8. TDM Mux_Demux.pdf

Multiplexing – Demultiplexing
Dr. S. Ravishankar
Professor, ECE, RVCE

Format
•Sampling
•Quantizing
•Encoding
Source Coding
•Vocoders
•CELP
•Encryption
Multiplexing
•Framing
•Engg OH
•Rate Match
Channel Coding
•Block Code
•Interleave
•Convolution
Baseband Mod
•LP Line Code
•M-PAM
Bandpass Mod
•BW limited
•Power limited
Channel Access
•SSMA
•FDMA
•TDMA
Channel Access
•SSMA
•FDMA
•TDMA
Equalization
•Chnl Estm
•Adaptation
Detection
•CP sample
•Averaging
•Matched Fil
Estimation
•MAP
•MLE
•Pe
Channel Decoder
•Block
•DeInterleave
•Convolution
Demultiplexer
•Data Retime
•Frame Recov
•Data Parsing
Source Coding
•Vocoders
•CELP
•Decryption
Synchronization
•Carrier Recovery
•Timing Recovery
•Frame Recovery
RF Transmitter
RF Receiver
Format
•Decoding
•Reconstruct
•Eqlr/Filtering
Transmit Chain Processing
Receive Chain Processing
Bit Processing Blocks
Bit Processing Blocks
Symbol Processing
Symbol Processing
Channel
• Understand the physical functions of the block
• Mathematical formulation of the functions
• Engineering Considerations and approximations
• Algorithmic formulation with precision considerations
• Performance analysis wrt parameters
• Implementation – Platform Architecture and SW flow

Multiplexing is a set of techniques that allows the simultaneous
transmission of multiple signals across a single data link.
 When the bandwidth of a medium linking two devices is greater than the
bandwidth needs of the devices, the link can be shared by others.
 Transmission Efficiency can be achieved by multiplexing (How?)
 Pack in more users or higher data rate implies (data rate in bps/ Hz of
Channel Bandwidth)
 Provide for Framing at Multiplexer to identify data at Demultiplexer.
(Like a dabbawalla or military dobhiwala handling uniforms)
 Provide for Engg Overhead (OH) to monitor channel status
 Provide for Rate Matching between user data and channel access rate
(useful for cellular 4G/5G/Wi-fi)
• Corresponding actions at demultiplexer
 Data Retiming at Receiver to local station clock. (Data from Transmit
end has been timed with Transmit station clock. No two clocks are
same!!) (Ex: 100 Kbps one end, 100.000001 Kbps other end. So loss of
sync leading to call drop occurs every 10^6 / 100K = 10 secs)
 Frame Recovery to identify specific data samples
 Data Parsing

6.5
Categories of multiplexing

6.6
Frequency-division multiplexing

Frequency Division Mux and Demux

TDM on the channel
TDM is a digital multiplexing technique for combining
several low-rate channels into one high-rate one

Synchronous time-division multiplexing
• In synchronous TDM, the data rate of the link is n times faster, and the unit
duration is n times shorter.
• The Inter-sample time for each signal is to be maintained for perfect
reconstruction.
• Same timing source should be available both at the Local Txr and distant Rcvr ???

Frame Duration – simple example
• So pick up one byte from each input stream to form a 4-byte frame
• To maintain 100 bytes/sec for each stream at o/p need to send 100 frames/sec
• So bit rate over channel is 100frames/sec x 32 bits/frame = 3200 bps.
• Time span of one frame is (1/100) secs.

Multiplex – Demultiplex Modes
Iso chronous –
isolated clocks.
(Quasi synchronous)

 Time division multiplexing is a natural consequence of sampling since channel is
free between samples of the same signal.
 In a set of PAM samples from M- users existing on a line - the crucial issue is to
identify which one is sample 1, sample 2 so on at Receiver (No sample identity !!)
Commutator De-Commutator

6.14
Need for Frame Marker
• Receiver is located elsewhere – Has its own nominally same frequency and clock as Txr
• User data is random and receiver has no control on time to start picking up valid samples
• Receiver needs to be capture valid frame alignment at the receiver – demultiplexer.

