Comp [34]49 Week 3, LT 412

	* bandwidth note
	* Antenna losses
	* noise
	* multipath
	* Ch 6: digital modulation of an analog carrier
	
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Whatever encryption you can install to ensure authentication and message integrity,
you can NOT ensure wireless network availability. It is trivial to "jam"
a wireless zone by injecting collisions.

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Bandwidth note:

Another way to explain why an information-carrying signal needs bandwidth:
1. All signals are a combination of sine waves at different frequencies.
2. If there is only one frequency, your signal is a perfect sine wave,
   which cannot carry any data.
3. Therefore, if you do carry data, you have to have a RANGE of frequencies.


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Look at 
	ifconfig
	iwconfig
	iwlist <interface> scan
	
	Connection means to set the ESSID or AP. 
	ESSID: allow host to connect to AP with best signal.
	
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Antenna gain is generally a measure of non-isotropicness.

Antenna losses, continued

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Antenna calculations

Pt = transmitted power
Pr = received power
all antennas are perfect isotropic
d = distance away

	Pr/Pt = L^2 / (4pi*d)^2		(done week 2; inverted from book)
or
	Pr/Pt = (L/d)^2 / (4pi)^2 = 1/(4pi*D)^2, 
where D =d/L is distance in wavelengths

Consequence: (week 2)

	Loss is inverse-square
	Loss is much faster (by a constant) for higher wavelengths
	
Ratio applies when d is big enough; when 4pi*d = L (d = L/4*pi)
then formula says no loss. This is too close to be meaningful, though.

Decibel loss example:
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Loss of 2.4 GHz (L=12.5 cm) for 
(actually for D=7.96 & multiples; this makes 4piD = 100)
	d	  D	Pr/Pt		dB
	 1 m	  8	1/10,0000	-40
	 2 m	 16			-46
	 5 m	 40			-54
	10 m	 80	1/10^6		-60
	20 m	160			-66
	50 m	400			-74
	100m	800	1/10^8		-80
	

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At first glance, the formula
	loss ratio Pr/Pt = const * L^2 / d^2
makes it look like the loss ratio gets smaller as L gets smaller;
ie higher frequencies are less efficient. But this is only because
the antenna itself is getting smaller.

When we take into account receiver/transmitter antenna gains, Gr & Gt,
we get

	Pr/Pt = Gr*Gt*L^2 / (4pi*d)^2 

This works out to the following, where Ar and At are the effective areas:

	Pr/Pt = Ar*At / (L^2 d^2)

For the same effective areas (which means keeping antenna size in rough
proporition to wavelength), doubling the wavelength (halving the freq)
now means a fourfold LOSS in power ratio. Higher frequency is better!

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Absorbtion: 

Water: peak absorbtion at 22 GHz; not significant below 15GHz
Oxygen: peak at 60 GHz; not significant below 30 GHz

Rain fade: scattering due to rain or fog *droplets*
This is often very significant.

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Noise:

THERMAL NOISE

Thermal noise is spread throughout the spectrum. 
We measure thermal noise in watts per Hz of bandwidth.

	N0 watts/Hz = kT

T = temp in Kelvins, K
k = Boltzmann's constant: 1.38 E-23 Joules/K

Particularly an issue for satellites.


INTERMODULATION NOISE

comes when two signals mix in a NONLINEAR fashion.

	linear: sin(2pi*f1*t) + sin(2pi*f2*t)

Here we get exact separation. But if there are nonlinear parts, 
we get noise, especially at frequencies f1+f2 and f1-f2.

Nonlinear mixing is most common in amplifiers/repeaters.


CROSSTALK:

when wires are close. Signal interference is universal in w-fi ISM band,
though the term "crosstalk" is not always used.


IMPULSE NOISE

The microwave

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Eb/N0: Energy/bit divided by noise/Hz

Eb = power rate in watts * time for one bit
units: joules

Higher power => faster transmission rate, but Eb is independent of that!

In general, the bit error rate (BER) decreases with increasing Eb.
In fact, BER decreases with increasing Eb/N0 (increasing Eb, or decreasing N0)

Note Fig 5.9 has no units, and no description of what encoding technique
is used.

Another issue is distance. In the usual Eb/N0 formulation,
increasing distance doesn't change the radiated power,
but it greatly decreases the *received* Eb energy.
Noise typically is fixed.

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Multipath propagation: section 5.4

Fig 5.11: reflection, scattering, diffraction around a corner.

Fast and Slow fading

Fast fading: on the order of 1/2 L.

Slow fading: due to multipath propagation, generally.

Figure 5.12 on what multipath propagation does to the received signal pulses;
this is "intersymbol interference".

Figure 5.13: fast and slow fading.

Slow fading can also be FLAT or SELECTIVE, referring to the frequency spectrum.

