Motivation

• One of the most important characteristics of a digital receiver is the Bit Error Rate (BER) versus Input Power Level (Eb/No)* curve.
• Depending on the data rate, the time these tests take can become impractical.
• There are trade-offs between:
  • Being confident that the BER at a given Eb/No is below a certain value, or
  • Being accurate in measuring the precise value of the BER.

There are situations where precision is important, but typically test time can be significantly reduced by testing only to a confidence level rather than measuring the precise BER.

*- Normalized per bit over the noise spectral density

Background on EbNo and Statistical Models of Bit Errors

The EbNo Curve

Simply put, the EbNo curve shows number of bit errors at a given input power for digital communications systems.

The theoretical curve of EbNo vs BER can be plotted by using the complementary error function (erfc):

$$ \text{BER}=\frac{1}{2}\text{erfc}\Bigg(\sqrt{\frac{E_b}{N_0}}\Bigg) $$

Where

• $E_b$ is the energy per bit
• $N_0$ is the spectral noise density

The implementation loss $I$ of a receiver reduces the energy per bit and the EbNo equation becomes:

$$ \text{BER}=\frac{1}{2}\text{erfc}\Bigg(\sqrt{-I\cdot\frac{ E_b }{N_0}}\Bigg) $$

Figure 1 contains the plots for EbNo vs BER with an implementation loss of 0 dB (theoretical), 1 dB, and 2 dB.

Figure 1: Eb/No vs BER for a BPSK signal with Increasing Implementation Losses

From the plot, it is shown that increased implementation loss shifts the theoretical curve to the right. So it’s useful to determine: