Telecom Signal Processing: PCM, Quantization, Multiplexing
Digitalization of Telephone Channels and Quantization Distortion
The telephone channel, a unidirectional path with a bandwidth of 3100 Hz (300 Hz to 3400 Hz), can be digitalized using Pulse Code Modulation (PCM). When combined with Time Division Multiplexing (TDM), it enhances the efficiency of transmission paths. PCM converts analog samples into digital forms, improving noise immunity during transmission. The analog signal undergoes three operations in an Analog-to-Digital (A/D) converter before multiplexing and transmission:
- Sampling: The signal becomes discrete in time. According to the sampling theorem (fmax = fs/2), with a maximum frequency (fmax) of 3400 Hz for telephony, the sampling frequency (fs) is set to 8000 Hz (with some reserve).
- Quantization: The signal becomes discrete in both time and amplitude.
- Coding: The signal is converted to binary.
The emitter multiplexes the digital signal for transport. The receiver then demultiplexes it, and a Digital-to-Analog (D/A) converter (or PCM decoder) restores the converted signal. Digitalization introduces distortions in the original signal, known as quantization distortion or quantization noise. This is a key quality parameter in the digital transmission of analog signals, with its frequency spectrum distributed equally across the transmitted frequency band.
Nonlinear Quantization: A-law and Mu-law Compression
To ensure sufficient quality for transmitting lower-level signals, non-uniform quantization levels are employed. Two primary compression types exist:
- Mu-law: Used in PCM 24-digital signal of 1st order (DS1) in the USA and Japan.
- A-law: Used in PCM 30/32-digital signal of 1st order (E1) in Europe.
Quantization and coding reduce the signal from 12 to 8 bits. The transmission rate (vp) is determined by the sampling frequency (fs) and the length of the code word after compression: vp = N·fs = 8·8K = 64 kbit/s.
CRC-4 Utilization with PCM Signals
The CRC-4 protection method, based on a cyclic coding scheme as per ITU-T G.706, involves the gradual transmission of a 4-bit control group. Each block of information elements (k-bits) is supplemented with control elements (r-bits), resulting in a final group of n = (k + r) elements that form the protected transmitted signal. This method is applied in TS0.
- Information pattern: A(D)
- Protection pattern: R(D) – remainder of 2r*A(D)/G(D), where r zeros are appended to A and divided by G (e.g., 1/1 0 0/1 1 1/0 1).
- Generating pattern: G(D)
- Protected pattern: F(D)
Methods for Multiplexing Signals
Telecommunication systems support various functions, including efficient signal multiplexing before transmission and adapting aggregated signals for specific media. Several methods exist for utilizing transmission paths:
Frequency Division Multiplexing (FDM)
Each signal is modulated to a specific carrier frequency. Signals are bundled and transmitted simultaneously but independently. Protection bands prevent signal overlap. Demultiplexing requires proper filtering. A key advantage is signal independence. FDM is used in cable and wireless applications like CATV and ADSL/VDSL.
Time Division Multiplexing (TDM)
Data from different channels is transmitted in specific timeslots (Δt) over a single line. Two options exist:
- Synchronous TDM (STD): Each input channel always gets a timeslot.
- Asynchronous TDM (ATD) or Statistical TDM: Timeslots are assigned only when needed, carrying extra information about the channel.
TDM allows the transmission of analog or processed samples via impulse modulation (PAM, PPM, PWM). It’s used in cable and wireless applications, such as PCM 30/32.
Wavelength Division Multiplexing (WDM)
Similar to FDM, but used for optical signals. Two options are available:
- Dense WDM (DWDM): Carrier spacing under 1 nm.
- Coarse WDM (CWDM): Carrier spacing over 10 nm.
Code Division Multiplexing (CDM)
Utilizes specific properties of a suitably constructed code. Used in modern wireless systems like 3G and Wi-Fi.