Transcript Time Division Frames - Stanford University

EE360 – Lecture 5 Outline
• Announcements:
– Revised lecture 4 slides (minus typos) posted
– Paper summary deadlines: 4/27, 5/23
– Project deadlines: Abstract 5/11, Progress report 6/6
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•
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•
•
MAC Channels
Time Division and GSM
Direct Sequence Spread Spectrum
Frequency Hopping
Tradeoffs
• User Capacity
Multiple Access Channels
• Multiple users transmitting to a single receiver
• Signals have different path gains (near-far problem)
• Channel can be divided using TD, FD, or CD
Time Division Frames
Frame (Tf)
Information Message
Preamble
Slot 1
Header
Slot 2
Synch
Bits
Slot 3
Control,
Signaling
Guard Time
...
Info. Bits
(Training)
Slot N
CRC
Guard
Time
• In TDD half the slots are for upstream traffic and half for downstream traffic
• Generic structure: not all frames used in all systems, and order may vary
Frame Details
• Preamble contains address and sync information
used by base and mobile
• Guard times allow sync of receivers between
different frames
• Users are assigned a position in each frame (delay
of Tf between bursts)
• Superframes (frames of frames) may have
additional control frames
Slot Structure
• Header: guard (ramp) time for receiver synch. between slots
• Synch: Used to establish bit synch (also for equalizer
training)
• Control: Used for handshaking, control, and supervisory
messages
• Info. Bits: Coded or uncoded information bits, may include
pilot symbols/sequences for channel measurement and
equalizer training.
• Guard Time: Prevents overlap at base of slots arriving from
different terminals.
Requirements
• Equalizer requirements: adaptive equalizer must compensate for timevarying ISI.
– Minimum N=t/Ts symbols for training.
– For t=20msec and Rb=280 Kbps, N=6 minimum (GSM: N=26)
– If Tf~Tc, need to retrain every frame (GSM: Tf=4.615 ms,
Tc=1/fD=12.5ms for fD=80 Hz, retrains every frame).
• Guard time requirements: must compensate for LOS propagation delay (R/c
for R the cell radius) and delay spread t due to multipath (reverse link only).
– No delay spread: Tg>R/c=3.3 msec for R=1Km.
– Do not need guard time for LOS propagation delay if base station
synchronizes to received (instead of transmitted) signal.
– With delay spread t: Tg>R/c+t, but typically have a smaller guard time.
GSM Slots
Tail
3b
Data
57b
Flag
1b
Equal. Train
26b
Flag
1b
Data
57b
Tail
3b
Guard
8.25ms
• Multiframe has 26 frames (each frame is 4.615ms), with
24 for data and 2 for control. Each call in progress
assigned a control channel.
• Slot time is 577ms
• 26b equalizer training designed to handle delay spread up
to 20 msec. (equalizer design not part of spec.)
• Guard time less than maximum t.
• Flag bits distinguish voice from data
• Transmission rate approx. 270 Kb/s
Spread Spectrum MAC
• Basic Features
–
–
–
–
signal spread by a code
synch. between pairs of users
compensation for near-far problem (in MAC channel)
compression and channel coding
• Spreading Mechanisms
– direct sequence multiplication
– frequency hopping
Note: spreading is 2nd modulation (after bits encoded into digital
waveform, e.g. BPSK). DS spreading codes are inherently digital.
Direct Sequence
Linear
Modulation.
(PSK,QAM)
d(t)
X
Sci(t)
SS Modulator
s(t)
Channel
Synchronized
X
Linear
Demod.
Sci(t)
SS Demodulator
• Chip time Tc is N times the symbol time Ts.
• Bandwidth of s(t) is N+1 times that of d(t).
• Channel introduces noise, ISI, narrowband and multiple
access interference.
–
–
–
–
Spreading has no effect on AWGN noise
ISI delayed by more than Tc reduced by code autocorrelation
narrowband interference reduced by spreading gain.
MAC interference reduced by code cross correlation.
BPSK Example
d(t)
Tb
Tc=Tb/10
sci(t)
s(t)
Spectral Properties
Narrowband
Filter
Narrowband
Interference
Data Signal
with Spreading
Modulated
Data
8C32810.117-Cimini-7/98
ISI
Receiver
Input
Other
SS Users
Original
Data Signal
Other
SS Users
ISI
Demodulator
Filtering
Code Properties
Autocorrelation:
1
r (t ) 
Ts
Ts

