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bersync

BER for imperfect synchronization

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Syntax

ber = bersync(EbNo,timerr,'timing')
ber = bersync(EbNo,phaserr,'carrier')

Description

Thebersyncfunction returns the bit error rate (BER) for uncoded coherent BPSK over an additive white Gaussian noise (AWGN) channel for imperfect synchronization. For more information, seeAnalytical Expressions Used in bersync Function and Bit Error Rate Analysis App。

example

ber= bersync(EbNo,timerr,'timing')returns the BER from uncoded coherent binary phase shift keying (BPSK) modulation over an additive white Gaussian noise (AWGN) channel at the specifiedEb/N0with imperfect timing specified bytimerr。The normalized timing error is assumed to have a Gaussian distribution.

ber= bersync(EbNo,phaserr,'carrier')returns the bit error rate (BER) from uncoded BPSK modulation over an AWGN channel at the specifiedEb/N0with a noisy phase reference specified byphaserr。The phase error is assumed to have a Gaussian distribution.phaserris the standard deviation of the phase error of the reference carrier phase.

Examples

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Open Live Script

Compute the BER for coherent BPSK modulation over an AWGN channel with imperfect timing. Vary the ratio of bit energy to noise power spectral density ( E b / N 0 ) and the standard deviation of the timing error. Whentimerrassumes the final value of0,bersyncfunction produces the same result asberawgn(EbNo,'psk',2)。

EbNo = [4 8 12]; timerr = [0.2 0.07 0]; ber = zeros(length(timerr),length(EbNo));forii = 1:length(timerr) ber(ii,:) = bersync(EbNo,timerr(ii),'timerr');end

Display the result using scientific notation.

formatshorte; ber
ber =3×30.0521 0.0205 0.0112 0.0189 0.0008 0.0000 0.0125 0.0002 0.0000

Switch back to default notation format.

format;

Input Arguments

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Ratio of bit energy to noise power spectral density (Eb/N0) in dB, specified as a scalar or vector.

Data Types:single|double

Standard deviation of the timing error, specified as a scalar in the range [0, 0.5]. Provide the timing error normalized to the symbol interval. The normalized timing error is assumed to have a Gaussian distribution.

Data Types:double|single

Standard deviation of the phase error for the reference carrier phase in radians, specified as a scalar. The phase error is assumed to have a Gaussian distribution.

Data Types:double|single

Output Arguments

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BER for uncoded coherent BPSK modulation over an AWGN channel returned as a scalar or vector with

  • imperfect timing if you specified thetimerrinput

  • a noisy phase reference if you specified thephaserrinput

The BER is computed for eachEb/N0setting specified by the input argumentEbNo。

IfEbNois a vector, the outputberis a vector of the same size as inputEbNoand its elements correspond to the different elements of theEbNovector.

Data Types:double

Limitations

In general, the numerical accuracy for the output BER is limited to approximately two significant digits. The numerical accuracy output by this function is limited by:

  • Approximations in the analysis leading to the closed-form expressions used by the function

  • Approximations related to the numerical implementation of the expressions

Inherent limitations in numerical precision force the function to assume perfect synchronization if the value oftimerrorphaserris less than the positive distance from the absolute value of the error value to the next larger in magnitude floating point number as determined by theepsfunction. This table indicates how the function behaves under these conditions.

Condition Behavior ofbersyncFunction
timerr < eps bersync(EbNo,timerr,'timing')相当于berawgn(EbNo,'psk',2)with a timing error less thaneps。
phaserr < eps bersync(EbNo,phaserr,'carrier')相当于berawgn(EbNo,'psk',2)with a phase error less thaneps。

Algorithms

This function uses formulas from[3]。

When the last input is'timing',function computes

1 4 π σ ∫ − ∞ ∞ exp ( − ξ 2 2 σ 2 ) ∫ 2 R ( 1 − 2 | ξ | ) ∞ exp ( − x 2 2 ) d x d ξ + 1 2 2 π ∫ 2 R ∞ exp ( − x 2 2 ) d x

σ is thetimerrinput, andRis the value of theEbNoinput converted from dB to a linear scale.

When the last input is'carrier',function computes

1 π σ ∫ 0 ∞ exp ( − ϕ 2 2 σ 2 ) ∫ 2 R cos ϕ ∞ exp ( − y 2 2 ) d y d ϕ

σ is thephaserrinput, andRis the value of theEbNoinput converted from dB to a linear scale.

Alternatives

You can configure theTheoreticaltab in theBit Error Rate Analysisapp to compute theoretical BER values instead of using thebersyncfunction.

References

[1]Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan.Simulation of Communication Systems。第二次编辑ion. Boston, MA: Springer US, 2000.

[2]Sklar, Bernard.Digital Communications: Fundamentals and Applications。2nd ed. Upper Saddle River, N.J: Prentice-Hall PTR, 2001.

[3]Stiffler, J. J.Theory of Synchronous Communications。Englewood Cliffs, NJ.: Prentice-Hall, 1971.

See Also

Apps

Functions

Topics

Introduced before R2006a

Communications Toolbox Documentation

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Bridging Wireless Communications Design and Testing with MATLAB

Bridging Wireless Communications Design and Testing with MATLAB

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