RF Analog Impairments Modeling for Communication Systems Simulation: Application to OFDM-based Transceivers

1.4 SNR, EVM, and E_b/N₀ Definitions and Relationship

1.4.1 Bit Error Rate

In order to quantify the performance of communication systems, we often find in the literature the use of a BER metric giving the probability of error in terms of the number of corrupted bits per bits received (Proakis, 1995). Depending on the application the BER target can vary from 10⁻³ to 10⁻¹⁵, that is, one erroneous bit every 1000 or 10¹⁵ bits, respectively. Consequently, the system simulations for measuring these very low BER levels are generally time consuming and cumbersome because large amounts of data, several millions of bits, have to be processed using an accurate model of the DBB chain.

Because the AFE is composed of several blocks (LNA, phase-locked loop (PLL), mixer, etc.) designed by different engineers, it is not practical to directly use the BER as a specification. RF analog designers prefer to work with SNR and/or EVM as performance metrics for specifying and designing the AFE blocks. So it is important that the system designer be able to translate the BER target into SNR or EVM specifications for the AFE development. One technique is to extract the required SNR or EVM from the BER curves, but as they are commonly represented as a function of E_b/N₀, a relationship between these various performance metrics is needed.

Figure 1.29 is a plot of BER curves as a function of E_b/N₀ for four different modulations: 4-QAM, 16-QAM, 64-QAM, and 1024-QAM. If the goal is to achieve a BER lower than 10 ...