Physical Layer 2

1
Physical Layer (2)
2
Goal

• Physical layer design goal send out bits as fast
  as possible with acceptable low error ratio
• Goal of this lecture
• Review some of the important concepts
• Modulation, demodulation, maximum likelihood
  detection
• Introduction to wireless communications, CDMA,
  OFDM, MIMO

3
Review

• What is bandwidth (how it is defined)? What it
  means to have high(low) bandwidth?
• What is noise?
• Shannons theorem?
• If a link has a bandwidth of 4KHz and the signal
  to noise power ratio is 15, what is the capacity
  of the channel?
• Why we have limited bandwidth?

4
Modulation

• Even in the simplest 10Mbs Ethernet case, the
  signals you send out is different from the 0-1
  waveform.
• Modulation is to convert the 0-1 waveform to the
  actual signal to be sent out.
• In most cases the signals are derived from sine
  waves.
• Given the 0-1 waveform, you do some tricks to the
  sine wave at some frequency f, and send it out
• This sine wave is called the carrier

5
Different modulation techniques

• Amplitude modulation
• Frequency modulation
• Phase modulation
• In digital communications, phase modulation is
  used
• Simplest case BPSK
• Given a 0-1 stream, regard it as a -1 and 1
  stream and multiply it with the sine wave. The -1
  and 1 stream is called the baseband signal (no
  exactly, but for our purpose it is)

6
Demodulation

• The problem is, given a (0,180) phase modulated
  signal on frequency f, how to determine whether
  the bit is 0 or 1?
• This is demodulation.
• Assume that you know the beginning of a binary
  symbol.

7
Demodulation

• Three steps
• You multiply the received signal with a sine wave
  on f, and pass it to a low-pass filter only
  allowing signals with frequency less than f to
  pass
• Do an integral to the output of the filter from 0
  to T where T is the symbol time.
• If the result is positive, it was 1 and if it was
  negative, it was 0.
• If no noise, things are simple!

8
Demodulation

• With noise, its all about guessing, because you
  dont know what the noise is when this symbol is
  sent as noise is random.
• You may know some statistics of the noise, based
  on which you make your best guess.
• For example, lets say -1 is -2.5 volts 1 is 2.5
  volts. Suppose you know that very rarely the
  noise exceeds 2.5 volts. If you received a 0.3
  volts, you would guess it to be -1 or 1? What is
  the chance that you got it right/wrong?

9
Maximum Likelihood Detection

• Detection given a received signal, determine
  which of the possible original signals was sent.
  There are finite number of possible original
  signals (2 for the binary case -1 or 1)
• Compute a likelihood value for every possible
  input, choose the one with largest likelihood
  maximum likelihood detection

10
Maximum Likelihood Detection

• There are two inputs, x1 and x2. Noise is n. What
  you receive is y.
• If I sent x1, you receive yx1 n. If I sent x2,
  you receive yx2n. You dont know what I sent
  and how large n is.
• You compute the likelihood of receiving y if I
  sent xi, Li (i1,2). If L1 gt L2, you say I sent
  x1. Else you say I sent x2.
• How to compute L1 and L2?

11
Maximum Likelihood Detection

• If n0 always, yx1 if I sent x1 and yx2 if I
  sent x2. Of course x1 ! x2. Will you make
  mistake in this case? What is the likelihood of
  yx2 if I sent x1?
• If n is not always zero, we assume n follows some
  probability distribution. If it is Gaussian, the
  channel is called AWGN.
• Given y, the likelihood of x1 being sent is the
  likelihood that ny-x1. Similarly, the likelihood
  of x2 being sent is the likelihood that ny-x2.
  (likelihood is derived from probability, but
  likelihood could be taking some values that
  probability cannot take depending on how you
  define likelihood)
• So what you are doing is to compare the
  likelihood of ny-x1 and ny-x2. So the detection
  rule is if p(ny-x1)/p(ny-x2) gt 1, output x1,
  else output x2.
• Thats all!
• Wait, what if you know that x1 is more likely to
  be sent than x2?

12
Question left in last lecture

• How do you demodulate 10Mbps Ethernet signal?

