1. Multiple Access Channels (MAC)
Objectives
Understand the the MAC concept
Become familiar with two common forms of MAC
Outline
Narrowband MAC (TDMA in GSM)
Spread-Spectrum MAC (DS-SS in CDMA)
DS-SS capacity and spectral properties
Lecture 8: MAC & Broadcast channels
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Multiple Access Wireless Channel (MAC)
Multiple transmitters (TXR) and one receiver (RCV)
A common transmission resource is shared by all
Frequency bandwidth and time domain
E.g., an uplink channel in a cellular network
Sharing done by multiplexing across 3 dimensions
Frequency Division (FD)
Time Division (TD)
Code Division (CD)
Required bandwidth (Hz) is proportional to source data rate
Narrowband: TXR bandwidth as required for coded voice (20-30 KHz)
Spread-spectrum: TXR bandwidth is much larger than its data rate
Lecture 8: MAC & Broadcast channels
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MAC Design Concerns
Synchronization and Alignment overheads
Synchronization in time and code between TXRs and RCV
Inter Symbol Interference (ISI)
Frequency boundary alignment
Adjacent channel interference
TXR signal propagation and fading
TXR signal power may “leak” to other TXR signals
TXR signal powers degrade differently (unequal received power)
TXR signal may follow multiple paths with different delays
TXR power and complexity more restrictive than RCV’s
MAC is a limiting factor in Cellular networks
Lecture 8: MAC & Broadcast channels
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Narrowband: TDMA Frame in GSM
Frame
Preamble: Addresses and sync data for TRXs and RCV
Trail: Sync RCVs between different frames
A user uses 1 slot to transmit and 1 to receive
A user may use other slots to measure signal strength from BTS
Users are assigned time slots within a frame
Speech frames are grouped into multi-frames and those into super-frames
They have their control fields too
Lecture 8: MAC & Broadcast channels
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Narrowband: TDMA Slot in GSM
control &
signaling
slot
Frame
Slot
200 KHz/frame and 25 KHz/time slot (burst) at Kbps
T: Tail bits at start/end to sync between TRX and RCV
GP: guard period to prevent TRX (call) overlap
TS: Training sequence used by the adaptive equalizer to analyze
channel parameters before decoding
S: Stealing bits to indicate voice or control
Lecture 8: MAC & Broadcast channels
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Guard Period (GP) Requirement
Must compensates for LOS propagation and multi-path delays
GP > R/c + t
R – cell radius
c - speed of light
t – multi-path delay spread (mainly in uplink – due antenna heights)
Equalizer Training Sequence Requirement
Used to eliminate ISI that occurs in narrowband TDMA
Matches the last N received signals against a known training sequence
Adapts the matching filter weights every step until convergence
The converging weights are used for the symbol decoder
N is determined to be immune against ISI and multi-path delay spread
Lecture 8: MAC & Broadcast channels
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Spread-Spectrum MAC
Spread-spectrum
Users share the bandwidth all time
Reuse-distance = 1
Spreading mechanisms
Direct sequence (DSSS)
Frequency hopping (FHSS)
DSSS done by coding user digital data) in
Wireless Systems
LAN: IEEE
2G: IS-95
3G: cdma2000, WCDM
Narrowband
Each user gets a frequency during all or part of the time
SIR is relatively high (~18 dB)
Cochannels must be far apart
Adjacent channel interference
Requires careful frequency and time slot planning
Reuse-distance > 1
Meaningful Inter Symbol Interference (ISI)
All above addressed better by Spread Spectrum
Lecture 8: MAC & Broadcast channels
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DSSS Mechanism
n(t)
narrowband
narrowband
Channel
Bandwidth W
source
data a
Linear
Modulation
(PSK,QAM)
x(t)
s(t)
Linear
Demodulator X
a(t) X
a(t)
Synchronized
Symbol period T
x(t)
Chip period
Tc=T/10
a(t)
s(t)
Lecture 8: MAC & Broadcast channels
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Spreading-Despreading PSD & Bandwidth
PSD (Power Spectral Density)
PSD
PSD
PSD
Lecture 8: MAC & Broadcast channels
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Narrowband Interference Spreading
interference
Multiply ONCE spreads the signal – Multiply TWICE recovers the signal
Lecture 8: MAC & Broadcast channels
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DSSS Spectral Properties - Summary
Original
Data Signal
Narrowband
Filter
Other
SS Users
Demodulator
Filtering
ISI
Modulated
Data
with Spreading
Interference
Receiver
Input
Lecture 8: MAC & Broadcast channels
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DSSS Properties
Multiplication ONCE spreads the signal
Multiplication TWICE followed by filtering recovers the signal
Orthogonal sequences & TRX-RCV sync is essential for perfect recovery
The bandwidth of signal s(t) is about (Symbol period)/(Chip period)
times that of signal x(t).
Spreading is done by a sequence code (“signature”)
In WCDMA:
minimum chip rate = 3.84 Mcps (~Mbps)
minimum bandwidth = 4.5 MHz
The spreading sequence has a crucial effect on the channel spectral
properties – Let’s see how
Lecture 8: MAC & Broadcast channels
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The data sequence can be represented by waveform in time t
is the symbol period,
is a unit flat signal
The direct sequence generator produces the spreading waveform
is the spreading sequence,
is the chip period and
is the chip amplitude shaping function.
