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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.

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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

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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

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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.

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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

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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

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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

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

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