1. Define an ordered sample sequence called ‘Frame’, maintaining inter sample
spacing for individual channels, while also maintaining adjacent sample
spacing within a frame.
2. Add an identity marker called Frame Header or Header or Start Flag,

Add more channels means
• Including additional bits in the same
frame time so line rate = (no of bits/
Frame time ) will increase.
• Also bits will occupy less time width
so the band width would also need to
be increased.

Synchronous transmission
• Needs both data and clock to be sent from transmitter to receiver
• Therefore band width requirement is doubled
• Issue – One Receiver is in contact with multiple distant Transmitters. So Rcvr has to
operate with multiple Transmitter clocks. However actual users are further downstream
of the first receiver (Trunk exchange / Operator's Internet server) at the local station.
• It has to pass through several servers/ exchanges before it reaches the intended user.

Asynchronous
• Most famous example is that used by Internet (TCP/IP)
• Overhead is a little over 60%
• However advantage is it needs no clock to be transmitted and each receiver uses his
own clock to recover data.

Functional Operations of a Mux / Demux - MUX Operations (Quasi Synchronous)
• Establish a frame as the smallest time interval containing one sample or at least
one bit from each input.
• Assign to each input a unique number of slots within the frame.
• Tx and Rx frame hold Buffer builds up one frame to be clocked at higher frame
bit clock.
• Add signaling and bits for call control
•Insert frame, Multiframe bits for frame identification and Housekeeping bits.
• Insert data bits for synchronization (Carrier recovery all 1’s, Clock recovery
alternate 1,0 and frame recovery) at receiver.
Data bits Frame Marker
Signaling bits
1/0 clk bits All 1’s Carr Recov
Data bits Frame Marker
Signaling bits
Aided Carrier and clock recovery – Acquisition - Training (Non Data dependent)
Unaided Aided Carrier and clock recovery – Tracking phase - Showtime Data dependent

Functional Operations of a Mux / Demux - DEMUX Operations
• Capture Frame alignment (header) bits to facilitate frame parsing and
extraction of data bits corresponding to user samples.
• Managing differences in clocks between Tx and Rx stations in Three
different types of Mux-Demux Scenarios
 Synchronous
 Data and clock sent from Transmitter to Receiver.
 Includes pulse stuffing.
 No overhead required.
 Rcvr works off the clock received from transmitter.
 Issue – Bandwidth, dependency on Tx clock implies multiplicity
of receivers corresponding to Transmitters.
 Only for very small numbers of Transmitters and Receivers in
close proximity
 Asynchronous – Next Slide.
 Quasi synchronous (P / D buffer – Elastic buffer) – Next to Next slide

 Asynchronous
 Suited when there is a Large difference in line rates (clock rates)
between Tx and Rx, Example Internet services
 Can use own clocks - Needs buffering and retiming
 Packet transmission - needs significant overhead SOF,EOF, sizing info,
sequencing; origin, destination, Addresses, routing information.
 Every packet is small limited to a few bytes. The time between two
packets is not fixed and is essentially a random phenomenon. and
needs overhead for each and every packet rendering it inefficient for
stream type of transmission. Typically suited for enquiry and
response type of traffic.
 For Internet TCP-IP is used with 70% OH – quite Inefficient- suffers
routing delays that impacts latency.
 Widely used at very high data rates through multiple transmission
media and switches.
 Quasi synchronous (P / D buffer – Elastic buffer) – Next slide

 Quasi synchronous (Plesiochronous and Doppler buffer – Elastic
buffer) –
 widely used for direct device to device streaming data transfer
over single transmission media. Typical in a multiplex hierarchy
 Minimal overhead required since it is essentially stream data
transfer but with slightly differing clocks at Tx and Rx
 Employs PD buffers for retiming data at receivers
 Multiple PD buffers employed over end to end link comprising
different transmission media and different transmission rates
over each media section. One PD buffer at each link receiver.
 Ex: Phone - DSL two wire line – local switch – fiber/microwave
backhaul – Trunk switch – fiber – overseas switch – fiber – local
switch – coax line – wired Modem – wireless router – Distant
user Device.

