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Calculate bit error rate (BER) using semianalytic technique

`ber = semianalytic(txsig,rxsig,`

* modtype*,

`M`

ber = semianalytic(txsig,rxsig,

`modtype`

`M`

ber = semianalytic(txsig,rxsig,

`modtype`

`M`

ber = semianalytic(txsig,rxsig,

`modtype`

`M`

[ber,avgampl,avgpower] = semianalytic(...)

`ber = semianalytic(txsig,rxsig,`

returns
the bit error rate (BER) of a system that transmits the complex baseband
vector signal * modtype*,

`M`

`txsig`

and receives the noiseless
complex baseband vector signal `rxsig`

. Each of these
signals has `Nsamp`

samples per symbol. `Nsamp`

is
also the sampling rate of `txsig`

and `rxsig`

,
in Hz. The function assumes that `rxsig`

is the input
to the receiver filter, and the function filters `rxsig`

with
an ideal integrator. `modtype`

is the modulation
type of the signal and `M`

`modtype`

`M`

Modulation Scheme | Value
of modtype | Valid Values of M |
---|---|---|

Differential phase shift keying (DPSK) | `'dpsk'` | 2, 4 |

Minimum shift keying (MSK) with differential encoding | `'msk/diff'` | 2 |

Minimum shift keying (MSK) with nondifferential encoding | `'msk/nondiff'` | 2 |

Phase shift keying (PSK) with differential encoding, where the phase offset of the constellation is 0 | `'psk/diff'` | 2, 4 |

Phase shift keying (PSK) with nondifferential encoding, where the phase offset of the constellation is 0 | `'psk/nondiff'` | 2, 4, 8, 16, 32, or 64 |

Offset quaternary phase shift keying (OQPSK) | `'oqpsk'` | 4 |

Quadrature amplitude modulation (QAM) | `'qam'` | 4, 8, 16, 32, 64, 128, 256, 512, 1024 |

`'msk/diff'`

is
equivalent to conventional MSK (setting the `'Precoding'`

property
of the MSK object to `'off'`

), while `'msk/nondiff'`

is
equivalent to precoded MSK (setting the `'Precoding'`

property
of the MSK object to `'on'`

).

The output `ber`

is an *upper bound* on
the BER in these cases:

DQPSK (

=`modtype`

,`'dpsk'`

`M`

= 4)Cross QAM (

=`modtype`

,`'qam'`

`M`

not a perfect square). In this case, note that the upper bound used here is slightly tighter than the upper bound used for cross QAM in the`berawgn`

function.

When the function computes the BER, it assumes that symbols
are Gray-coded. The function calculates the BER for values of E_{b}/N_{0} in
the range of [0:20] dB and returns a vector of length 21 whose elements
correspond to the different E_{b}/N_{0} levels.

You must use a sufficiently long vector `txsig`

,
or else the calculated BER will be inaccurate. If the system's impulse
response is L symbols long, the length of `txsig`

should
be at least `M`

^{L}. A common
approach is to start with an augmented binary pseudonoise (PN) sequence
of total length `(log`

_{2}M)M^{L}.
An *augmented* PN sequence is a PN sequence with
an extra zero appended, which makes the distribution of ones and zeros
equal.

`ber = semianalytic(txsig,rxsig,`

is
the same as the previous syntax, except that the function filters * modtype*,

`M`

`rxsig`

with
a receiver filter instead of an ideal integrator. The transfer function
of the receiver filter is given in descending powers of z by the vectors `num`

and `den`

.`ber = semianalytic(txsig,rxsig,`

is
the same as the first syntax, except that * modtype*,

`M`

`EbNo`

represents E`EbNo`

is
a vector, then the output `ber`

is a vector of the
same size, whose elements correspond to the different E`ber = semianalytic(txsig,rxsig,`

combines
the functionality of the previous two syntaxes.* modtype*,

`M`

`[ber,avgampl,avgpower] = semianalytic(...)`

returns
the mean complex signal amplitude and the mean power of `rxsig`

after
filtering it by the receiver filter and sampling it at the symbol
rate.

A typical procedure for implementing the semianalytic technique is in Procedure for the Semianalytic Technique. Sample code is in Example: Using the Semianalytic Technique.

The function makes several important assumptions about the communication
system. See When to Use the Semianalytic Technique to find out
whether your communication system is suitable for the semianalytic
technique and the `semianalytic`

function.

As an alternative to the `semianalytic`

function,
invoke the BERTool GUI (`bertool`

) and use the **Semianalytic** tab.

[1] Jeruchim, M. C., P. Balaban, and K. S. Shanmugan, *Simulation
of Communication Systems*, New York, Plenum Press, 1992.

[2] Pasupathy, S., “Minimum Shift
Keying: A Spectrally Efficient Modulation,” *IEEE
Communications Magazine*, July, 1979, pp. 14–22.

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