1. CS434/534: Topics in Networked (Networking) Systems Wireless Foundation: OFDM Implementation Wireless MAC Layer Design Yang (Richard) Yang Computer Science Department Yale University 208A Watson

2. Outline Recap Wireless background Wireless MAC design Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading
design for ISI
what is ISI
band limited ISI
symbol wave shaping
multi-path ISI
equalization (Viterbi)
OFDM
Wireless MAC design

3. Admin.
PS2 on wireless posted
Please see potential projects

4. Recap: Inter-Symbol Interference (ISI)
ISI happens when the signaling for one symbol leaks into that of another symbol
Why does ISI happen?
Band limit produced ISI
Multipath produced ISI 1 2

5. Recap: Band-Limited ISI
a g(t)
A design of p(t) has no ISI iff folded spectrum is flat

6. Recap: Multipath ISI
The problem: given received y[m], m = 1, …, L+2, where L is frame size and assume 3 delay taps (it is easy to generalize to D taps): y[1] = x[1] h0 + w[1] y[2] = x[2]h0 + x[1] h1 + w[2] y[3] = x[3]h0 + x[2]h1 + x[3] h2 + w[3] y[4] = x[4]h0 + x[3]h1 + x[2] h2 + w[4] y[5] = x[5]h0 + x[4]h1 + x[3] h2 + w[5] … y[L] = x[L]h0 + x[L-1]h1 + x[L-2]h2 + w[L] y[L+1] = x[L]h1 + x[L-1]h2 + w[L+1] y[L+2] = x[L]h2 + w[L+2]
determine x[1], x[2], … x[L]

7. observe y[1]
observe y[2]
observe y[3]
observe y[4]
s[0]
s[1]
s[2]
s[3]
s[4]
x[1]=0
x[2]=0
x[3]=0 00
000
000
x[3]=1
001
001
x[1]=1
x[2]=1
x[3]=0 01
010
010
x[3]=1
011
011
x[2]=0
x[3]=0 1 10
100
100
x[3]=1
x[2]=1
101
101
x[3]=0 11
110
110
x[3]=1
111
111
prob. of observing y[1]: w[1] = y[1]-x[1]h0
prob. of observing y[2]: w[2] = y[2]-x[1]h0-x[2]h1
prob. of observing y[4]: w[4] = y[4]-x[4]h0-x[3]h1-x[2]h2

8. Recap: Multiple Carrier Modulation and OFDMj i
Despite wave shaping, there can be leak from one subcarrier to another subcarrier
if integer number of cycles in [0, T]

9. OFDM Modulation

10. OFDM Implementation
Take N symbols and place one symbol on each subcarrier (freq.)
Q: complexity of the implementation strategy?
Freq0
FreqN-1
Ts: per sample time

11. OFDM: Implementation Issue
Hardware implementation can be expensive if we use one oscillator for each subcarrier
Software implementation requires N multiplications per time output => N2 multi. per N outputs
Freq0
FreqN-1

12. OFDM: Key Idea 2 Assume N outputs per symbol time T, fsc=1/T
Consider data as coefficients in the frequency domain, use inverse Fourier transform to generate time-domain sequence

13. OFDM Implementation: FFT
channel

14. OFDM Implementation
Parallel data streams are used as inputs to an IFFT
IFFT does multiplexing and modulation in one step !

15. Guard Interval: Removing ISI
Orthogonal subcarriers remove inter-carrier interference
Slow symbol rate reduces inter-symbol interference, but may still have ISI
Basic idea of GI: skip the first part “damaged” signal 1 2 1 2
More details: Chap Gast

16. OFDM Guard Interval

17. OFDM Implementation

18. OFDM in 802.11a: Channels+Subcarriers
Symbol time T = 1/312.5KHz = 3.2us
Each physical channel is 20 MHz
Each channel is divided into subcarriers (48 data, 4 pilot (requirement on subcarrier freq?)
5150
[MHz]
5180
5350
5200 36 44
center frequency =
*channel number [MHz]
channel# 40 48 52 56 60 64
149
153
157
161
5220
5240
5260
5280
5300
5320
5725
5745
5825
5765
5785
5805

19. OFDM in 802.11a: FFT + GI 64 samples FFT + 16 GI
OFDM in a: FFT + GI
64 samples FFT + 16 GI
Office: delay spread ns (up to 200 ns)

20. Other Multipath Techniques
There are other techniques to handle multipath such as Rake Receiver
See backup slides for some details

21. Summary of Wireless PHY

22. Wireless PHY Wireless PHY

23. Physical Communication in Context
data
application
transport
network
link
physical
network
link
physical
application
transport
network
link
physical
data
application
transport
network
link
physical
application
transport
network
link
physical
PHY considers only a sender sends a seq. of bits to a receiver