Three fading models:

1. AWGN: simple noise, not really fading.

2. Rayleigh: no distinct dominant path (eg Line of Sight, or LOS).
Difficult to deal with.

3. Rician, or Rice, fading

	K = dominant-path power / scattered-path power

K = 0: Rayleigh case
K = infinity: AWGN case

Fig 5.14: Eb/N0 curves for fading: AWGN, Rician (K=4,16), Rayleigh

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How to cope

1. Forward Error Correction. We will get to these later. 
Simple example: 2-D parity

note that the ratio of FEC bits / data bits here is << 1.
Often it is ~2-3!

2. Adaptive equalization: keep running sum of

	SE = C(-2)S(t-2dt) + C(-1)S(t-dt) + C0 S(t) + C1 S(t+dt) + C2 S(t+2dt)
	
can assume C(-2) + C(-1) + C(0) + C(1) + C(2) = 1.0

See circuit block diagram in Fig 5.15

Coefficients are set using a "training sequence"; these may be sent 
rather frequently. 



3. Diversity: space, frequency, time.
Space: multiple antennas. Not so practical.
Frequency: spread spectrum; to be addressed later
Time: goal is to spread blocks so one burst affects more blocks,
but fewer bits/block. Then the FEC on each block can recover!

Fig 5.16a: TDM spreads errors over multiple channels

Fig 5.16b: block interleaving. Blocks are A2-A5, A6-A9, ...A[N]-A[N+3]...
We interleave so any one block has at worst 1/4 (one sub-block) in any
one burst.


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Chapter 6: 

symbols v bits: one SYMBOL can encode several bits. 
bps: bit rate
baud: symbol rate
56K modem example: 7 bits at a time, sent at rate of 8,000 baud

The more bandwidth, the better the data rate.

The carrier CAN be at a frequency comparable to the bit rate,
but typically bandwidth = O(bitrate), and for legal reasons
bandwidth needs to be relatively small in proportion to the carrier frequency.
Hence typically carrier_freq >> bit_rate

6.3: sending analog data on a carrier:
	AM: note DC component
	fig 6.11
	bandwidth diagram
	
	FM & PM: fig 6.13
	FM: low points in data signal are low-freq places
	PM: lowest-freq places are those where data signal is decreasing fastest.
	
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6.2: sending digital data on a carrier

ASK, BFSK, BPSK: quick overview

MFSK: use more frequencies in FSK.
Selecting one of four frequencies sends 2 bits. 
p 133: note that the frequencies are actually spaced at difference 2fd.
fc = carrier frequency
fi = ith frequency = fc + (2i - 1 - M)*fd , i = 1..M
L: bits/symbol
M = 2^L = # of different frequencies
T = time for one bit
Ts = L*T = time for one symbol = time to hold one frequency
Stallings has the actual frequencies arranged symmetrically around fc, the carrier.
eg	fc - 3fd, fc - fd, fc + fd, fc + 3fd.

How close can two frequencies f1, f2 be? You need a period Ts long enough
so that f1 and f2 differ by at least one full cycle by the end of Ts.
Number of cycles of f1 in interval Ts: Ts*f1
Difference: Ts(f1-f2). Need this at least 1, or (f1-f2) = 1/Ts.
Min separation between frequencies is 2fd, so this means 2fd = 1/Ts.

Example 6.1. Note that fc = 250kHz, and data rate = 150 Kbps, 
and nominal bandwidth = 150 kHz. 

Fig 6.4

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BPSK: changing phase by pi is the same as multiplying signal by -1.
Changing by pi/2 is the same as replacing sin with cos, and vice-versa.

Decoding BPSK: subtract local oscillator, A cos 2pi*fc*t
Get zero or doubled signal.

Differential PSK: 

QPSK: use 4 phase angles: 
	00	-3/4 pi
	01	 3/4 pi
	10	-1/4 pi
	11	 1/4 pi
fig 6.7 stuff: QPSK can be seen as alternating In-phase (I) / Quadrature (Q) bits 
Note that fig 6.7 in the book (at least my printing) is WRONG:

Explain why OQPSK is a good thing:
each individual phase change is by at most pi/2
but rate of phase changes is twice as fast.

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Note on modulation: it can be hard to tweak microwaves that fast!

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MPSK: old 9600-bps modems used 12 phases.
four phases had two possible amplitudes.
so there were 16 possible symbols.
symbol rate (baud rate) was 2400 baud

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Performance:
bandwidth, Eb/N0

R = signal bit rate

ASK bandwidth is (1+r)R, 0<r<1.
Another way, R/bw = 1/(1+r) ranges from 0.5 to 1.0
we want R/bw to be LARGE.

MPSK: R/bw = Log2(M)/(1+r)

FPSK: R/bw = Log2(M) / M*(1+r)

Table 6.2 shows values. Not available as a slide.

Note that FSK gets worse as M increases
PSK gets BETTER as M increases

Fig 6.8: typical Eb/N0 v BER for all three. Note 3 db range
Fig 6.9: effect of chaging M on FSK and PSK.
FSK: BER gets BETTER as M increases
PSK gets WORSE as M increases

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QAM: two AM (ASK) channels, separated by a pi/2 phase change.