Need for Tx and Rx clock synchronization in stream Transfer

User Device
• Voice + Data SQE format block
• Uses Device clock
• Async transfer of TCP/IP Packets over
ethernet over WLAN connector to
wireline Modem
• TCP/IP over Wi-Fi
DSL Modem
•Ethernet I/O to user
•TX - Uses own clock or derived
clock from Xch using PLL for TX.
• Rate matching buffers from slower
user device to faster DSL link
transmission. Needed for Wi-Fi /
cellular transmission also
•Strips Ethernet and reformats the
TCP/IP Packets for framed
transmission over DSL Frames
depending on link speed.
•RX - Performs retiming of recd
data to own clock (P+D buffer)
•Restores Ethernet packets for
transmission to user
At Xch or Switch
• RX – from DSL Modem Performs
retiming (P+D buffer) to Xch local
clock for switching and forward.
• Adds ATM framing and performs
Rate matching for transmission to
gateway or other switches. Uses own
clock.
• TX to user – Strips ATM framing and
reformats the TCP/IP packets to DSL
framing depending on DSL link
speed. Uses own clock
• Extracts clock from data recd from
DSL and other switch side to perform
retiming to local clock
Notice that every stage we need to
1. Generate local clock (TCXO/OCXO)
2. Extract clock from received data from every linked distant end by PLL locked to local VCXO
3. Retiming the received data to local generated clock.
4. Detection, Parsing and transfer of received data has to be done with local clocked data

(Synchronization operations are done in three stages to recover unknown user data. Carrier
Recovery, Clock recovery, Frame recovery)
• Perform Aided Carrier recovery and clock recovery during Training phase.
• Perform Unaided Carrier and clock recovery during Tracking phase / Showtime
• Carrier Recovery needs PLL, Clock recovery needs Tx PSD and PLL. Note that these two
entities are independent of user data, hence needs use of PLL that compares two closely
matching waveforms (received signal and local reference) and induces modifications in
the reference to match the received signal to a desired accuracy.
• Frame Recovery has access to data so receiver initiates a Capture Frame alignment
(header) to facilitate frame parsing and extraction of sample data bits.
• Also need to manage differences in clocks between Tx and Rx stations. This is done at
receiver prior to frame recovery. No two clocks are same.
Data Retiming
Frame Recovery
and Parse Frame
for user data

Line Codes and their Transmit PSD

We Examine three Applications of Multiplexing and Demultiplexing
1. E1 Frame - European ITU-T Hierarchy standard and also adopted in
India.
2. T1 Frame – North American Standard adopted also in Japan, Korea.
3. Digital Speech Processing (Vocoders and LPC Codecs)

T-1 line for multiplexing telephone lines

T1 – Channel Framing
Speech sampling rate = 8 Ksps.
Time between samples = 1/8 KHz = 125 msecs
Each sample has 8 bits. PCM Rate = 64 Kbps
Frame has 24 slots or channels
Each slot has one sample of voice with 8 bits
Frame size = 24chls x 8 bits/chl + 1 framing bit
Line Rate = 193bits/ 125 msecs = 1.544 Mbps

North American Digital Hierarchy

Digital System (DS) and T line rates
Note
• 24 x 64 Kbps = 1.536 Mbps < 1.544 Mbps. OH has been added
• 4 x 1.544 = 6.176 < 6.312 . OH has been added.

