Communications Toolbox

berawgn

Bit error rate (BER) for uncoded AWGN channels

Syntax

ber = berawgn(EbNo,'pam',M)
ber = berawgn(EbNo,'qam',M)
ber = berawgn(EbNo,'psk',M,dataenc)
ber = berawgn(EbNo,'dpsk',M)
ber = berawgn(EbNo,'fsk',M,coherence)
ber = berawgn(EbNo,'msk',dataenc)
berlb = berawgn(EbNo,'cpfsk',M,modindex,kmin)

Graphical Interface

As an alternative to the berawgn function, invoke the BERTool GUI (bertool) and use the Theoretical panel.

Description

For All Syntaxes

The berawgn function returns the BER of various modulation schemes over an additive white Gaussian noise (AWGN) channel. The first input argument, EbNo, is the ratio of bit energy to noise power spectral density, in dB. If EbNo is a vector, then the output ber is a vector of the same size, whose elements correspond to the different E_b/N₀ levels. The supported modulation schemes, which correspond to the second input argument to the function, are in the table below.

Most syntaxes also have an M input that specifies the alphabet size for the modulation. M must have the form 2^k for some positive integer k.

For Specific Syntaxes

ber = berawgn(EbNo,'pam',M) returns the BER of uncoded PAM over an AWGN channel with coherent demodulation, assuming a Gray-coded signal constellation.

ber = berawgn(EbNo,'qam',M) returns the BER of uncoded QAM over an AWGN channel with coherent demodulation, assuming a Gray-coded signal constellation. The alphabet size, M, must be at least 4. For cross QAM (M not a perfect square), the output ber is an upper bound on the BER. (Note that the upper bound used here is slightly looser than the upper bound used for cross QAM in the semianalytic function.)

ber = berawgn(EbNo,'psk',M,dataenc) returns the BER of coherently detected uncoded PSK over an AWGN channel, assuming a Gray-coded signal constellation. dataenc is either 'diff' for differential data encoding or 'nondiff' for nondifferential data encoding. If dataenc is 'diff' then M must be no greater than 4. For details on this calculation, see [2].

ber = berawgn(EbNo,'dpsk',M) returns the BER of uncoded DPSK modulation over an AWGN channel.

ber = berawgn(EbNo,'fsk',M,coherence) returns the BER of orthogonal uncoded FSK modulation over an AWGN channel. coherence is either 'coherent' for coherent demodulation or 'noncoherent' for noncoherent demodulation. M must be no greater than 64.

ber = berawgn(EbNo,'msk',dataenc) returns the BER of coherently detected uncoded MSK modulation over an AWGN channel. dataenc is either 'diff' for differential data encoding or 'nondiff' for nondifferential data encoding. For details on this calculation, see [2].

berlb = berawgn(EbNo,'cpfsk',M,modindex,kmin) returns a lower bound on the BER of uncoded CPFSK modulation over an AWGN channel. modindex is the modulation index, a positive real number. kmin is the number of paths having the minimum distance; if this number is unknown, you can assume a value of 1.

Examples

An example using this function is in Comparing Theoretical and Empirical Error Rates.

Limitations

The numerical accuracy of this function's output is limited by

• Approximations in the analysis leading to the closed-form expressions that the function uses

• Approximations related to the numerical implementation of the expressions

You can generally rely on the first couple of significant digits of the function's output. However, DQPSK ('dpsk' with M=4) and differentially encoded PSK ('psk' with 'diff') have additional limitations, such that the function produces an output of 0 if EbNo is large.

See Also

bercoding, berfading, bersync, Theoretical Performance Results

References

[1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg, Digital Phase Modulation, New York, Plenum Press, 1986.

[2] Lindsey, William C. and Marvin K. Simon, Telecommunication Systems Engineering, Englewood Cliffs, N.J., Prentice-Hall, 1973.

[3] Proakis, John G., Digital Communications, 4th ed., New York, McGraw-Hill, 2001.

bchgenpoly

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