Package 'binfunest'

B2BConvert Converts a function of SNR into one of SNR, B2B, and Offset.

Description

Creates a function f( -dB( undB( -s) + undB( -B2B)) - offset)

Usage

B2BConvert(f)

Arguments

f

A function of a single argument f( s). f can be a symbol, a string, or an anonymous function. If a symbol, the symbol name will be remembered. If a string, it will be passed to match.fun which will return the function form that is the value of the named symbol (i.e., not the symbol the string named).

Details

Note that all quantities are assumed to be in Decibels.

Value

A function of three arguments function( x, B2B, offset){...} where x is the symbol SNR, B2B is the back-to-back SNR (i.e. the equivalent SNR when the input SNR (x) is infinite), and offset is the offset to the function f (i.e., if B2B where infinite).

Examples

QPSKdB.B2B <- B2BConvert( QPSKdB)

---

An example BERDF dataframe created by simsigs(), a function in a forthcoming package coherent.

Description

BERDF is a standard R data frame created by the simsigs() function in the forthcoming coherent package. The observations have been condensed

Usage

BERDFc

Format

A dataframe with the following fields:

Name

Name of constellation used to create the record.

SNR

The SNR in Decibles of the observation.

Bps

The number of bits per symbol. The number of bits in a simulation run is Bps * N

NoisePower

The actual noise power in the simulation run. Since the noise is randomly generated, this is a stochastic item.

N

The number of symbols in the simulation run.

SER

The number of symbols errors observed in the simulation run.

BER

The number of bit errors observed in the simulation run.

---

cor.mle returns the correlation matrix of an mle fit.

Description

This simple function will return the correlation matrix for mle fits of more than one variable. Note that this function is not an S3 generic.

Usage

cor.mle(m)

Arguments

m	an mle object with a fit of more than one variable.

Value

a symmetric matrix with ones on the diagonal.

See Also

stats4::mle()

Examples

Q_ab <- function( gamma, a, b)
cor.mle( mle1)

---

mleB2B Estimates Back-to-Back "Q" and Offsets to a bit error rate function.

Description

Bit error counts modeled as independent binary decisions result in a log-likelihood dependent on the bit error probability. This function inserts the supplied bit error probability function into the binomial log-likelihood function, and passes that to stats4::mle, which ultimately calls stats::optim. The function will optimize a binomial probability of the form $r = N * P( x_1, x_2, ..., x_n, a_1, a_2, ... a_k)$, where the $x_i$ are variables from data, and the $a_j$ are parameters to be estimated.

Usage

mleB2B(data = NULL, Errors, N, f, fparms, start, method = "Nelder-Mead", ...)

Arguments

data	a data frame or list with named components. If a list, each component must be the same length (just like a data frame). This is not checked, so usual rules of recycling will apply. Partial matching not performed, so you must use full column names.
Errors	A vector of error counts, or a string identifying a column of data from which to draw the error counts
N	A single number, or a vector of the same length as data, or a string identifying a column of data specifying the number of trials used to measure the error counts in Errors. If a single number, then that number is used as the number of trials for all error counts.
f	A function that predicts the probability of errors.
fparms	a list of named components that are the arguments of f. Each component can be a string, a single number, or a vector. If a string that names a column of data, that column will be used, otherwise the string will be passed to f. Note the potential for errors if a column name was misspelled. A single number or vector will be passed to f. Between fparms, start, and function defaults, all parameters that need to be supplied to f should be specified, and (except for defaults) not duplicated.
start	Named list of initial values for the parameters of f to be estimated.
method	Optimization method. See stats::optim().
...	Optional arguments to be passed to mle.

Details

The function estimates the parameters identified in start in the constructed call to f. For a function f of the form fun( SNR, x2, x3, B2B, offset) A call of the form

mleB2B( data=df, Errors="r", N="trials", f=fun, fparm=list( SNR="s", x2=1, x3="noise"), start=list(B2B=1, offset=2))

will construct a call to mle of the form:

mle( minuslogl=ll, start=start, nobs=length( Errors), method=method)

where the function ll is defined as

ll <- function( a, b) -sum( dbinom( df$r, df$n, fun( SNR=df$s, x2=1, x3=df$noise, B2B=B2B, offset=offset), log=TRUE))

Value

An object of class stats4::mle with the parameters identified in start estimated.