E1 Frame -Used in Europe, India
E1 Frame structure
Ch 1
125µsec , 256 bits
0 1 31
15
8 bit
times
lots
Frame
alignment
signal
Signaling
Information

E line rates
Note
• 4 x 2.048 = 8.192 Mbps < 8.448 Mbps. So OH has been added

MUX HIERARCHY
1st Level 24 (T1) 1.544 Mbps Frame 30 (E1) 2.048 Mbps
2nd Level 4 T1
(T2)
6.312 Mbps
Multiframe
4 E1
(E2)
8.448 Mbps
3rd Level 7 T2
(T3)
44.736 Mbps
Super frame
4 E2
(E3)
34.368 Mbps
4th Level 6 T3
(T4)
274.176 Mbps
Hyperframe
4 E3
(E4)
139.264 Mbps

Choice of Frame Header
1. Any specific pattern like (7E)Hex could be used in links with very low noise levels.
However for noisy channels Poor CCF is an issue for detection of unique word
pattern. Random user data could easily mimic Unique word and cause false
detections.
2. Better choice is a PN sequence that has good ACF properties

Unique word Correlator - for Detection of Frame Alignment Signal
(Frame Recovery)
Intialize UW(k); k = 1,N
UW(k) = 2*UW(k) – 1; k=1,N
Load Rcv(k) ; k = 1,N
Pcv(k) = 2*Rcv(k) – 1; k=1,N
V = Sum (UW(k) * PCV(k); k= 1,N)
If(V=Threshold) Go to another FSM stage
Else (Shift Rcv(k) 1 bit right and return to Pcv

FSM for frame Identification of E1 frames
Sliding Correlator
Window Open always
Set threshold=8
Value<Threshold
Close Window
Open after 256 bits
Close Window
Open after 256 bits
If Value = Threshold , Count =1
Value<Threshold
Value<Threshold
Close Window
Open after every256 bits
Threshold-- , count=0
Close Window
Open after 256 bits
Count =1 or 2
Value<Threshold
Value>=Threshold
Count = 2
Value <Threshold
Value =Threshold
Value<Threshold

FSM for frame Identification of T1
frames
T1 Frame -Used in North America
T1 Frame structure
For frame Identification
1
194
388
X
X
X
X
X
X
1
1
1

Value
Channel 1
Channel 24
One bit frame
alignment signal
125µsec , 193 bits
8–bit

FSM for frame Identification of T1 frames
Sliding Correlator
Window Open always
Set threshold=3
Value<Threshold
Close Window
Open after 387 bits
Close Window
Open after 387 bits
Value<Threshold
Value<Threshold
Close Window
Open after every 387 bits
Threshold-- , count=0
Close Window
Open after 387 bits
count=1 or 2
Value<Threshold
Value>=Threshold
Count = 2
Value <Threshold
Value =Threshold
Value<Threshold

Data
Write Clk
Data
Read Clk
Write
Address
Pointer
Read
Address
Pointer
Buffer Length=2*Frame length
WP RP
WP RP
F
H
F
H
F
H
F
H
1Frame length
Read clock faster
Repeat Frame.
Just passed FH
and maintains
same position wrt
previous frame
Read clock slower
Skip Frame. Same
relative position
wrt Frame Header
RP
RP
1Frame length

P/D Buffer
Buffer Length=2*Frame length
Read Cycle Decrements Read pointer (RP),
Write Cycle increments Read pointer (RP)
Read and Write cycles same – Pointers will remain at the same position
Read slow –RP increases
Read fast – RP decreases
WP RP

Fill Buffer to 50% (one
frame) with data
Write clock
Increments RP
Read clock
Decrements RP
Skip one frame
RP address= RP address-
one frame length bits
Difference > 2*FL-3
Initialize Read pointer
(RP) and write
pointers (WP)
Difference =
RP -WP
Repeat one frame
RP address= RP address+
one frame length bits
Difference < 3
3 < Difference < 2*FL--3
FSM for P/D
Buffer

