Ecu302_pcm

ECU302 Digital Communication Topics: Time Division Multiplexing Pulse Code Modulation

Time Division Multiplexing Definition: Time Division Multiplexing (TDM) is the time interleaving of samples from several sources so that the information from these sources can be transmitted serially over a single communication channel. At the Transmitter Simultaneous transmission of several signals on a time-sharing basis.  Each signal occupies its own distinct time slot, using all frequencies, for the duration of the transmission.  Slots may be permanently assigned on demand. At the Receiver  Decommutator (sampler) has to be synchronized with the incoming waveform  Frame Synchronization  Low pass filter  ISI – poor channel filtering  Feedthrough of one channel's signal into another channel -- Crosstalk Applications of TDM: Digital Telephony, Data communications, Satellite Access, Cellular radio.

Time Division Multiplexing

Conceptual diagram of multiplexing-demultiplexing.

PAM TDM System

Illustrating 4-Channel PAM TDM Multiplexing

Digital Time Division Multiplexing  Time Division Multiplexing (TDM) can be accomplished at bit or byte (word) level.  Channhels having different data rates can also be TDM multiplexed but must be interleaved accordingly.

Digit Interleaving

WORD or Byte Interleaving

Interleaving channel with different bit rates

Interleaving channel with different bit rates using two multiplexers

Block diagram of TDM system. PAM TDM System

A Typical Framing Structure for TDM

Time Division Multiplexing

Frame structure of a certain TDM signal

Composite Signal Format

Time Division Multiplexing

Pulse width of TDM PAM: Ts 1 = 3 3 fs

fs 

1 Ts

fs satisfies Nyquist rate

Pulse Stuffing in TDM  Stuff bits, which are dummy bits are inserted in the TDM output data when the different inputs are not completeley synchronized or the different input rates are not related by a ratinal number.

Pulse Stuffing in TDM  Stuff bits, which are dummy bits are inserted in the TDM output data when the different inputs are not completeley synchronized or the different input rates are not related by a ratinal number.

TDM Example (Multiplexing Analog and Digital) Source 1: 2 kHz bandwidth. Source 2: 4 kHz bandwidth.  Source 3: 2 kHz bandwidth.  Source 4-11: Digital 7200 bits/sec.

8x7.2=57.6 kb/s Use stuff bits to complete 7.2 to 8 kb/s. Now 8 and 64 rates are complete multıples

16 ksam/s

64 kb/s

128 kb/s

Frame Synchronization  To sort and direct the received multiplexed data to the appropriate output channel  Frame sync (unique k-bits) +Information words of an N-channel TDM

 Two system ways to provide frame sync to the demultiplexer circuit - Over a separate channel - Deriving from the TDM signal itself

TDM PAM for Radio Telemetry

CCITT Digital TDM Hierarchy

Packet Transmission System  TDM is Synchronous Transfer Mode (STM) technology

- Data source is assigned a specific time slot – fixed data rate - More efficient when sources have a fixed data rate - Inefficient to accommodate bursty data source Solution?

 Packet Transmission System

- Partitions source data into data packets (destination address, header) - Efficiently assigns network resources when the sources have bursty data - Examples : Internet TCP/IP technology and the Asynchronous Transfer Mode (ATM) technology.

Pulse Code Modulation     

Pulse Code Modulation Quantizing Encoding Analogue to Digital Conversion Bandwidth of PCM Signals

PULSE CODE MODULATION (PCM)  DEFINITION: Pulse code modulation (PCM)the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream.  The advantages of PCM are: • Relatively inexpensive digital circuitry may be used extensively. • PCM signals derived from all types of analog sources may be merged with data signals and transmitted over a common high-speed digital communication system (multiplexing).

PULSE CODE MODULATION (PCM) • In long-distance digital telephone systems requiring repeaters, a clean PCM waveform can be regenerated at the output of each repeater, where the input consists of a noisy PCM waveform. • • The noise performance of a digital system can be superior to that of an analog system. • The probability of error for the system output can be reduced even further by the use of appropriate coding techniques.

Sampling, Quantizing, and Encoding 

• •

4.

The PCM signal is generated by carrying out three basic operations: 1. Sampling 2. Quantizing 3. Encoding Sampling operation generates a flat-top PAM signal. Quantizing operation approximates the analog values by using a finite number of levels. This operation is considered in 3 steps a) Uniform Quantizer b) Quantization Error c) Quantized PAM signal output PCM signal is obtained from the quantized PAM signal by encoding each quantized sample value into a digital word.

Analog to Digital Conversion  The Analog-to-digital Converter (ADC) performs three functions:

– Sampling

Analog Input Signal

• Makes the signal discrete in time. • If the analog input has a bandwidth of W Hz, then the minimum sample frequency such that the signal can be reconstructed without distortion.

