Modulation Scheme for link between Moon Base Station and Earth Station

Multi-Level Gaussian Frequency-Shift Keying (MGFSK)

GMFSK is a narrow-band FM scheme that provides an increased bandwidth of 2 to 3 times that which is currently available commercially with QAM schemes [10]. MGFSK has been demonstrated to offer a bandwidth efficiency of nearly 6 bits/s/Hz (uncoded) whereas 8PSK offers under 3 bits/s/Hz (uncoded). This efficiency is comparable to 64QAM, but the use of 64QAM over satellite is not considered viable because it requires the channel to be highly linear and well equalized.

Our mission requires us to transmit high-definition video and pictures back to earth. We would use a video compression format that yields better picture quality at reasonable rate. We propose to use MPEG4 Part 10 (H.264) video compression standard. H.264 uses Content Adaptive Binary Arithmetic Coding (CABAC) that encodes symbols adaptively to yield 10Mbps bit rate for DVD quality video compared to 20Mbps for MPEG2.

Our modulation scheme for link between Moon Base Station and Earth Station will have following salient design features :

  1. Multiple Levels: We will use 16 levels i.e. 4 bits per symbol.
  2. Partial response signaling: The symbols are formed by the impulse response of a low-pass Gaussian filter that stretches over adjacent symbols, similar to that in use with GSM.
  3. Low modulation index: The filtered waveform is frequency modulated onto a carrier using a low modulation index (β) in order to keep the occupied bandwidth in the narrow-band class.

  4. The modulation index of the FM modulator is held at β = 1, which according to Carson’s rule means that the occupied bandwidth can be considered as 2fm, where fm is the maximum frequency component of the modulating (baseband) signal which is set by the bandwidth of the Gaussian filter. Under this condition the occupied bandwidth is

    BW = 2 * fm = 2 * (symbol rate * BT)
    (where, BT = 3-dB bandwidth * Time period of pulse
    and, symbol rate = 1 / Time period of pulse
    so, fm = symbol rate * BT)

    Using, symbol rate = (H.264 bit rate for HD video) / (# of bits in a symbol)
    = 10 Mbps / (4 bits/symbol)
    = 2.5 M symbols/sec.
    and, BT = 0.35 same as GSM

    So, BW = 2 * 2.5 * 0.35 = 1.75 MHz
  5. The combination of multiple levels and partial response signalling results in a bandwidth efficiency of almost 6 bits/s/Hz.

    BW Efficiency E (uncoded) = 4 (bits/symbol) / 0.7 = 5.71 bits/s/Hz.
  6. The below equation is used to calculate the noise for the system where Tphys is estimated to be 290k since the dish will be pointing at the moon. Additionally, the noise temperature for a typical X-band receiver is 50k.

    Pnoise = kTsysB where Tsys=Tphys+T1+T2/G1+..
    Pnoise =-137.8 dB

    The Shannon Nyquist theorem states that flawless transmission can occur with a signal to noise ratio (SNR) given by

    C=Blog2(1+SNR) where C: bit rate, B: bandwidth [Hz]

    Using the values calculated above, the SNR for perfect transmission is 6.25 dB. With Turbo coding, the SNR can lie within 1 dB of the Shannon-Nyquist limit. Therefore, this link requires a SNR of 7.24 dB or a power level above -130.6 dB.

  7. The use of frequency modulation (FM) instead of the more common PSK makes the signal highly tolerant to equalization errors (amplitude and group-delay ripple) in the channel. The cost of setting up earth stations to achieve the required equalization across the signal bandwidth is very high which becomes worse for wide-band signals.
  8. The scheme is also highly tolerant to non-linearities owing to its use of constant envelope FM. This is advantageous such as one or more amplifiers/transceivers could be running close to saturation point providing more gain. This has an edge over its competitor 64QAM scheme, which needs to back off its amplifiers by at least 10dB.

Modulation Scheme for link between Moon Base Station and Moon Rover

For the shorter distance between the moon rover and the moon base station (approximately 1000 m), pi/4 QPSK will be used. The signal constellation is shown below.

The design features of our modulation scheme for link between Moon Base Station and Moon Rover are as follows :

  1. In order to reduce bit error while keeping the power requirement low, Turbo coding will be used. 1/2 Turbo coding was chosen as it provides adequate bit error rate around 10^-6. For, a bit rate of 10Mbps for DVD quality video, turbo coding will result in an overall bit rate of 20Mbps.

    Symbol Rate = 20 Mbps / 2 bits/symbol = 10M symbols/s.

    The bandpass filter has been designed to have a roll-off factor of 0.3 and the bandwith calculation is as follows:

    BW = 10M symbols/s (1+ 0.3) = 13 MHz
  2. The noise in this link is primarily due to thermal noise. The mean temperature on the moon on the equitorial plane is 220K [6]. Therefore, the noise power is calculated.

    Pnoise = kTsysB where Tsys=Tphys+T1+T2/G1+...

    The LNA chosen for this link offers a gain of 15dB and therefore using the first two terms of Tsys is adequate for the noise estimation. The LNA has a noise figure of .8dB which corresponds to 57 K.

    All of that taken into consideration, the Shannon Nyquist theorem states that flawless transmission can occur with a signal to noise ratio (SNR) given by

    C=Blog2(1+SNR) where C: bit rate, B: bandwidth [Hz]

    Using the values calculated above, the SNR for perfect transmission is 1.9 dB. With Turbo coding, the SNR can lie within 1 dB of the Shannon-Nyquist limit. Therefore, this link requires a SNR of 2.9 dB or a power level above -104.28 dBm.