T1 digital carrier system; adaptive delta modulation

T1 digital carrier system

T1 is the North American TDM-PCM carrier that sends 24 voice channels over one twisted-pair line at 1.544 Mb/s.

• Each voice channel is band-limited to 3.4 kHz and sampled at 8 kHz.
• Each sample is µ-law compressed ($\mu = 255$) and coded into 8 bits, giving 64 kb/s per channel.
• One frame = one 8-bit sample from each of the 24 channels + 1 framing bit = 193 bits in 125 µs.

|<--------- one frame = 125 us = 193 bits --------->|
+---+--------+--------+--------+-------+--------+
| F |  Ch 1  |  Ch 2  |  Ch 3  |  ...  | Ch 24  |
+---+--------+--------+--------+-------+--------+
 1 bit  8 bits  8 bits  8 bits           8 bits
 F = framing bit (pattern spread over 12 frames)

$$\begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frames per second} &= f_s = 8000\ \text{frames/s} \\ R_b &= 193 \times 8000 = 1\,544\,000\ \text{b/s} = 1.544\ \text{Mb/s} \end{aligned}$$

• Signalling uses robbed bits (the LSB in frames 6 and 12 of a 12-frame superframe).
• The line code is bipolar AMI (B8ZS on newer lines). Repeaters are placed about every 1.8 km.

Multiplexing hierarchy:

 24 voice ch x 64 kb/s
        |
   [ DS1 / T1 ]  1.544 Mb/s    24 ch
        | x4
   [ DS2 / T2 ]  6.312 Mb/s    96 ch
        | x7
   [ DS3 / T3 ]  44.736 Mb/s   672 ch
        | x6
   [ DS4 / T4 ]  274.176 Mb/s  4032 ch

Higher levels add framing and stuffing bits, so DS2 = 6.312 Mb/s rather than $4 \times 1.544 = 6.176$ Mb/s.

Adaptive Delta Modulation (ADM)

Linear delta modulation (DM) sends 1 bit per sample, which says whether the signal is above or below its staircase approximation. A fixed step size $\Delta$ causes two problems:

• Slope overload when the signal changes faster than $\Delta f_s$.
• Granular noise when the signal is nearly flat.

ADM changes the step size to suit the signal slope:

• If several successive output bits are the same (e.g. 1 1 1), the staircase is lagging behind, so the step size is increased. A common rule is to multiply it by 1.5 or 2.
• If the bits alternate (1 0 1 0), the signal is flat, so the step size is decreased (e.g. divided by the same factor), down to a minimum $\Delta_{min}$.

 m(t) -->(+)--> [Comparator] --+--> output bits b(k)
          ^-                   |
          |                    v
          |            [Step size logic]
          |                    | delta(k)
          +--- [Accumulator] <-+

The receiver uses the same logic on the received bits, so no extra side information is sent.

Advantages: much less slope overload and granular noise, a wider dynamic range, and good speech quality at 16–32 kb/s. An example is CVSD (continuously variable slope DM), used in military and Bluetooth voice.