Perfect: TETRA

TETRA (TErrestrial Trunked RAdio) is a wireless specification intended to be used by government agencies, public health services, rail transport, military etc. TETRA specification comes from ETSI (European Telecommunication Standards Institute). We plan to start a post series on the building blocks of TETRA physical layer and radio specifications and this is the first post towards that step.

Documents

a) All the standardization documents from ETSI are available online here

b) From the above list, the key document for us to study the physical layer and RF specification is

Doc. Nb. EN 300 392-2 Ver. 3.2.1, Terrestrial Trunked Radio (TETRA); Voice plus Data (V+D); Part 2: Air Interface (AI). Ref. REN/TETRA-03152

Physical Layer Overview

TETRA specification allows for two modulation types

a) Phase Modulation

The overview of the building blocks in phase modulation is as shown below

Overview of TETRA phase modulation

Figure: Overview of TETRA phase modulation (reference Fig 4.1 ETSI EN 300 392-2 Ver 3.2.1)

For phase modulation, based on the data type, the following channel coding schemes are employed

a) Reed Muller (30,14) code or Block Code

b) Rate Compatible Punctured Convolutional code (RCPC)

c) Block Interleaver

d) Scrambler

e) Modulation of $\frac{\pi}{4}$ Differential Quarternary Phase Shift Keying ( DQPSK) or Differential 8PSK ( D8PSK)

Figure: Overview of TETRA QAM modulation (reference Fig 4.2 ETSI EN 300 392-2 Ver 3.2.1)

For QAM modulation, based on the data type, the following channel coding schemes are employed

a) Reed Muller (16,5) code or Block code

b) Parallel Concatenated Convolutional Code (PCCC)

c) Interleaver

d) Scrambler

e) Modulation of 4-QAM, 16-QAM or 64–QAM

In the upcoming posts in this series we will discuss each of these building blocks in more detail.

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In TETRA specifications, one of the modulation technique used is Differential 8 Phase Shift Keying (D8PSK). We will discuss the bit error rate with non-coherent demodulation of D8PSK in Additive White Gaussian Noise (AWGN) channel.

pi/8 D8PSK

The incoming bit sequence is grouped into three bits and is mapped into differential phase as follows:

B(3k-2)	B(3k-1)	B(3k)
0	0	0
0	0	1
1	0	1
1	0	0
0	1	0
0	1	1
1	1	1
1	1	0

Table : Phase transitions for $\frac{\pi}{8}$ D8PSK modulation (Ref Table 5.2 of ETSI 301-893 V3.2.1)

The modulation symbol is formed by applying a phase offset to previous symbol and is defined as follows:

and

Alternately, the phase transitions can be represented as

The constellation of the D8PSK occupies phase values separated by as shown below in the blue dots. The red lines shows all possible phase transitions.

Figure: Constellation of $\frac{\pi}{8}$ D8PSK (Ref Figure 5.2 of ETSI 301-893 V3.2.1)

Channel Model

The transmitted waveform gets corrupted by noise , typically referred to as Additive White Gaussian Noise (AWGN).

Additive : As the noise gets ‘added’ (and not multiplied) to the received signal

White : The spectrum of the noise if flat for all frequencies.

Gaussian : The values of the noise follows the Gaussian probability distribution function,

with mean and

variance .

The received symbol is,

Non Coherent Receiver

A non-coherent receiver relies on the phase transitions between consecutive symbols to form an estimate of the transmitted bits. The sequence of operation is as follows:

a) On the received symbols estimate the phase