Meteor-M weather satellite (LRPT)

Meteor-M satellites circle the Earth over the poles about every 100 minutes, 820 km up. From any spot on the ground, one is in view for up to about 15 minutes at a time. It rises, climbs to a peak elevation that depends on how close its track passes, and sets. Because it moves at 7.4 km/s, first towards and then away from you, its 137 MHz signal arrives shifted in frequency by up to about 3 kHz (the Doppler effect). The shift sweeps through zero fastest when the satellite is overhead.

How strong the signal is when it reaches the receiver, compared with the noise. The satellite's transmit power is spread over a distance that grows from 820 km overhead to over 3000 km at the horizon, so a satellite on the horizon is about 12 dB weaker. The antenna's gain changes with elevation too. At 137 MHz the sky itself is noisy: radio noise from the galaxy and from nearby electrical equipment often outweighs the receiver's own noise. The result is Es/N0, the energy of one symbol over the noise density, which decides whether frames decode. Move the antenna gain or the SNR offset and watch where the image breaks up.

The receiver tunes to the nominal frequency and samples the band at 288 000 complex samples per second, four per symbol. The QPSK signal occupies about 115 kHz: the symbol rate times one plus the roll-off. The Doppler shift moves it by a few kHz, a small fraction of its width but far too much for the demodulator to ignore. When the satellite is low, the signal sinks into the noise.

QPSK carries two bits per symbol in the phase of the carrier: one of four points at 45°, 135°, 225° and 315°. To read them the receiver must spin its reference in step with the incoming carrier, Doppler and all. It first estimates the frequency coarsely: raising the signal to the fourth power removes the modulation and leaves a spectral line at four times the frequency offset. A Costas loop then locks the phase: for each symbol it measures how far the point sits from the nearest ideal point and nudges its oscillator. Its bandwidth trades tracking speed against noise. The loop cannot tell the four 90° positions apart; frame sync (stage 6) resolves that.

The matched filter (the same root-raised-cosine shape as the transmitter's) maximizes the signal against the noise, but only at the right instant in each symbol. The receiver's clock and the satellite's never agree exactly: here the Doppler effect also stretches and squeezes the symbol rate by up to about 22 parts per million. A Gardner detector compares the sample halfway between two symbols with their difference; if the waveform is still moving there, the sampling instant is early or late. A loop steers an interpolator to the right point.

Every 1024-byte frame starts with the same 32-bit attached sync marker, 1ACFFC1D. It goes through the convolutional encoder with everything else, so on the air it becomes a fixed 64-bit pattern: FC A2 B6 3D B0 0D 97 94 (its first few bits depend on the end of the previous frame, so the receiver compares the last 52). The receiver slides the pattern along the symbol stream and compares it in all four orientations of the constellation. The orientation that matches tells it how to undo the Costas loop's 90° ambiguity; the position tells it where the frame starts. After that it expects the next marker exactly 8192 symbols later.

The convolutional encoder sends two bits for every data bit, each a mix of the last seven data bits. The Viterbi decoder finds the data sequence whose encoding is closest to what arrived, tracking all 64 encoder states at once. With soft decisions it weighs each received value by how confident it is; for the same bit error rate that is worth about 2 dB over hard 0/1 decisions. Even with one channel bit in 25 wrong, it usually delivers the frame without a single error.

For rate 1/2 coding on QPSK, one symbol carries exactly one data bit, so Eb/N0 equals Es/N0. Points from this pass are grouped by the link budget's Es/N0 when each frame was sent; frames the receiver never found are not counted.

After the marker, the receiver removes the randomizer: a fixed pseudo-random sequence the satellite added so the signal never stays at one value for long. Then each frame splits into four interleaved Reed–Solomon codewords of 255 bytes, 32 of them parity. Each codeword can repair up to 16 wrong bytes anywhere in it; interleaving spreads a burst of Viterbi errors across all four. With more than 16, the decoder normally detects that it cannot correct the codeword, and the frame is lost.

Newest first. Frame number, content and the two error counts come from the simulator's record of what was sent; a real receiver sees only the frame counter, the marker and the Reed–Solomon result. Rotation is the constellation orientation frame sync chose.

Good frames carry CCSDS packets; a pointer in each frame says where the first new packet starts, so a lost frame costs only the packets it touched. Each image packet holds 14 compressed 8×8 blocks of one channel, so a lost frame leaves black gaps in a strip 8 lines tall, the characteristic look of LRPT dropouts. At low elevation whole rows are lost. Blocks that do arrive are identical to what was sent.