13
I,Q channels

• In modern communications, you have two carriers
  on the same frequency but their phases differ by
  90 degrees. So one is sine and the other is
  cosine. You can apply two symbol streams (the
  baseband signals) to them separately, and add
  the two together and send out.
• The receiver wont be confused because what he
  does is to multiply the received signal with two
  locally generated sine waves on the same
  frequency as the sender side, one sine and one
  cosine. Then he passes each of the two multiplied
  signals to a device that only allows signals on
  frequency no higher than B to pass (assuming the
  highest frequency of your signal is B). Why?

14
QAM

• With two carriers, you have two dimensions. So
  the signal will appear on a plane. 16-QAM,
  64-QAM, 256-QAM

15
Cellular Phone Networks

• User base station Telephone network
• FDMA Frequency division multiplexing
• How to make sure that you are using this band,
  not that band?
• TDMA Time division multiplexing
• CDMA Code division multiplexing

16
GSM Global System for Mobile Communications

• Second generation cell phone system (digital,
  first generation analog).
• GSM-900 and GSM-1800 are most widely used
• GSM-900 uses 890 - 915 MHz to send information
  from the Mobile Station to the Base Transceiver
  Station (uplink) and 935 - 960 MHz for the other
  direction (downlink).
• FDMA TDMA
• Each user transmitting on a frequency and
  receiving on another frequency.
• 124 pairs of 200 KHz channels. Each channel
  divided into time slots for 8 users.
• Each user is has a chance to transmit every 4.615
  ms. Each time he can send 114 data bits
  24.7kbps.

17
CDMA

• Described in IS-95.
• A good analogy in the book You have a group of
  people in a room. TDMA means they talk in turn.
  FDMA means that those who wants to talk sit in
  different corners and cant hear other pair. CDMA
  means each pair talks in a different language and
  other peoples voice is noise to them.

18
CDMA

• The whole bandwidth is used by every user.
  Meaning that they can send out symbols really
  fast.
• The trick is to make what A sent appear as 0 to
  B.
• Because we have a fast symbol rate, for each data
  bit, we send out, say, 8 bits, call the small
  bits chips.
• Given a bit, if 1, send out, say,
  -1,-1,-1,1,1,-1,1,1, and if 0, 1,1,1,-1,-1,1,-1,-1
  
• This is called the chip sequence.
• The key is that each station has a unique chip
  sequence (language), and different languages are
  orthogonal.

19
Wireless LAN Physical Layer

• 802.11b,g in the 2.4G band and 802.11a in the 5G
  band. People now consider 802.11 as the notion of
  MAC layer protocol, while a, b, g, or n, are
  about physical layer.
• 802.11b. 1, 2, 5.5, 11Mbps.
• 1Mbps BPSK modulation. 1 bit into 11 chips with
  Barker sequence 1 1 1 -1 -1 -1 1 -1 -1 1 -1.
  Why spread spectrum? Required by FCC but was
  later removed
• 2Mbps QPSK.
• 5.5M and 11M use some bits to select chip
  sequence and use two bits for QPSK
• 802.11a. Up to 54Mbps. OFDM.
• 802.11g. Up to 54Mbps. OFDM.

20
OFDM (Orthogonal Frequency Division Multiplexing)

• In wireless communications, in addition to the
  bandwidth limit and additive noise, you also have
  multipath fading!
• The faster your symbol rate is, the more badly
  you will be affected by multipath fading.
• In effect, OFDM is like DSL given a wideband
  channel, divide it into many sub channels. Each
  sub-channel can be modulated/demodulated
  independently. Because each sub-channel is of a
  much smaller bandwidth, multipath fading is much
  less severe.
• In implementation, use IFFT and FFT.

21
MIMO

• Used in 802.11n.
• t transmit antennas and r receive antennas. With
  the knowledge of channel matrix, by
  pre-processing the data, equivalent to mint,r
  channels.

22
Wired communication Optical Backbone

• SONET Synchronous Optical Network
• OC-1 51.84Mbps
• OC-3 351.84Mbps
• OC-9 951.84Mbps
• Used for backbone switching