Sample

ADC

– Quantization

Quantize

Encode

111 110 101 100 011 010 001 000

• Makes the signal discrete in amplitude. • Round off to one of q discrete levels.

– Encode • Maps the quantized values to digital words that are ν bits long.

Digital Output Signal 111 111 001 010 011 111 011

 If the (Nyquist) Sampling Theorem is satisfied, then only quantization introduces distortion to the system.

Quantization  The output of a sampler is still continuous in amplitude. – Each sample can take on any value e.g. 3.752, 0.001, etc. – The number of possible values is infinite.  To transmit as a digital signal we must restrict the number of possible values.  Quantization is the process of “rounding off” a sample according to some rule. – E.g. suppose we must round to the nearest tenth, then: 3.752 --> 3.8 0.001 --> 0

Illustration of the Quantization Error

 The difference between the analog signal and the quantized signal is the quantization error.

PCM TV transmission:

(a) 5-bit resolution;

(g) 8-bit resolution.

 As the number of bits per sample increases the quantization error decreases and picture resolution improves.

Uniform Quantization • Most ADC’s use uniform quantizers.

Dynamic Range: (-8, 8) Output sample XQ

7

• The quantization levels of a uniform quantizer are equally spaced apart.

5 3 1

-8

-6

-4

-2

-1 2

4

6

8

Input sample X -3 -5 -7

Quantization Characteristic

Example: Uniform ν =3 bit quantizer q=8 and XQ = {±1,±3,±5,±7}

• Uniform quantizers are optimal when the input distribution is uniform. When all values within the Dynamic Range of the quantizer are equally likely.

Quantization Example Analogue signal

Sampling TIMING

Quantization levels. Quantized to 5-levels

Quantization levels Quantized 10-levels

PCM encoding example Levels are encoded using this table

Table: Quantization levels with belonging code words

M=8

Chart 1. Quantization and digitalization of a signal. Signal is quantized in 11 time points & 8 quantization segments.

Chart 2. Process of restoring a signal. PCM encoded signal in binary form: 101 111 110 001 010 100 111 100 011 010 101 Total of 33 bits were used to encode a signal

Encoding

• The output of the quantizer is one of M possible signal levels. – If we want to use a binary transmission system, then we need to map each quantized sample into an n bit binary word. n

M  2 , n  log 2 ( M )

• Encoding is the process of representing each quantized sample by an ν bit code word. – The mapping is one-to-one so there is no distortion introduced by encoding. – Some mappings are better than others. • A Gray code gives the best end-to-end performance. • The weakness of Gray codes is poor performance when the sign bit (MSB) is received in error.

Gray Codes • With gray codes adjacent samples differ only in one bit position. • Example (3 bit quantization): XQ Natural coding Gray Coding +7 111 110 +5 110 111 +3 101 101 +1 100 100 -1 011 000 -3 010 001 -5 001 011 -7 000 010 • With this gray code, a single bit error will result in an amplitude error of only 2. – Unless the MSB is in error.

Waveforms in a PCM system for M=8 M=8

(a) Quantizer Input output characteristics

(b) Analog Signal, PAM Signal, Quantized PAM Signal

(c) Error Signal

(d) PCM Signal

M  2n

n  log 2 ( M )

M is the number of Quantization levels n is the number of bits per sample

PCM Transmission System

PCM Communication System

Practical PCM Circuits •

Three popular techniques are used to implement the analog-to-digital converter (ADC) encoding operation: 1. The counting or ramp, ( Maxim ICL7126 ADC) 2. Serial or successive approximation, (AD 570) 3. Parallel or flash encoders. ( CA3318)

•

The objective of these circuits is to generate the PCM word. Parallel digital output obtained (from one of the above techniques) needs to be serialized before sending over a 2-wire channel This is accomplished by parallel-to-serial converters [Serial Input-Output (SIO) chip] UART,USRT and USART are examples for SIO’s

• • •

• • •

•

Bandwidth of PCM Signals The spectrum of the PCM signal is not directly related to the spectrum of the input signal. The bandwidth of (serial) binary PCM waveforms depends on the bit rate R and the waveform pulse shape used to represent the data. The Bit Rate R is R=nfs M=2n Where n is the number of bits in the PCM word and fs is the sampling rate. For no aliasing case (fs≥ 2B), the MINIMUM Bandwidth of PCM Bpcm(Min) is:

Bpcm(Min) = R/2 = nfs//2 The Minimum Bandwidth of nfs//2 is obtained only when sin(x)/x pulse is used to generate the PCM waveform.