0
sci (t ) sci (t  t )dt
Cross Correlation
1
r ij (t ) 
Ts
Ts

0
sci (t ) scj (t  t )dt
• Good codes have r(t)=d(t) and rij(t)=0 for all t.
– r(t)=d(t) removes ISI
– rij(t)=0 removes interference between users
– Hard to get these properties simultaneously.
ISI Rejection
•
•
•
•
Transmitted signal: s(t)=d(t)sci(t).
Channel:h(t)=d(t)+d(t-t).
Received signal: s(t)+s(t-t)
Received signal after despreading:
r (t ) sci (t )  d (t ) sci (t )  d (t  t ) sci (t  t ) sci (t )
2
 d (t )  d (t  t ) sci (t  t ) sci (t )
• In the demodulator this signal is integrated over a symbol
time, so the second term becomes d(t-t)r(t).
– For r(t)=d(t), all ISI is rejected.
MAC Interference Rejection
• Received signal from all users (no multipath):
M
M
j 1
j 1
r (t )   s j (t  t j )   d j (t  t j ) s cj (t  t j )
• Received signal after despreading
r (t )sci (t )  di (t )sci (t ) 
2
M
 d (t t
j 1, j i
j
j
)scj (t  t j )sci (t )
• In the demodulator this signal is integrated over a symbol
time, so the second term becomes
M
d
j 1, j i
j
(t  t j )rij (t j )
– For rij(t)=0, all MAC interference is rejected.
Walsh-Hadamard Codes
• For N chips/bit, can get N orthogonal codes
• Bandwidth expansion factor is roughly N.
• Roughly equivalent to TD or FD from a capacity
standpoint
• Multipath destroys code orthogonality.
• Used in IS-95 MAC
Semi-Orthogonal Codes
• Maximal length feedback shift register sequences have good
properties
– In a long sequence, equal # of 1s and 0s.
• No DC component
– A run of length r chips of the same sign will occur 2-rl times in l chips.
• Transitions at chip rate occur often.
– The autocorrelation is small except when t is approximately zero
• ISI rejection.
– The cross correlation between any two sequences is small (roughly
rij=G-1/2 , where G=Bss/Bs)
• Minimizes MAC interference rejection
Frequency Hopping
Nonlinear
Modulation.
(FSK,MSK)
d(t)
Sci(t)
FM
Mod
s(t)
VCO
FH Modulator
Channel
FM
Demod
VCO
Nonlinear
Demod.
Sci(t)
FH Demodulator
• Spreading codes used to generate a (slow or fast) “hopping”
carrier frequency for d(t).
• Channel BW determined by hopping range.
– Need not be continuous.
• Channel introduces ISI, narrowband, and MAC interference
–
–
–
–
Hopping has no effect on AWGN
No ISI if d(t) narrowband, but channel nulls affect certain hops.
Narrowband interference affects certain hops.
MAC users collide on some hops.
Spectral Properties
1
3
2
4
2
4
Di(f-fc)
1
Dj(f-fc)
3
Slow vs. Fast Hopping
• Fast Hopping - hop on every symbol
– NB interference, MAC interference, and channel nulls affect just one
symbol.
– Correct using coding
• Slow Hopping - hop after several symbols
– NB interference, MAC interference, and channel nulls affect many
symbols.
– Correct using coding and interleaving if # symbols is small.
– Slow hopping used in cellular to average interference from other cells
FH vs. DS
• Linear vs. Nonlinear
– DS is a linear modulation (spectrally efficient) while FH is nonlinear
• Wideband interference/jamming
– Raises noise spectral density, affects both techniques equally.
• Narrowband interference/jamming
– DS: interfering signal spread over spread BW, power reduced by spreading
gain in demodulator
– FH: interference affects certain hops, compensate by coding (fast hopping) or
coding and interleaving (slow hopping).
• Tone interference
– DS: tone is wideband, raises noise floor for duration of the tone. Compensate
by coding (tone duration=symbol time) or coding and interleaving (tone
duration>symbol time). Similar affect as NB interference in FH.
– FH: Tone affects certain hops. Compensate by coding or coding and
interleaving.
FH vs. DS
• ISI Rejection
– DS: ISI reduced by code autocorrelation.
– FH: ISI mostly eliminated.
• MAC interference
– DS: MAC interference reduced by cross correlation of spreading codes.
Each additional user raises noise floor.
• Overall SNR reduced
– FH: MAC interference affects certain hops. Each additional user causes
more hops to be affected.
• More bits likely to be received in error.
• Overlay systems: high-power NB interferers
–
–
–
–
Similar impact as with regular interferers
DS: Noise floor raised significantly
FH: Hops colliding with interferers are lost
Can notch out interfering signals
Evolution of a Scientist turned
Entrepreneur
• “Spread spectrum communications - myths and realities,”
A.J. Viterbi, IEEE Comm. Magazine, May ‘79 (Linkabit 5
years old - A TDMA company).
• “When not to spread spectrum - a sequel,” A.J. Viterbi, IEEE
Comm. Magazine, April 1985 (Linkabit sold to M/A-Com in
1982)
• “Wireless digital communications: a view based on three
lessons learned,” A.J. Viterbi, IEEE Comm. Magazine,
Sept.’91. (Qualcomm CDMA adopted as standard).
Myths and Realities
• Myth 1: Redundancy in error correction codes spreads signal bandwidth
and thereby reduces processing gain
– Reality: Effective processing gain increased by coding by considering
symbol rate and energy
– Reality today: coded modulation more efficient even without symbol
argument. But tradeoffs between coding and spreading an open issue.
• Myth 2: Error correction codes only good against uniform interference
– Reality: Not true when coding combined with spread spectrum, since SS
averages interference.
– Reality today: Unchanged.
• Myth 3: Interleaving destroys memory which can be used to correct
errors, hence interleaving is bad
– Reality: Memory preserved by soft-decisions even with an interleaver
– Reality today: Unchanged, but interleavers may require excessive delays for
some applications.
• Myth 4: Direct sequence twice as efficient as frequency hopping
– Myth=Reality. Argument is that DS is coherent and that accounts for 3dB
difference. Analysis shows that higher level signaling alphabets does not
help FH performance with partial band jammer.
– Reality today: A true efficiency tradeoff of FH versus DS has not been
done under more general assumptions. FH typically used to average
interference. Appealing when continuous spreading BW not available.
When not to Spread Spectrum - A
Sequel
• Conclusion 1: When power is limited, don’t contribute to the noise by
having users jam one another.
• Conclusion 2: Network control is a small price to pay for the efficiency
afforded by TDMA or FDMA
– Power control is a big control requirement.
• Conclusion 3: Interference from adjacent cells affects the efficiency of
TDMA or FDMA less severely than in CDMA.
• Conclusion 4: Treating bandwidth as an inexpensive commodity and
processing as an expensive commodity is bucking current technology
trends.
• Caveat: Application was small earth terminals for commercial satellits.
Three Lessons Learned
• Never discard information prematurely
• Compression can be separated from channel
transmission with no loss of optimality
• Gaussian noise is worst case. Optimal signal in
presence of Gaussian noise has Gaussian
distribution. So self-interference should be
designed as Gaussian.
Realities
• Never discard information prematurely
– Use soft-decisions and sequence detectors, if
complexity okay.
• Compression can be separated from channel
transmission
– For time-invariant single-user channels only.
• Self-interference should be designed as Gaussian
– Based on Viterbi’s argument, this represents a saddle
(not optimal) point.
– If the self-interference is not treated as interference,
then Gaussian signaling is suboptimal (by Shannon
theory).
MAC Capacity
• User Capacity
– How many users can be accommodated in the channel given
performance specs.
- Assumes identical users and white noise model for interference
• Shannon Capacity Region
– Upper bound on rate vector that all users can achieve
simultaneously
– No complexity or delay constraints.
– Optimal signaling and reception (unless constraints are added)
– Asymptotically small error probabilty.
– Signals from other users not treated as interference
User Capacity
• Applicable to CDMA, since TDMA and FDMA have fixed
capacity (# of channels).
• S/(N+I(M)) determined based on the total number of users M
and the system model.
– Can be deterministic or random (fading).
– Interference I(M) modeled as AWGN
• Based on the modulation, coding, channel model, etc., we
find the probability of bit error Pe=f[S/(N+I(M))]
• For a given performance Pe we invert the above expression
to get the maximum possible M.
– Often set N=0 to simplify inversion, implies an
interference-limited system.
Probability of Error
• Coherent BPSK: for m users, and a spreading gain G:
Pe