24. Outline Recap Wireless background Wireless MAC design Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design

25. Link Layer Services Framing
separate bits into frames; each frame has header, trailer and error detection/correction
Multiplexing/demultiplexing
use frame headers to identify src, dest
Media access control
Reliable delivery between adjacent nodes
seldom used on low bit error link (fiber, some twisted pair)
common for wireless links: high error rates

26. Wireless Access Problem
Single shared broadcast channel
thus, if two or more simultaneous transmissions by nodes, due to interference, only one node can send successfully at a time

27. Multiple Access Control (MAC) Protocol
Protocol that determines how nodes share channel, i.e., determines when nodes can transmit
MAC is hard because communication about channel sharing must use channel itself !
We start with the simplest scenario (e.g., or cellular up links) in this class:
a single receiver (the Access Point)

28. Properties of Ideal MAC Protocol
Efficient
Fair/rate allocation
Simple

29. MAC Protocols: a Taxonomy
Goals
efficient, fair, simple
Three broad classes:
channel partitioning
divide channel into smaller “pieces” (time slot, frequency, code)
non-partitioning
random access
allow collisions
“taking-turns”
a token coordinates shared access to avoid collisions

30. Outline Recap Wireless background Wireless MAC design Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design
wireless access problem and taxonomy
resource partitioning MAC

31. Example Partitioning: FDMA
FDMA: frequency division multiple access
Channel divided into frequency bands
A transmission uses a frequency band
frequency bands
time 5 1 4 3 2 6

32. Example Partitioning: TDMA
TDMA: time division multiple access
Time divides into frames; frame divides into slots
A transmission uses a slot in a frame

33. Recall: GSM
A GSM operator uses TDMA and FDMA to divide its allocated frequency
divide allocated spectrum into different physical channels; each physical channel has a frequency band of 200 kHz
partition the time of each physical channel into frames; each frame has a duration of ms
divides each frame into 8 time slots (also called a burst)
each slot is a logical channel
user data is transmitted through a logical channel

34. Example Partitioning: CDMA
CDMA (Code Division Multiple Access)
Unique “code” assigned to each user; i.e., code set partitioning
All transmissions share the same frequency and time; each transmission uses DSSS, and has its own “chipping” sequence (i.e., code) to encode data
e.g. code =
Examples: Sprint and Verizon, WCDMA

35. DSSS Revisited tb: bit period tc: chip period tb user data d(t) 1 -1 X
code c(t) -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 =
resulting
signal -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1
tb: bit period
tc: chip period

36. Illustration: CDMA/DSSS Using BPSK
Assume BPSK modulation using carrier frequency f :
yi(t) = A xi(t)ci(t) sin(2 ft)
A: amplitude of signal
f: carrier frequency
xi(t): data of user i in [+1, -1]
ci(t): code of i (a chipping sequence in [+1, -1])
Suppose only i transmits
y(t) = yi(t)
Decode at receiver i
incoming signal multiplied by ci(t) sin(2 ft)
since, ci(t) ci(t) = 1, yi(t)ci(t) sin(2 ft) = A xi(t) sin2(2ft)

37. Illustration: Multiple User CDMA
Assume M users simultaneously transmit: y(t) = y1(t) + y2(t) … + yM(t)
At receiver i, incoming signal y(t) multiplied by ci(t) sin(2 ft)
consider the effect of j’s transmission
yj(t)ci(t) sin(2 ft) = A cj(t)ci(t)xj(t) sin2(2 fct)
Condition for signal from j on effect on i?

38. CDMA: Deal with Multiple-User Interference
Two codes Ci and Cj are orthogonal, if
, where we use “.” to denote inner product, e.g.
If codes are orthogonal, multiple users can “coexist” and transmit simultaneously with minimal interference
C1:
C2:
C1 . C2 = (-1) (-1) (-1)+(-1)=0
Analogy: Speak in different languages!

