wireless network please answer correct 5 and 6a and 6b Digital data source with

Question

wireless network
please answer correct 5 and 6a and 6b

Digital data source with digital communication signal Modem 5. You have a wide new wireless channel occupying frequency spectrum from 3.5GHz to 5.8GHz. The SNR of this channel is 20 dB. What is the channel capacity in Gbps, according to Shannon Theory? (5 points) 6. Calculate the Packet Error Rate (10 points). a) The probability that a single bit will be in error on a typical public telephone line is 0.001. The packet header is 10 bytes. Assume there is no other overhead. What is the packet error rate (PER) for a communication line using 128-byte packet?

Explanation / Answer

(5)

Given,

Bandwidth (B) = 5.8 GHz - 3.5 GHz = 2.3 GHz = 2.3 * 109 Hz = 2300000000 Hz
Signal to Noise Ratio in dB (SNRdB) = 20 dB

SNR is computed as follows.

10 * log10(SNR) = SNRdB = 20
=> log10(SNR) = 2
=> SNR = 102 = 100

Achievable channel capacity (C) is computed using Shannon's Theorem as follows.

C = B * log2(1 + SNR)
= 2300000000 * log2(1 + 100) = 2300000000 * log2(101) = 15.31 Gbps

(6a)

Bit Error Rate (BER) = 0.001
Packet Length (N) = 128 bytes = 128 * 8 bits = 1024 bits
Packet Error Rate (PER) = 1 – (1 – BER)N = 1 - (1 - 0.001)1024 = 0.641

(6b)

Bit Error Rate (BER) = 0.0001
Packet Length (N) = 1024 bytes = 1024 * 8 bits =8192 bits
Packet Error Rate (PER) = 1 – (1 – BER)N = 1 - (1 - 0.0001)8192 = 0.559

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