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Some general questions on capacity in FDMA, TDMA and CDMA

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Part A:

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$\\frac{S}{I}_{linear}=10^{\\frac{27}{10}}=501.19$ 

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$C_{FDMA}=\\frac{B_T}{\\frac{B_c}{3}\\left(M\\left(\\frac{S}{I}_{min}\\right)\\right)^{\\frac{2}{v}}}$

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$C_{FDMA}=\\frac{B_T}{\\frac{B_c}{3}\\left(M\\left(\\frac{S}{I}_{min}\\right)\\right)^{\\frac{2}{v}}}=\\frac{20,000,000}{\\frac{10,000}{3}\\left(M\\left(6\\cdot501.19\\right)\\right)^{0.5}}=109.41$ channels/cell

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109.41 channels is not possible, therefore $C_{FDMA}=109$channels/cell

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Part B:

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$C_{FDMA}=\\frac{B_T}{\\frac{B_c}{3}\\left(M\\left(\\frac{S}{I}_{min}\\right)\\right)^{\\frac{2}{v}}}$

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Rearrange for $\\frac{S}{I}_{min}$:

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$\\frac{S}{I}_{min}=\\frac{1}{M}\\left(\\frac{B_T}{\\frac{B_c}{3}C}\\right)^\\frac{v}{2}=31.56$

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$\\frac{S}{I}_{dB}=10\\log_{10}\\left(31.56\\right)\\approx15$ dB

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Part C:

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$\\frac{S}{I}=\\frac{S}{I_s+I_a}=\\frac{S}{\\left(M-1\\right)S+I)a}=\\frac{1}{(M-1)+\\frac{I_a}{S}}$

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$I_a$ is negligible, therefore $I=I_s$:

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$\\frac{S}{I}=\\frac{1}{(M-1)}$

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$M=C_{CDMA}=\\frac{I}{S}+1$

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Part D:

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Data rate: $R_b=1$ Mb/s

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Bit period: $T_b=1/R_b=1\\mu s$

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One slot duration: $1500\\cdot T_b=1500\\cdot 10^{-6}

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Total slot time = $16\\cdot 0.0015=24\\mu s$

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The capacity of a cellular system employing FDMA is defined as

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$C_{FDMA}=\\frac{B_T}{\\frac{B_c}{3}\\left(M\\left(\\frac{S}{I}_{min}\\right)\\right)^{\\frac{2}{v}}}$

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where $B_T$ is the total bandwidth, $B_c$ is the channel bandwidth, $M$ is the number of interferers, is the minimum signal-to-interference ratio and $v=4$ is the path-loss exponent.

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A cellular system has a total bandwidth of 20 MHz and each channel has a bandwidth of 10 kHz. If the mobile user can tolerate a minimum signal-to-interference ratio of 27 dB and there are 6 interferers effecting the mobile user, determine the capacity of the system.

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$C_{FDMA}=$[[0]] channels/cell

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An equivalent cellular system employing FDMA occupies the same total bandwidth as the cellular system in part a), but each channel has a bandwidth of 40 kHz. Determine the minimum signal-to-interference ratio that is required for this system to achieve the same capacity as the system in part a).

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$\\frac{S}{I}_{dB}=$[[0]] dB

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The capacity of a CDMA cellular system, $C_{CDMA}$ is dependent on the number of users, $M$, in each cell.

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If each user in the cell is transmitting at $S$ Watts and intercell interference $I_a$ is assumed to be neglible, then derive the overall capacity of the system.

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$C_{CDMA}=$[[0]]

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A TDMA frame comprises 16 time slots, where each time slot contains 1500 bits. The data is transmitted as a rate of 1 Mbps.

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Determine the duration of the frame: [[0]] ms

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