The received signal in a digital base band system is either +A or -A, equally likely, for T-second contiguous intervals. However, the timing is off at the receiver so that the integration starts ΔT seconds late (positive) or early (negative). Assume that the timing error is less than one signaling interval. By assuming a zero threshold and considering two successive intervals [i.e., (+A, +A), (+A, -A), (-A, +A), and (-A, -A)] obtain an expression for the probability of error as a function of ΔT. Show that it is

Plot curves of PE versus E_b / N₀ in dB for |ΔT|/T = 0, 0.1, 0.2, and 0.3 (four curves). Estimate the degradation in E_b / N₀ in dB at P_E = 10^-4 imposed by timing misalignment.

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2|ΔΤΙ) 2E, 2E, No No PE