Physical Layer (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

Review What is bandwidth (how it is defined)? What it means to have high(low) bandwidth? What is noise? Shannon’s 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?

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

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)

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.

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!

Demodulation With noise, it’s all about guessing, because you don’t 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, let’s 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?

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

Maximum Likelihood Detection There are two inputs, x1 and x2. Noise is n. What you receive is y. If I sent x1, you receive y=x1 + n. If I sent x2, you receive y=x2+n. You don’t know what I sent and how large n is. You compute the likelihood of receiving y if I sent xi, Li (i=1,2). If L1 > L2, you say I sent x1. Else you say I sent x2. How to compute L1 and L2?

Maximum Likelihood Detection If n=0 always, y=x1 if I sent x1 and y=x2 if I sent x2. Of course x1 != x2. Will you make mistake in this case? What is the likelihood of y=x2 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 n=y-x1. Similarly, the likelihood of x2 being sent is the likelihood that n=y- 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 n=y-x1 and n=y-x2. So the detection rule is if p(n=y-x1)/p(n=y-x2) > 1, output x1, else output x2. That’s all! Wait, what if you know that x1 is more likely to be sent than x2?

Question left in last lecture How do you demodulate 10Mbps Ethernet signal?

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 won’t 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?

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

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

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 MHz to send information from the Mobile Station to the Base Transceiver Station (uplink) and MHz for the other direction (downlink). Mobile StationBase Transceiver Station 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 ms. Each time he can send 114 data bits – 24.7kbps.

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 can’t hear other pair. CDMA means each pair talks in a different language and other people’s voice is noise to them.

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.

Wireless LAN Physical Layer b,g in the 2.4G band and a in the 5G band. People now consider as the notion of MAC layer protocol, while a, b, g, or n, are about physical layer b. 1, 2, 5.5, 11Mbps. – 1Mbps: BPSK modulation. 1 bit into 11 chips with Barker sequence −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 a. Up to 54Mbps. OFDM g. Up to 54Mbps. OFDM.

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.

MIMO Used in n. t transmit antennas and r receive antennas. With the knowledge of channel matrix, by pre- processing the data, equivalent to min{t,r} channels.

Wired communication – Optical Backbone SONET – Synchronous Optical Network – OC-1: 51.84Mbps – OC-3: 3*51.84Mbps – OC-9: 9*51.84Mbps – … Used for backbone switching