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System Simulator >
System Component Models >
Equalizers >
   Least Mean Square Equalizer, Complex (CLMSE)       

Least Mean Square Equalizer, Complex (CLMSE)

 

 


Property

Description

Units

Default

Range/Type

NTAPS

The number of filter coefficients

None

4

(-Inf, Inf)/Integer

DELTA

The LMS algorithm step size

None

1

(-Inf, Inf)/Real

RIN1

Input1 impedance

Ohm

Inf

(0, Inf]/Real

RIN2

Input2 impedance

Ohm

Inf

(0, Inf]/Real

RIN3

Input3 impedance

Ohm

Inf

(0, Inf]/Real

RIN4

Input4 impedance

Ohm

Inf

(0, In]f

ROUT1

Output1 impedance

Ohm

0

[0, Inf)/Real

ROUT2

Output2 impedance

Ohm

0

[0, Inf)/Real

Ports

Input1

Real part of the complex input signal (real)

Input2

Imaginary part of the complex input signal (real)

Input3

Real part of the error signal (real)

Input4

Imaginary part of the error signal (real)

Output1

Real part of the complex output signal (real)

Output2

Imaginary part of the complex output signal (real)


 

Notes

1. This model updates the filter coefficients of the equalizer based on the input signal and the error signal (i.e., the difference between the output of the equalizer and the actual desired out­put). The update is based on minimizing the mean square error.

2. Let X(n) and h(n) denote the complex input signal vector and the vector of the complex filter coefficients respectively at time instant n. Each vector is assumed to be of length NTAPS (i.e., number of filter taps). The update of the filter coefficients is done according to

h(n+1) = h(n) + DELTA * e(n) * conj(X(n))

where: conj(X(n)) is the complex conjugate of the vector X(n) and e(n) = d(n) - y(n), where
d(n) is the desired output and y(n) is the equalizer output at time instant n.

3. The complex output of the equalizer at instant n + 1 is given by
y(n+1) = transpose(X(n+1)) * h(n+1)

4. The following initial conditions are always assumed:
h(-1) = 0, X(-1) = 0

Netlist Form

CLMSE:NAME n1 n2 n3 n4 n5 n6 NTAPS=val DELTA=val [RIN1=val] [RIN2=val] [RIN3=val] [RIN4=val] [ROUT1=val] [ROUT2=val]

Netlist Example

CLMSE:1 1 2 3 4 5 6 NTAPS=6 DELTA=.005

References

1. G. Proakis, Digital Communications, McGraw-Hill, 1989.

2. G. Proakis and D. G. Manolakis, Digital Signal Processing, Macmillan, 1988.




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