SIMULATION TOOLS: The BERGulator

Download the most recent version of the BERGulator (.zip)

(The most recent version of the BERGulator is dated Sun Aug 19 10:08 EDT 2001. It includes .mexlx files for Linux-based systems and a workaround for some Matlab-6 bugs. You may compile the *.c files yourself for other platforms using matlab's "mex" command.)

The BERGulator allows you to specify the channel impulse response coefficients, the level of channel noise, and the source alphabet used for experimentation. The channel may be complex-valued, and complex-valued noise is assumed if either the source or the channel is complex-valued. Furthermore, the channel may be baud-spaced or T/2 fractionally-spaced.

Given such a channel/noise combination, The BERGulator is capable of plotting the frequency/impulse responses of the channel, the MMSE optimal equalizer, and the optimal system (chan+eq). For length-2 real-valued channels, it can also plot contours of the CMA surface in equalizer space (with an overlay of the principle axes of the quadratic-cost ellipsoid approximating the neighborhoods of CM minima, and with *'s and x's indicating the locations of MMSE and MSE minima). When a valid surface is present, The BERGulator can superimpose the CM-error-function sign-boundaries (for real-valued sources) and indicate the magnitude and direction of the (constant) cost-gradient within a given constant-sign region. This feature is motivated by the convergence behavior of signed algorithms.

Finally, the BERGulator can plot the tap-trajectories of an equalizer adaptation algorithm and plot the CM- and mean-squared error histories. When an error surface is present and the tap-trajectories will be real-valued, the user can select the equalizer intialization from the surface and the resulting trajectory will be superimposed on it. For higher-dimensional and/or complex-valued equalizers, the user selects the location of a single/double spike (BSE/FSE) initialization. The equalizer-length, stepsize, and the number of iterations can be varied. Numerous variants of the CMA algorithm are available for experimentation.

After simulation run has completed, the frequency/impulse response of any equalizer along the adaptation history can be displayed. In addition the selected equalizer, the local MMSE equalizer, the corresponding system response and the local MMSE system response are also displayed. If a surface trajectory is present, this equalizer selection is obtained from the surface. If only the coefficient history is present, this equalizer is selected from a selected point in the adaptation history. A round/diamond marker is then placed on graph to indicate a frequency/impulse response analysis.

When parameter changes are made that invalidate the currently displayed frequency/impulse responses or error surface, the offending object is automatically erased. On the contrary, any analyses based on an simulation run is retained (for comparison to other experiments) until the "Clear Traces" button is pressed.

Actions

• CM Cost Surface: Plots contours of the Godard 2-2 cost surface in eq space
• Sign Boundaries: Overlays CM-error-function sign-boundaries on surface
• Facet Gradients: Displays the 2D gradient of the signed-Godard cost surface
• FREQ: Frequency response analysis
• IMP: Impulse response analysis
• Adapt Equalizer: Runs a simulation using the selected parameters
• Clear Traces: Erases all adaptation-based tap/error/freq/imp-rspn traces
• Help: Prints help screen.
• Quit: Quit!

Channel Options

• Channel Type: Offers a choice between preselected channel coefficients, user-selectable ("custom") ones, and ".mat" file input where the coefs must be stored in a vector named "c"
• Source Type: A choice between a number of QAM and PAM source alphabets
• Spacing: T/2 Fractionally-spaced (FS) or Baud-spaced (BS)
• dB SNR: Signal-to-AWGN level in decibels
• Normalize Channel: Normalizes the channel coeficient vector (to unit norm)
• Equal Axes : Forces the surface plot x/y-axes to be equally scaled (unfortunately this interferes with zooming)

Equalizer Algorithms

• CMA: The Godard 2-2 constant modulus algorithm
• N-CMA: Normalized CMA
• SE-CMA: Signed-error CMA (i.e. Godard 1-1)
• SR-CMA: Signed-regressor CMA
• SS-CMA: Signed-error, signed-regressor CMA
• DSE-CMA: Dithered signed-error CMA
• WSGA: "Signed Godard Algorithm" (Weerackody)
• CMA-GD: Godard 2-2 gradient descent (i.e. CMA avg-system behavior)

Algorithm Options

• Eq Len: The number of coefficients in the equalizer
• Init Spike: The T-spaced location of single/double spike initialization for BS/FS equalizers
• Num Iter: The number of (baud-spaced) symbols used in the adaptation
• Trace Color: The color of the trace used to display tap/error histories and frequency/impulse response analysis
• Stepsize: The stepsize used by the coefficient update algorithm
• Error Smooth: The amount of smoothing performed on the CM error history (min = no smoothing)

Misc

• the T/2 implementation samples on "odd" outputs (assume {0,1,2,...}) when the equalizer length is even and "even" outputs when the equalizer length is odd
• all "local-MSE" quantities are calculated based on the delay and phase obtained from the maximum-magnitude entry of the latest simulation's final system response
• the error-trace smoothing uses a 2nd-order butterworth filter all signed CMA algorithms (except WSGA) compute the sign of a complex number as the sign of the real part plus sqrt(-1) times the sign of the imaginary part

Send comments, bug reports, or cold hard cash to schniter@ee.eng.ohio-state.edu.