The complex envelope of the DSSS signal is
Lecture 8: MAC & Broadcast channels
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Correlation Functions
Types of direct sequences depend on relative N, the length of sequence
(chips), G, the processing gain (chips/data bit):
long code: G << N, each data bit is spread by a subsequence
short code: G = N, each data bit is spread by a full period sequence
Consider the spreading waveforms
The auto-correlation function of is
The cross-correlation function is
If G=N, these are full period correlation; if G<N, they are partial period
correlations
Lecture 8: MAC & Broadcast channels
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Good codes have and for all t
removes ISI
removes interference between users
Hard to get these properties simultaneously
Lecture 8: MAC & Broadcast channels
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Demodulation at the Receiver
n(t)
- noise
narrowband
narrowband
Channel
Bandwidth W
source
data a
Linear
Modulation
(PSK,QAM)
x(t)
s(t)
Linear
Demodulator X
a(t) X
a(t)
Synchronized
b(t)
other
users X X
Details in subsequent slights ….
Lecture 8: MAC & Broadcast channels
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Spreading Sequences
Walsh-Hadamard Spreading Code
Also known as
Orthogonal / channelisation / Orthogonal variable spreading Factor
Used for spreading in 3G when sync is possible
In downlink – to separate data channels from the same BTS
In uplink – to separate data channels from the same mobile
PN Code
Also known as
Pseudorandom-Number / Gold / Scrambling code
Used to isolate a BTS or a Mobile in 3G
Used for a very large number of users or when sync can’t be kept
Lecture 8: MAC & Broadcast channels
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Lecture 8: MAC & Broadcast channels
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Generating Walsh-Hadamard Orthogonal Seq.
Binary Tree Representation
(can be implemented with n-stage feedback shift registers)
Lecture 8: MAC & Broadcast channels
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Example: Verifying Orthogonality
Code orthogonality at the receiver is hard to get
Mobiles cannot sync at chip rate
TRX-RCV sync is practically impossible
Multi-path delay spread distorts original orthogonality
Lecture 8: MAC & Broadcast channels
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ISI Rejection
Transmitted signal: s(t)=x(t) a(t)
Channel response: h(t)=d(t) + d(t-t)
Received signal: s(t) + s(t-t)
Received signal after de-spreading:
In the demodulator this signal is integrated over symbol time, so the second term becomes
For all ISI is rejected
Lecture 8: MAC & Broadcast channels
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22. MAC Interference Rejection
Received signal from K users (non fading channel)
Received signal after de-spreading
In the demodulator this signal is integrated over symbol time, so the second term becomes:
For all MAC interference is rejected
Lecture 8: MAC & Broadcast channels
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Semi-Orthogonal Sequences
With orthogonal code origin data can be fully recovered (up to noise):
Requires full chip and phase synchronization and
ideal channel (no signal fading nor distortion)
Semi-orthogonal codes
Code orthogonality at the RCV is hard to preserve – on one hand
Semi-orthogonal codes are faster to generate – on the other hand
A common semi-orthogonal code is the Pseudorandom Noise (PN)
PN sequence of length N >> G
with amplitude 1 for each user k and element n
Nearly equal number of 0’s and 1’s within any long subsequence
A run of length r chips with the same sign occurs with prob. 2-r
Low correlation between any two shifted versions
Generated by N stage-Feedback Shift Register (Rappaport Ch )
Lecture 8: MAC & Broadcast channels
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Intra-Cell SIR value with PN
Assume
Intra-cell interference
Equal received power at BTS
TRX-RCV of user i are in sync
No multi-path fading
Ideal rectangular pulse shape
AWGN noise with PSD /symbol
Received signal in RCV i from K intra-cell users (during symbol period)
Average received signal after de-spreading with the PN of user i
Due to “random” PNs and equal received power, I is an average of i.i.d r.v.’s, and therefore can be approximated by a Gaussian r.v.
(in a time-discrete vector form)
Lecture 8: MAC & Broadcast channels
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Users PNs are selected randomly – thus, can be regarded as r.v.’s
Assuming perfect power control (PC) that equalizes the received power
(8.1)
NOTE: Recall that we ignore
Inter-cell interference, actual symbol shape, non-perfect PC, multi-path fading, imperfect PN randomness, imperfect sync
Lecture 8: MAC & Broadcast channels
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Further assuming
Stationary and ergodic channels
Cell independency
Equal average received power from every uplink (intra & inter)
(8.2)
- Adjacent Interfering Cell Factor
- Voice Activity Factor
- Coefficient rising from non-rectangular pulse shape
Eq. (8.2) expresses the SIR of channel i as function of:
the number of chips per symbol, G
the number of users per cell, K
the topology of adjacent cells
recovered signal power at the receiver
added white noise spectral density
Lecture 8: MAC & Broadcast channels
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Eq. (8.2) doesn’t provide the channel capacity yet
The channel capacity is expressed by Shannon coding Theorem (and its extensions )
Bits/sec
(8.2)
- Received signal bandwidth (Hz)
- Average received SNR
- Symbol signal received power (watts)
- Gaussian noise spectral level (watts/Hz)
The Theorem and its extensions will be covered later on
Lecture 8: MAC & Broadcast channels
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DSSS MAC Spectral Properties - Summary
Channel introduces noise, ISI, Narrowband and MAC interference
Spreading has no effect on AWGN noise
ISI delayed by more than Tc is reduced by code auto-correlation
Narrowband interference is reduced by de-spreading at RCV
MAC interference is reduced by code cross-correlation
Frequency diversity – overcomes frequency selective impairments
Welsh-Hadamard code has low cross and auto correlation
reduces multi-path signals delay spread of more than one chip
Sync between TRX and RCV is essential
Orthogonality between spreading codes enhances MAC capacity
TRX power control to resolve ”near-far problem”
Macro-Diversity, Voice-Activity-Detection, Soft-handoff are integral parts
Lecture 8: MAC & Broadcast channels
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