# Physical Layer¶

## 4FSK generation¶

M17 standard uses 4FSK modulation running at 4800 symbols/s (9600 bits/s) with a deviation index h=0.33 for transmission in 6.25 kHz channel bandwidth. Channel spacing is 12.5 kHz. The symbol stream is converted to a series of impulses which pass through a root-raised-cosine (α=0.5) shaping filter before frequency modulation at the transmitter and again after frequency demodulation at the receiver.

The bit-to-symbol mapping is shown in the table below.

Information bits | Symbol | 4FSK deviation | |
---|---|---|---|

Bit 1 | Bit 0 | ||

0 | 1 | +3 | +2.4 kHz |

0 | 0 | +1 | +0.8 kHz |

1 | 0 | -1 | -0.8 kHz |

1 | 1 | -3 | -2.4 kHz |

The most significant bits are sent first, meaning that the byte 0xB4 in type 4 bits (see Bit types) would be sent as the symbols -1 -3 +3 +1.

## Preamble¶

Every transmission starts with a preamble, which shall consist of at least 40ms of alternating -3, +3… symbols. This is equivalent to 40 milliseconds of a 2400 Hz tone

## Bit types¶

The bits at different stages of the error correction coding are referred to with bit types, given in Table 2.

Type 1 | Data link layer bits |

Type 2 | Bits after appropriate encoding |

Type 3 | Bits after puncturing (only for convolutionally coded data, for other ECC schemes type 3 bits are the same as type 2 bits) |

Type 4 | Decorrelated and interleaved (re-ordered) type 3 bits |

Type 4 bits are used for transmission over the RF. Incoming type 4 bits shall be decoded to type 1 bits, which are then used to extract all the frame fields.

## Error correction coding schemes and bit type conversion¶

Two distinct ECC/FEC schemes are used for different parts of the transmission.

### Link setup frame¶

240 DST, SRC, TYPE, NONCE and CRC type 1 bits are convolutionally coded using rate 1/2 coder with constraint K=5. 4 tail bits are used to flush the encoder’s state register, giving a total of 244 bits being encoded. Resulting 488 type 2 bits are retained for type 3 bits computation. Type 3 bits are computed by puncturing type 2 bits using a scheme shown in chapter 4.4. This results in 368 bits, which in conjunction with the synchronization burst gives 384 bits (384 bits / 9600bps = 40 ms).

Interleaving type 3 bits produce type 4 bits that are ready to be transmitted. Interleaving is used to combat error bursts.

### Subsequent frames¶

A 48-bit (type 1) chunk of LICH is partitioned into 4 12-bit parts and encoded using Golay (24, 12) code. This produces 96 encoded LICH bits of type 2.

FN, payload and CRC is 160 bits which are convolutionally encoded in a manner analogous to that of the link setup frame. A total of 164 bits is being encoded resulting in 328 type 2 bits. These bits are punctured to generate 272 type 3 bits.

96 type 2 bits of LICH are concatenated with 272 type 3 bits and re-ordered to form type 4 bits for transmission. This, along with 16-bit sync in the beginning of frame, gives a total of 384 bits

The LICH chucks allow for late listening and indepedent decoding to check destination address. The goal is to require less complexity to decode just the LICH and check if the full message should be decoded.

### Convolutional encoder¶

[ECC] | Moreira, Jorge C.; Farrell, Patrick G. “Essentials of Error‐Control Coding” Wiley 2006, ISBN: 9780470029206 |

The convolutional code shall encode the input bit sequence after appending 4 tail bits at the end of the sequence. Rate of the coder is R=½ with constraint length K=5 [NXDN]. The encoder diagram and generating polynomials are shown below

The output from the encoder must be read alternately.

[NXDN] | NXDN Technical Specifications, Part 1: Air Interface; Sub-part A: Common Air Interface |

### Code puncturing¶

Removing some of the bits from the convolutional coder’s output is called code puncturing. The nominal coding rate of the encoder used in M17 is ½. This means the encoder outputs two bits for every bit of the input data stream. To get other (higher) coding rates, a puncturing scheme has to be used.

Two different puncturing schemes are used in M17:

- leaving 46 from 61 encoded bits
- leaving 34 from 41 encoded bits

Scheme P1 is used for the initial LICH link setup info, taking 488 bits of encoded data and selecting 368 bits. The \(gcd(368, 488)\) is 8 which, when used to divide, leaves 46 and 61. A full puncture pattern requires the output be divisible by the number of encoding polynomials. For this case the full puncture matrix should have 122 entries with 92 of them being 1.

Scheme P2 is for frames (excluding LICH chunks, which are coded differently). This takes 328 encoded bits and selects 272 of the bits. The \(gcd(272, 328)\) is 8 which results in the 34 and 41 reduced ratio. The full matrix will have 82 entries with 68 being 1.

The matrices can be represented more concisely by duplicating a
smaller matrix with a *flattening*.

The puncturing schemes are defined by their partial puncturing matrices:

The complete linearized representations are:

```
P1 = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1,
0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,
1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]
P2 = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1,
0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]
```

### Interleaving¶

For interleaving a Quadratic Permutation Polynomial (QPP) is used. The polynomial \(\pi(x)=(45x+92x^2)\mod 368\) is used for a 368 bit interleaving pattern [QPP]. See appendix Table 14 for pattern.

[QPP] | Trifina, Lucian, Daniela Tarniceriu, and Valeriu Munteanu. “Improved QPP Interleavers for LTE Standard.” ISSCS 2011 - International Symposium on Signals, Circuits and Systems (2011): n. pag. Crossref. Web. https://arxiv.org/abs/1103.3794 |

### Data Decorrelator¶

To avoid transmitting long sequences of constant symbols (e.g. 010101…), a simple algorithm is used. All 46 bytes of type 4 bits shall be XORed with a pseudorandom, predefined stream. The same algorithm has to be used for incoming bits at the receiver to get the original data stream. See Table 13 for sequence.