bandwidth. This means that we will get a quantization SNR of 42dB and transmit a signal with a data rate of 42Gbps.

The figure below shows the operating principle of the system consisting of 6 1GHz A/D converters operating in a time-interleaved fashion and as such being equivalent to a single 6GHz A/D converter:

Solution 2

An easy solution would be to use two 3GHz 8bit A/D converters ADC083000 from the company National Semiconductor[8]. They are designed to be able to operate as an equivalent to a single 6GHz converter without any additional circuitry. This option is probably easier to implement since we do not need to worry about synchronization because that has already been taken care of. However this part is not yet available, the documentation on the webpage says "preliminary".