See Also

stats4::mle(), stats::optim()

Examples

QPSKdB.B2B <- B2BConvert( QPSKdB)
O1 <- 3
B1 <- 16
s <- 0:20
N <- 1000000
r <- rbinom( length( s), N, QPSKdB.B2B( s, B1, O1))
df <- data.frame( Errors=r, SNR=s, N=N)
llsb2 <- function( b2b, offset)
         -sum( dbinom( r, N, QPSKdB.B2B( s, b2b, offset), log=TRUE))
mle1 <- stats4::mle( llsb2, start=c( b2b=20, offset=0), nobs=length(s),
                     method="Nelder-Mead")
est1 <-  mleB2B( data=df, Errors="Errors", N=N, f=QPSKdB.B2B,
                 fparms=list( x="SNR"), start=c(b2b=20, offset=0))

---

Theoretical error rate functions

Description

Functions to calculate the theoretical performance of common modulation formats. Includes the functions dB(x) (returns 10*log10(x)), undB(x) (reverses dB(x)), Q_( x) (Markum's Q function), and Q_Inv(x) (returns the SNR in Decibels to get probability x). Also includes mod_Inv, which returns the SNR required for a the function f to reach the supplied BER (bit error rate, or bit error probability).

Usage

is.wholenumber(x, tol = sqrt(.Machine$double.eps))

dB(x)

undB(x)

Q_(x)

Q_Inv(perr)

marcumq(a, b, m = 1)

QPSKdB(x)

DBPSKdB(x)

DQPSKdB(x)

DQPSKDDdB(x)

PSQPSKdB(x)

MPSKdB(x, M)

MPSKdB.8(x)

QAMdB.8.star(x)

QAMdB(x, M)

QAMdB.16(x)

mod_Inv(f, perr, guess = Q_Inv(perr))

mod_InvV(f, pv, offset = 0)

Arguments

x	a real number
tol	the tolerance to test x with.
perr	a probability of a bit error.
a, b, m	marcumq input arguments: non-negative real numbers.
M	The integer number of symbols > 4.
f	a function (usually a BER function).
guess	a guess for the perr (the default usually works).
pv	a vector of BERs.
offset	an offset in Decibels for guesses in mod_InvV.

Details

The marcumq function is copied from the gsignal package, which copied it from the help file of the lmomco package, but is clear from Proakis equations 2-1-121 and 2-1-124.

The rest of the functions return the probability of a bit error given the SNR in Decibels.

• QPSKdB is Quadrature Phase shift keyed: two bits per symbol. Note that BPSK and QPSK have the same performance when SNR is $E_b/N_0$.

• DBPSKdB is differentially detected differential binary PSK.

• DQPSKdB is differentially detected differentially coded QPSK.

• DQPSKDDdB is differentially decoded differential QPSK (coherently detected but differentially decoded. See DQPSK above.

• PSQPSKdB is polarization-shifted QPSK: it is dual pole, but only one pole is active at any one time, thus supplying three bits per symbol. (See Agrell & Karlsson (2009, DOI:10.1109/JLT.2009.2029064)).

• MPSKdB(x, M) is generic M-ary phase shift keying of M points in a circle.

• MPSKdB.8 simply returns MPSKdB(x, 8)

• QAMdB.8.star is the optimal star configuration of 8-ary Quadrature Amplitude Modulation (QAM), such that the legs are at $\pm1$ and $\pm(1+\sqrt3)$.

• QAMdB(x, M) is generic rectangular QAM constellation of M points.

• QAMdB.16 Returns the BER for the rectangular QAM constellation according to Proakis Eq. 5-2-80.

• mod_Inv will take a function f(x) and return the x such that f(x)==perr but it does this based on the log( f(x)) and the log( perr), so f(x)>0.

• mod_InvV is a vectorized version (give it a vector of BERs and it returns a vector of SNRs).

Value

is.wholenumber(x) returns TRUE if c-round(x) < tol.

dB(x) returns 10*log10(x)

undB(x) returns 10^(x/10)

Q_Inv(x) returns 2*dB( -qnorm(x)), which is the SNR (in Decibels) required to get a probability of error of x. Q_Inv( Q_( undB( x/2))) = x and Q_( undB( Q_Inv( x)/2))=x

mod_Inv( f, x) returns a list with the SNR in Decibels to reach the BER perr such that f( mod_Inv( f, x)$x) = x. The returned list has elements $x as the SNR and $fval as the function value.

References

https://cran.r-project.org/package=lmomco

https://cran.r-project.org/package=gsignal

See Also

pracma::fzero()

Examples

dB( 10) # == 10
undB( 20) # == 100
Q_Inv( Q_( undB( 10/2))) # = 10
Q_( undB( Q_Inv( 0.001)/2)) # = 0.001

mod_Inv( QPSKdB, QPSKdB( 7)) # yields 7

mod_InvV(QPSKdB, QPSKdB(c(6,7)))

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