# berfading

BER and SER for uncoded data over Rayleigh and Rician fading channels

## Syntax

## Description

The `berfading`

function returns the bit error rate (BER)
and symbol error rate (SER) over a Rayleigh or Rician fading channel for uncoded data
using a specified modulation scheme. The first input argument,
`EbNo`

, is the energy per bit to noise power spectral density ratio
(*E*_{b}/*N*_{0})
in dB. Values in the `ber`

and `ser`

output
vectors correspond to the theoretical error rates at the specified
*E*_{b}/*N*_{0}
levels for a Gray-coded signal constellation. For more information, see Analytical Expressions Used in berfading Function and Bit Error Rate Analysis App.

specifies binary nonorthogonal FSK data over an uncoded Rayleigh fading channel.
`ber`

= berfading(`EbNo`

,'fsk',2,`divorder`

,`coherence`

,`rho`

)`rho`

specifies the complex correlation coefficient. The
modulation order is 2. For the definition of the complex correlation coefficient
and how to compute it for nonorthogonal BFSK modulation, see Nonorthogonal 2-FSK with Coherent Detection.

## Examples

## Input Arguments

## Output Arguments

## Limitations

The numerical accuracy of the output returned by this function is limited by approximations related to the numerical implementation of the expressions to roughly two significant digits.

## Alternatives

You can configure the **Theoretical** tab in the Bit
Error Rate Analysis app to compute theoretical BER values instead of using the
`berfading`

function.

## References

[1] Proakis, John G. *Digital Communications*.
4th ed. New York: McGraw Hill, 2001.

[2] Modestino, J. and Shou Mui. “Convolutional Code
Performance in the Rician Fading Channel.” *IEEE Transactions on
Communications* 24, no. 6 (June 1976): 592–606.
https://doi.org/10.1109/TCOM.1976.1093351.

[3] Cho, K., and D. Yoon. "On the General BER Expression of One- and Two-Dimensional Amplitude Modulations." *IEEE Trans. Commun.* 50, no. 7, (2002): 1074-1080.

[4] Lee, P. J. "Computation of the Bit Error Rate of Coherent M-ary PSK with Gray Code Bit Mapping." *IEEE Trans. Commun.* COM-34, no. 5, (1986): 488-491.

[5] Lindsey, W. C. "Error probabilities for Rician fading
multichannel reception of binary and N-ary signal." *IEEE
Transactions on Information Theory*, vol. 10, no. 4, pp. 339-350, October
1964, doi: 10.1109/TIT.1964.1053703.

[6] Simon, M. K, S. M. Hinedi, and W. C. Lindsey. *Digital Communication Techniques – Signal Design and Detection*. Prentice-Hall, 1995.

[7] Simon, M. K., and Alouini, M. S. *Digital
Communication over Fading Channels – A Unified Approach to Performance
Analysis*. 1st ed. Wiley, 2000.

[8] Simon, M. K. "On the Bit-Error Probability of Differentially
Encoded QPSK and Offset QPSK in the Presence of Carrier Synchronization." *IEEE Trans.
Commun.* 54, (2006): 806-812.

## Version History

**Introduced before R2006a**