 
 Q  
 
 


N

m
0 

2E
3G 
b

1 / 2 





Note that Pe is concave in m
• m is typically random. For L total users each with probability p
of active transmission and voice activity factor a:
L
k
Pe  
k 0 m 0

1 / 2 


  N
 L 
k

m
k
L

k
0
 a m (1a )k  m



Q  
 
p
(
1

p
)

 
  2E
 k 
3G 
m
  b
 



Pe Approximation
• By concavity of Pe and Jensen’s inequality:



1
/
2




N


~
M
,
Pe  Pe  Q   0  

 2 E 3G 
 

b



M  aLp.
Use RHS as approximation for Pe
``Spread spectrum for mobile communications”, Pickholtz, Milstein, Schilling
Effective Energy/Symbol
 Es 
 N0

2r



M (1  K )a 
N 

3N
 0  eff
 Es

– M is average number of active users.
– r is the code rate
– K is the out-of-cell interference ratio (equals zero for a purely
MAC channel)
– a is the voice activity factor
– N is the number of chips per symbol
– Factor of 2/3 assumes rectangular pulses, will decrease for other
shapes.
– Assumes no ISI, flat-fading, or diversity gain.
Required Es/N0
• Target Pe
 E  
target
Pe  s    Pe
 N o  reqd 
• Invert target Pe to get required Es/N0

 Es 
target


 Pe
 N o  reqd

1

y
target
• Example: DPSK Pe  .5e   reqd   ln Pe

Often cannot get reqd in closed form: Must use
numerical techniques or obtain from BER curve.
User Capacity
• Total number of users the MAC channel can support:
1
N 0  3 G
3 G   E s 
1
M  1


 
2 (1  K )a   N 0  reqd E s  2 (1  K )a  E s 


N 
 0  reqd
• A rougher approximation
G
M  1
 Es 


 N 0  reqd
Channel coding and interference mitigation increase user capacity
SS vs. Narrowband
M  1  G /[ Es / N0 ]reqd
• BPSK at a BER of 10-4 requires Es/N07.4dB
• Consider a two-user (M=2) DSSS system:
G
S/I (dB)
2
4
5
6
8
3
6
7
7.8
9
7.4
Two-user DSSS system requires spreading gain of 5-6 to get
desired BER, TD system could fit 5-6 users in this bandwidth
Argument for DSSS based on frequency reuse and soft capacity