1. ROBERT A. SCHOLTZ, FELLOW – IEEE, ‘Frame Synchronization Techniques’, IEEE
TRANSACTIONS ON COMMUNICATIONS, VOL. COM-28, NO. 8, AUGUST 1980.
2. DENIS T. R. MUNHOZ, JOSE ROBERTO B. DEMARCA, MEMBER, IEEE, AND DALTON
S. ARANTES, MEMBER, IEEE , ‘On Frame Synchronization of PCM Systems’., IEEE
TRANSACTIONS ON COMMUNICATIONS, VOL. COM-28, NO. 8, AUGUST 1980.
3. J. L. Massey, “Optimum frame synchronization.” IEEE Trans Commun., vol. COM-
20, pp. 115-1 19, Apr. 1972.
4. P. T. Nielsen, “Some optimum and suboptimum frame synchronizers for binary
data in Gaussian noise,” IEEE Trans. Commun., vol. COM-21, pp. 770-772, June 1973.
Literature on Frame Synchronization

 PCM, DPCM are all Waveform coding techniques –
Essentially Time domain Waveform analysis. No spectral analysis.
 Now Digital Speech Processing. However the context here is
multiplexing so we look briefly at this aspect of speech coding
Two types of Processed Speech coding
• Parametric Vocoders Channel and Formant (Frequency Domain
Modelling) (Voice is analyzed in spectral bands and transmitted)
• LPC – CELP Vocoders (Time Domain Modeling)
(Time domain filter model for vocal tract and pitch frequency analysis)

• Parametric Vocoders (Channel and Formant have 8 to 20 spectral
bands in spectral domain) (waveform coders used for each band)
• Speech Spectra shown here below

Frequency Domain modelling - Parametric Vocoders
 Channel Vocoders
 Formant Vocoders
Channel Vocoder based on sub bands

Waveform coders used for each sub-band

• Formant Vocoders have 4 to 19 spectral bands.
• Picks up a frame length of 20 msecs or so and analyses in spectral
domain.
•Two parts in a message (one for formant and other for amplitude)

LPC Vocoders – Time domain modelling.
Works off Speech samples over typical Frame length of 10 msecs or so

LPC codeword 80 bits – 260 bits
For 80 bits
6 bits pitch
5 bits amplifier gain
6 bits x 10 taps = 60 bits
1 bit voiced/ unvoiced
Remainder 8 bits error
Updated every 10 - 25 msecs
10msecs –> 80 bits works out to 8 Kbps

M1 - 1 M1 - 2 M1 - 3 M2 - 1 M3 - 1 M4 - 1
Signal Bandwidth in KHz Nyquist Rate (sps) Actual Rate (sps) Bits / sample
M1(t) 3.6 K 7.2 Ksps 7.2 Ksps 10
M2(t) 1.2 K 2.4 Ksps 2.4 Ksps 10
M3(t) 1.2 K 2.4 Ksps 2.4 Ksps 10
M4(t) 1.2 K 2.4 Ksps 2.4 Ksps 10
Total Rate (7.2 + 2.4 + 2.4 + 2.4) Ksamples/sec x 10 bits/sample = 144 K bits/sec
Frame time (FT) is (6 samples x 10 bits/sample) bits x (1 / Total Rate) = 0.4166666667 msecs/ Frame
To Demux add Mux OH. Frame time has to be kept same. Say add 8 bits Flag.
M1 - 1 M1 - 2 M1 - 3 M2 - 1 M3 - 1 M4 - 1 8 bits OH
So in the same ONE Frame time (FT) we have {(6 samples x 10 bits/ sample) + 8 bits} = 68 bits
New Line Rate is 68 bits/ Frame x (1/FT) = 163.2 Kbits/sec.
P and D Buffer depth ?
If one signal is say 3 KHz. Two ways to over come.
1. Allow oversampling of signal
2. Choose LCM

8. TDM Mux_Demux.pdf

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