•

For PCM waveform generated by rectangular pulses, the First-null Bandwidth is:

Bpcm = R = nfs

Quantization Noise  The process of quantization can be interpreted as an additive noise process. Signal X

Quantized Signal XQ Quantization Noise nQ

•

The signal to quantization noise ratio (SNR)Q=S/N is given as: Average Power{ X } ( SNR)Q  Average Power{nQ }

Effects of Quantizing Noise

•

If Pe is negligible, there are no bit errors resulting from channel noise and no ISI, the Peak SNR resulting from only quantizing error is:

•

The Average SNR due to quantizing errors is:

•

Above equations can be expresses in decibels as,

Where, M = 2n α = 4.77 for peak SNR α = 0 for average SNR

DESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMS

• • •

Assume that an analog audio voice-frequency(VF) telephone signal occupies a band from 300 to 3,400Hz. The signal is to be converted to a PCM signal for transmission over a digital telephone system. The minimum sampling frequency is 2x3.4 = 6.8 ksample/sec. The VF signal is oversampled with a sampling frequency of 8ksamples/sec - standard adopted by the Unites States telephone industry. Assume that each sample values is represented by 8 bits; then the binary PCM bit rate 8

• •

This 64-kbit/s signal is called a DS-0 signal (digital signal, type zero). The minimum absolute bandwidth of the binary PCM signal is

BPCM

R nf s   2 2

This B is for a sinx/x type pulse sampling

DESIGN OF A PCM SIGNAL FOR TELEPHONE SYSTEMS

•

If we use a rectangular pulse for sampling the first null bandwidth is given by

•

We require a bandwidth of 64kHz to transmit this digital voice PCM signal, whereas the bandwidth of the original analog voice signal was, at most, 4kHz.

•

We observe that the peak signal-to-quantizing noise power ratio is:

Nonuniform Quantization

Many signals such as speech have a nonuniform distribution. – The amplitude is more likely to be close to zero than to be at

higher levels. Nonuniform quantizers have unequally spaced levels be chosen to optimize the SNR for a particular – The spacing canOutput sample type of signal. X 6

Q

4

Example: Nonuniform 3 bit quantizer

2

-8

-6

-4

-2

2 -2

-4

-6

4

6

8

Input sample X

Uniform and Nonuniform Quantization

Companding • • • • •

Nonuniform quantizers are difficult to make and expensive. An alternative is to first pass the speech signal through a nonlinearity before quantizing with a uniform quantizer. The nonlinearity causes the signal amplitude to be Compressed. – The input to the quantizer will have a more uniform distribution. At the receiver, the signal is Expanded by an inverse to the nonlinearity. The process of compressing and expanding is called Companding.

µ -Law Companding 1

Output |x(t)|

• Telephones in the U.S., Canada and Japan use µ-law companding: ln(1   | x (t )|) | y (t ) | ln(1   )

– Where µ = 255 and |x(t)| < 1

0

1 Input |x(t)|

Non Uniform quantizing • • •

Voice signals are more likely to have amplitudes near zero than at extreme peaks. For such signals with non-uniform amplitude distribution quantizing noise will be higher for amplitude values near zero. A technique to increase amplitudes near zero is called Companding.

Effect of non linear quantizing can be can be obtained by first passing the analog signal through a compressor and then through a uniform quantizer.

x

x’ C(.) Compressor

x’

y

Q (.) Uniform Quantizer

Example: µ -law Companding 1

x[n]=speech /song/

0 .5 0

­ 0 .5 ­1

0

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

0

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1

y[n]=C(x[n]) Companded Signal

0 .5

0 ­ 0 .5 ­1

1

0 .5

Segment of x[n]

0

Close View of the Signal

­ 0 .5

­1 2 2 0 0

2 3 0 0

2 4 0 0

2 5 0 0

2 6 0 0

2 7 0 0

2 8 0 0

2 9 0 0

3 0 0 0

2 3 0 0

2 4 0 0

2 5 0 0

2 6 0 0

2 7 0 0

2 8 0 0

2 9 0 0

3 0 0 0

1

Segment of y[n] Companded Signal

0 .5

0

­ 0 .5

­1 2 2 0 0

µ -law Encoder Transfer Characteristics

• • •

A-law and µ− law Companding

These two are standard companding methods. u-Law is used in North America and Japan A-Law is used elsewhere to compress digital telephone signals

V.90 56-Kbps PCM Computer modem • The V.90 PC Modem transmits data at 56kb/s from a PC via an analog signal on a dial-up telephone line. • A μ law compander is used in quantization with a value for μ of 255. • The modem clock is synchronized to the 8-ksample/ sec clock of the telephone company. • 7 bits of the 8 bit PCM are used to get a data rate of 56kb/s ( Frequencies below 300Hz are omitted to get rid of the power line noise in harmonics of 60Hz). • SNR of the line should be at least 52dB to operate on 56kbps. • If SNR is below 52dB the modem will fallback to lower speeds ( 33.3 kbps, 28.8kbps or 24kbps).