# Quiz Determine the minimum number of shift register stages required to create a maximal length PN sequence which has a repetition time greater than 10.

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Quiz Determine the minimum number of shift register stages required to create a maximal length PN sequence which has a repetition time greater than 10 seconds and a chip rate of 1.23 Mc/s.

Multiple Access Systems FDMA 30 kHz FM channels – 900 Mhz band #users N T = B sys /B ch TDMA 3:1 compression of Old FDMA channels CDMA 2/4 PSK 1.23 Mhz Spreading codes Transmit Power control to equalize incoming power levels

Cellular Protocol Number of cells in cluster Reuse factor K r = a 2 + ab + b 2 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 2 K r = 1K r = 3K r = 7 dIdI For Co-channel Separation distance d I Cell Radius r r

Cellular CDMA Capacity Since all cells use the same bandwidth, and mobile unit power is controlled, it is only the presence of other users that limit capacity. G = B s /R v B s = Spreading Chip Rate ~ 1.23 Mb/s R v = Voice Bit Rate ~ 9.6 kb/s  = 0.5 Neighboring cell interference  = 0.85 Power Control Factor v = 0.6 Voice Activity factor For E b /I 0 = 7 dB, N CDMA = 25 CDMA is much less susceptible to fading than narrowband FM because of broad bandwidth used.

Cellular Radio Propagation Path Loss Doppler (for texting while driving) Slow log-normal fading Fast multipath fading 30-40 dB variations over fractional wavelengths Time dispersion Burst errors Rayleigh statistics if LOS is not dominant Rayleigh multipath + Dominant LOS > Rician fading statistics Note that Rice Rayleigh as k 0

Digital Transmission n bits/symbol M = 2 n channel states (phasors) Channel must switch between states every T s = 1/f s seconds, Thus f i = nf s Bandwidth efficiency unitless (Bits/sec per hz) Since there are n bits per symbol, E s = n E b and f s E s = f i E b For M-PSK, phase noise required for an error is And the noise voltage to signal voltage for an error would be

Probability of Error is the magnitude of the symbol phasor. The probability of symbol error is given by Erfc(x) is the complimentary error function for Gaussian Distributions: The probability of bit error is

Probability of Error (cont) For M-FSK, The probability of symbol error is Viterbi sez...

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