39. Capacity of CDMA B
In realistic setup, cancellation of others’ transmission is incomplete
Assume the received power at base station from all nodes is the same P (how?)
The power of the transmission with known code is increased to N P, where N is chipping expansion factor
The others remain on the order of P
Assume a total of M users
Then
For IS-95 CDMA, N = 1.25M/4800 = 260

40. Generating Orthogonal Codes
The most commonly used orthogonal codes in current CDMA implementation are the Walsh Codes

41. Walsh Codes
1,1,1,1,1,1,1,1
1,1,1,1
...
1,1,1,1,-1,-1,-1,-1
1,1
1,1,-1,-1,1,1,-1,-1
...
1,1,-1,-1
X,X
1,1,-1,-1,-1,-1,1,1 1 X
1,-1,1,-1,1,-1,1,-1
X,-X
...
1,-1,1,-1
1,-1,1,-1,-1,1,-1,1
1,-1 n 2n
1,-1,-1,1,1,-1,-1,1
...
1,-1,-1,1
1,-1,-1,1,-1,1,1,-1 1 2 4 8

42. Orthogonal Variable Spreading Factor (OSVF)
Variable codes: Different users use different lengths spreading codes
Orthogonal: diff. users’ codes are orthogonal
1,1,1,1,1,1,1,1
1,1,1,1
...
1,1,1,1,-1,-1,-1,-1
1,1
1,1,-1,-1,1,1,-1,-1
...
1,1,-1,-1
X,X
1,1,-1,-1,-1,-1,1,1 1 X
1,-1,1,-1,1,-1,1,-1
X,-X
...
No parent-child on the code tree
1,-1,1,-1
1,-1,1,-1,-1,1,-1,1
1,-1
SF=n
SF=2n
1,-1,-1,1,1,-1,-1,1
...
1,-1,-1,1
1,-1,-1,1,-1,1,1,-1
SF=1
SF=2
SF=4
SF=8
If user 1 is given code [1,1], what orthogonal codes can we give to other users?

43. WCDMA Orthognal Variable Spreading Factor (OSVF)
Flexible code (spreading factor) allocation
up link SF: 4 – 256
down link SF:
WCDMA downlink
No parent-child on the code tree

44. Summary
SDMA, TDMA, FDMA and CDMA are basic media partitioning techniques
divide media into smaller “pieces” (space, time slots, frequencies, codes) for multiple transmissions to share
A remaining question is: how does a network allocate space/time/freq/code?

45. Outline Recap Wireless background Wireless MAC design Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design
wireless access problem and taxonomy
resource partitioning MAC
media access protocols

46. GSM Logical Channels and Request
call setup from an MS
Control channels
Broadcast control channel (BCCH)
from base station, announces cell identifier, synchronization
Common control channels (CCCH)
paging channel (PCH): base transceiver station (BTS) pages a mobile host (MS)
random access channel (RACH): MSs for initial access, slotted Aloha
access grant channel (AGCH): BTS informs an MS its allocation
Dedicated control channels
standalone dedicated control channel (SDCCH): signaling and short message between MS and an MS
Traffic channels (TCH) MS
BTS
RACH (request signaling channel)
AGCH (assign signaling channel)
SDCCH (request call setup)
SDCCH message exchange
SDCCH (assign TCH)
Communication

47. Slotted Aloha [Norm Abramson]
Time is divided into equal size slots (= pkt trans. time)
Node with new arriving pkt: transmit at beginning of next slot
If collision: retransmit pkt in future slots with probability p, until successful. A B
Success (S), Collision (C), Empty (E) slots

48. Slotted Aloha Efficiency
Q: What is the fraction of successful slots?
suppose n stations have packets to send
suppose each transmits in a slot with probability p
- prob. of succ. by a specific node: p (1-p)(n-1)
- prob. of succ. by any one of the N nodes
S(p) = n * Prob (only one transmits)
= n p (1-p)(n-1)

49. Goodput vs. Offered Load Curve
Slotted Aloha
S = throughput = “goodput”
(success rate)
0.5
1.0
1.5
2.0
Define G = offered load = np
when G (=p*n) < 1, as p (or n) increases
probability of empty slots reduces
probability of collision is still low, thus goodput increases
when G (=p*n) > 1, as p (or n) increases,
probability of empty slots does not reduce much, but
probability of collision increases, thus goodput decreases
goodput is optimal when G (=p*n) = 1

50. Maximum Efficiency vs. n
At best: channel
use for useful
transmissions 37%
of time!

51. Dynamics of (Slotted) Aloha
In reality, the number of stations backlogged is changing
we need to study the dynamics when using a fixed transmission probability p
Assume we have a total of m stations (the machines on a LAN):
n of them are currently backlogged, each tries with a (fixed) probability p
the remaining m-n stations are not backlogged. They may start to generate packets with a probability pa, where pa is much smaller than p

52. each transmits with prob. p
Model
n backlogged
each transmits with prob. p
m-n: unbacklogged
each transmits with prob. pa

53. Dynamics of Aloha: Effects of Fixed Probability
- assume a total of
m stations
pa << p
success rate is the departure rate, the rate the backlog is reducing
desirable stable point
successful transmission rate at offered load np + (m-n)pa
dep.
and
arrival
rate of
backlogged
stations
new arrival rate: (m-n) pa
undesirable stable point m
n: number of backlogged
stations
offered load = 1
Lesson: if we fix p, but n varies, we may have an undesirable stable point

