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2. Consider a packet transmission system that requires a signal to interference noise plus noise ratio (SINR) of at least $\gamma_{SINR} = 7$ dB. Packets of length $T_p$ seconds are transmitted randomly and indepen- dently (Poisson arrival distribution) at a rate of $\lambda_p$ packets per second. This system operates in an environment with noise level that has an SNR of 10dB. Using code division multiple access (CDMA), suppose that the power received at a mobile has a single interferer that is suppressed by 10 dB com- pared to the desired signal. This is achieved from matched filtering with the desiried user's spreading code. (a) Compute the maximum packet fraction of overlap, $\alpha$, to ensure the minimum $\gamma_{SINR}$ requirement. (b) Compute the maximum effective throughput if a slotted ALOHA random access protocol is used to transmit packets in the above system. Hint: You need to modify the slotted ALOHA throughput expression from Lecture 23. (c) What would be the maximum throughput if instead pure slotted ALOHA were used instead and zero packet overlap were allowed?

          2. Consider a packet transmission system that requires a signal to interference noise plus noise ratio
(SINR) of at least $\gamma_{SINR} = 7$ dB. Packets of length $T_p$ seconds are transmitted randomly and indepen-
dently (Poisson arrival distribution) at a rate of $\lambda_p$ packets per second. This system operates in an
environment with noise level that has an SNR of 10dB. Using code division multiple access (CDMA),
suppose that the power received at a mobile has a single interferer that is suppressed by 10 dB com-
pared to the desired signal. This is achieved from matched filtering with the desiried user's spreading
code.
(a) Compute the maximum packet fraction of overlap, $\alpha$, to ensure the minimum $\gamma_{SINR}$ requirement.
(b) Compute the maximum effective throughput if a slotted ALOHA random access protocol is used
to transmit packets in the above system.
Hint: You need to modify the slotted ALOHA throughput expression from Lecture 23.
(c) What would be the maximum throughput if instead pure slotted ALOHA were used instead and
zero packet overlap were allowed?

$2. Consider a packet transmission system that requires a signal to interference noise plus noise ratio (SINR) of at least γSINR = 7 dB. Packets of length Tp seconds are transmitted randomly and indepen- dently (Poisson arrival distribution) at a rate of packets per second. This system operates in an environment with noise level that has an SNR of 10dB. Using code division multiple access (CDMA), suppose that the power received at a mobile has a single interferer that is suppressed by 10 dB com- pared to the desired signal. This is achieved from matched filtering with the desiried user's spreading code. (a) Compute the maximum packet fraction of overlap, α, to ensure the minimum γSINR requirement. (b) Compute the maximum effective throughput if a slotted ALOHA random access protocol is used to transmit packets in the above system. Hint: You need to modify the slotted ALOHA throughput expression from Lecture 23. (c) What would be the maximum throughput if instead pure slotted ALOHA were used instead and zero packet overlap were allowed?$

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