BER and SER for uncoded data over Rayleigh and Rician fading channels
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
in dB. Values in the
vectors correspond to the theoretical error rates at the specified
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(
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.
Generate a vector of values to evaluate.
EbNo = 8:2:20;
Initialize a BER results vector.
ber = zeros(length(EbNo),20);
Generate BER versus curves for 16-QAM in a Rayleigh fading channel. Vary the diversity order from 1 to 20.
for L = 1:20 ber(:,L) = berfading(EbNo,'qam',16,L); end
Plot the results.
semilogy(EbNo,ber,'b') text(18.5, 0.02, sprintf('L=%d',1)) text(18.5, 1e-11, sprintf('L=%d',20)) title('QAM over Rayleigh Fading Channel with Diversity Order 1 to 20') xlabel('E_b/N_0 (dB)') ylabel('BER') grid on
EbNo— Energy per bit to noise power spectral density ratio
Energy per bit to noise power spectral density ratio in dB, specified as a scalar or vector.
For cases where diversity is used, the
on each diversity branch is
modtype— Modulation type
Modulation type, specified as one of these options.
Pulse amplitude modulation (PAM)
Quadrature amplitude modulation (QAM)
The modulation order
Phase shift keying (PSK)
Offset quadrature phase shift keying (OQPSK)
Differential phase shift keying (DPSK)
Frequency-shift keying (FSK)
When you set the input
M— Modulation order
Modulation order, specified as an integer equal to 2k, where k is a positive integer.
divorder— Diversity order
0| nonnegative integer
Diversity order, specified as a nonnegative integer that represents the number of diversity branches.
When you specify a
divorder value greater than
0, the error rate is computed using diversity. For
cases where diversity is used, the
on each diversity branch is
coherence— Coherent detection type
Coherent detection type, specified as one of these options.
'coherent' — For coherent detection
'noncoherent' — For noncoherent
To enable this argument, set the
rho— Complex correlation coefficient
Complex correlation coefficient, specified as a complex scalar. For more information about the complex correlation coefficient and how to compute it for nonorthogonal binary FSK (BFSK) modulation, see Nonorthogonal 2-FSK with Coherent Detection.
Complex Number Support: Yes
K— Ratio of specular to diffuse energy
Ratio of specular to diffuse energy in linear scale, specified as a nonnegative scalar.
phaserr— Standard deviation of reference carrier phase error
Standard deviation of the reference carrier phase error in radians, specified as a nonnegative scalar.
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.
You can configure the Theoretical tab in the Bit
Error Rate Analysis app to compute theoretical BER values instead of using the
 Proakis, John G. Digital Communications. 4th ed. New York: McGraw Hill, 2001.
 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.
 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.
 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.
 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.
 Simon, M. K, S. M. Hinedi, and W. C. Lindsey. Digital Communication Techniques – Signal Design and Detection. Prentice-Hall, 1995.
 Simon, M. K., and Alouini, M. S. Digital Communication over Fading Channels – A Unified Approach to Performance Analysis. 1st ed. Wiley, 2000.
 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.