54. Summary of Problems of Slotted Aloha
Advantages
Simple, decentralized random access protocol
Issues
Low efficiency
Only ~37% at optimal transmission rate
Even lower efficiency at non-optimal (fixed p)
No rate allocation/fairness

55. Outline Recap Wireless background Wireless MAC design Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design
wireless access problem and taxonomy
wireless resource partitioning dimensions
media access protocols
ALOHA protocol
The Ethernet protocol

56. Ethernet Fix for Efficiency
Introduce collision detection: instead of wasting the whole frame transmission time (a slot), we waste only the time needed to detect collision.
Introduce adaptive probability: reduce probability of trans. as # of collisions increases
If more collisions => p is high => should reduce p P
P: packet size, C: contention window C

57. Q: Does Ethernet alg work well in wireless?
Ethernet Fix: Carrier-Sense Multiple Access /Collision Detection/Exponential Backoff
Carrier sense
The Ethernet algorithm
get a frame from upper layer;
K := 0; n := 0; // K: control wait time; n: no. of collisions
repeat:
wait for K * 512 bit-time;
while (network busy) wait;
wait for 96 bit-time after detecting no signal;
transmit and detect collision;
if detect collision
stop and transmit a 48-bit jam signal;
n ++;
m:= min(n, 10), where n is the number of collisions
choose K randomly from {0, 1, 2, …, 2m-1}.
if n < 16 goto repeat
else give up
else
declare success
Detect
Collision
Adapt
Probability
Q: Does Ethernet alg work well in wireless?

58. Rake Receiver

59. Multipath Diversity: Rake Receiver
Instead of considering delay spread as an issue, use multipath signals to recover the original signal
Used in IS-95 CDMA, 3G CDMA, and
Invented by Price and Green in 1958
R. Price and P. E. Green, "A communication technique for multipath channels," Proc. of the IRE, pp , 1958

60. Multipath Diversity: Rake Receiver
LOS pulse
multipath
pulses
Use several "sub-receivers" each delayed slightly to tune in to the individual multipath components
Each component is decoded independently, but at a later stage combined
this could very well result in higher SNR in a multipath environment than in a "clean" environment

61. Rake Receiver Blocks
Correlator
Combiner
Finger 1
Finger 2
Finger 3

62. Rake Receiver: Matched Filter
Impulse response measurement
Tracks and monitors peaks with a measurement rate depending on speeds of mobile station and on propagation environment
Allocate fingers: largest peaks to RAKE fingers

63. Rake Receiver: Combiner
The weighting coefficients are based on the power or the SNR from each correlator output
If the power or SNR is small out of a particular finger, it will be assigned a smaller weight:

64. Comparison [PAH95]
MCM is OFDM

65. Backup Slides: Error Corrections Codes

66. Reed-Solomon Codes
Very commonly used, send n symbols for k data symbols
e.g., n = 255, k = 223
We will discuss the original version (1960)
modern versions are slightly different; they use generator polynomial, but the idea is essentially the same
If the data we want to send is (x0, x1,…, xk-1), where xi are data symbols, define polynomial P(t) = x0 + x1t + x2t + …xk-1tk-1
Assume  is a generator of the symbol field (i.e., i not equal to j if i not equal to j)
Then for the data sequence, send
P(0), P(), P(2), P(n-1) to receiver

67. since any k equations are independent, they have a unique solution
Reed-Solomon Codes
Receive the message P(0), P(), P(2), P(n-1)
If no error, can recover data from any k equations:
since any k equations are independent, they have a unique solution

68. Reed-Solomon Codes: Handling Errors
But, what if s errors occur during transmission?
Keep a counter (vote) for each solution
Enumerate all combinations of k equations, for each combination, solve it, and increase the counter of the solution
Identify the solution which gets the largest # of “votes”

69. Reed-Solomon Codes
The transmitted data is the correct solution for n-s equations, and thus gets
votes (i.e., combinations of k equations)
An incorrect solution can satisfy at most k-1+s equations, and the # of votes it can get is at most:

70. Reed-Solomon Codes If
or (n-s > k – 1 + s) or (n-k > 2s – 1) or (n-k  s), it can correct any s errors

71. Reed-Solomon Codes
The voting-based decoding algorithm proposed in 1960 is inefficient
Berlekamp introduced first truly efficient algorithm for both binary and nonbinary codes. Complexity increases linearly with number of errors
Sugiyama, et al. Showed that Euclid’s algorithm can be used to decode R-S codes
Below is a typical current decoder