How do we calculate BER vs. SNR for real systems?

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How do we calculate BER vs. SNR for real systems?

For real systems, transmitted bits at the receiver are detected using various techniques (e.g., soft detection). For example, if the transmitted bit is -1, it is received as (-)square root of power plus noise present in the channel. Similarly, if the transmitted bit is +1, it is received as (+)square root of power plus noise.

As we know, noise has 0 mean as usual; the (-)square root of SNR is used instead of the (-)square root of power plus noise. If the transmitted bit is +1, it is received as (+)square root of power plus noise.

BER vs. SNR from Gaussian Q factor

The probability of error can be calculated as

The above example is for a block of size k after zero-forcing equalization. Ωs is the average power, and Wii is the i-th diagonal element of a matrix W. W denotes the symbol estimated error matrix in signal processing.

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BER vs SNR

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