The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C = W log2(1 + P/(σ² W)) bits per second (bps), where W is the channel bandwidth. P is the average power received and σ² is the one-sided power spectral density of the AWGN. For a fixed P/σ² = 1000, the

Question

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C = W log2(1 + P/(σ² W)) bits per second (bps), where W is the channel bandwidth. P is the average power received and σ² is the one-sided power spectral density of the AWGN. For a fixed P/σ² = 1000, the channel capacity (in kbps) with infinite bandwidth (W → ∞) is approximately

Accepted Answer

1.44. As the bandwidth approaches infinity, the capacity formula simplifies, and the term log2(1 + P/(σ² W)) approaches log2(1 + 1000) which is approximately 10. Therefore, the capacity becomes C = W * 10, and since W is infinite, the capacity approaches 1.44 kbps when considering the logarithmic scaling.

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