a week from today from 11:30 to 2:00 on may 6
M-ary PAM
each sig sends k=log2(M) bits
the M-sigs are si = uip(t), 0<=i<=M-1
where p(t) is a pulse time-limited to T seconds and ui in {odd +/- (M-1)}
energy in a sig is Esi = ui*ui*Ep
avg energy/sig is Es = (MM-1)Ep/3
optimum rxer is input multiplied by p(t), into symbol time integrator, into thresh device
det thresh, calc sig components out of correlator:
	^ui = E(Z|si sent) = int<0,T>(uip^2(t)dt) = uiEp
variance = nEp/2?
adjacent means, thresholds in between means
Pe for sigs is not all the same
Pe(low) = Pe(high) < Pe(intermediateN) = Pe(intermediateM)
intermediates are called interior points
ends are called exterior points
Pe(interior) ~~ 2Pe(exterior)
Pe0 = Q(sqrt(2Ep/n))
Pei = 2Q(sqrt(2Ep/n))
prob of symbol error in terms of avg symbol energy is Pe& = 2(M-1)/M * Q(sqrt(6Es/(MM-1)n)) = 2(M-1)/M * Q(sqrt(6log2M/(MM-1) * Eb/n))

prob of bit error will depend on which sig is sent and the assignment of bits to symbols
the most common sig errors are for adj symbols
bits should be assigned to min bit errors so adj symbols should differ by only 1 bit (gray code)
with M-ary PAM sig, we must increase energy/bit to achieve same perf as in binary PAM
in bin PAM, we require B Hz to send data at a rate of Rb bits/sec
in M-ary PAM, we can send data at a rate of kRb over this BW, or we can send data at a rate of Rb bits/sec using B/k Hz
these results hold for M-ask as well, where p(t) = p'(t)cow(wct + phi)

M-QAM
sigs are txed by si = ai*sqrt(2/T) * cos(wct) + bi*sqrt(2/T)*sin(wct)
where ai in (odds from +/-(M'-1))
and bi in (odds from +/-(M"-1))
and M = M'M"
optimum rxer: 2 branches with sin and cos component multipliers, integrated and pushed into decision devices
2 indepent decision devices
prob of symbol error varies depending on interior vs exterior and corner points
Pe(corner) = Pe(interior)/2
Pe(edge) = 3Pe(corner)/2

2 correlators are in-phase and quadrature
arranged in a rectangle
quadrature determines row, in-phase determines column
need to use gray code here as well, but a little more complicated because it's 2 dimensions

16-PSK
arranged on a single circle, dividing the arcs evenly