# Description of Channel Simulation

The ADS Channel Simulator operates in one of two modes chosen by the user:

## Bit-by-Bit Simulation

The bit-by-bit mode computes the response to a specific bit sequence. In this mode, the Channel Simulator relies on linearity and time invariance of linear channels to achieve rapid simulations and high throughput. To understand the principles behind bit-by-bit channel simulation, consider the response p_{n}(t) to an input NRZ pulse r_{n}(t):

Assuming linearity and time invariance, the response to an arbitrary bit pattern

x(t) = Σ

_{n}r_{n}(t-nT_{b})

is given by the superposition of individual pulse responses

y(t) = Σ

_{n}p_{n}(t-nT_{b})

where T_{b} is the bit duration, or UI. The response to pattern 10101000 and pulse superposition are shown in the following figures:

Classical transient simulation results are overlaid on the plot labeled *Pulse superposition* showing a perfect match, as expected.

In bit-by-bit channel simulation the pulse response is obtained, in turn, by superposition of two step responses. The rising and falling edges of the step inputs are modulated by the various jitter components, as specified.

Channel simulation in bit-by-bit mode, therefore, consists of two steps:

- Step characterization

During step characterization, the Channel Simulator invokes the ADS transient/convolution engine for accurate calculation of the system's step response. The simulator automatically detects step response duration, and accounts for the effects of transmit and receive equalizers, if any. - Pulse superposition

In this phase, the simulator adds up individual pulses and passes the output to eye probes for further processing. The simulator repeats this step for every eye probe and every crosstalk driver in the circuit.

## Statistical Simulation

In statistical channel simulation, system properties are derived from statistical calculations and not by brute-force superposition of pulse-reponses. The ADS implementation is based on the principles described in [Ref. 1], with new and proprietary algorithms for accurate treatment of random and periodic jitter, DCD and other effects.

In this mode, the output

y(t) = Σ

_{n}p_{n}(t-nT_{b})

is viewed as a function of random variables b_{k}, where b_{k} is the input bit sequence. At a given time within the bit interval, the probability density function p(y) is computed by statistical calculations, as shown below.

Similar to bit-by-bit mode, statistical simulation consists of two steps:

- Step characterization

During step characterization, the Channel Simulator invokes the ADS transient/convolution engine for accurate calculation of the system's step response. - Statistical calculation

Statistical calculations are used to produce the eye density from the ISI distribution, taking into jitter specification, effects of crosstalk drivers, equalizers, encoding, etc. The Eye Probe component extracts all relevant quantities from the eye density distribution, including bathtubs, BER contours and other eye diagram metrics.

Note

In ADS 2009 Update 1, 8B10B encoding constraints are not applied in the statistical analysis of the Channel Simulator. If statistical simulations are performed on channels with 8B10B encoder, results will be identical to those without encoder.

## Bit-by-bit vs. Statistical Simulations

In the limit as the number of bits increases to infinity, the two channel simulation modes give identical results. Choose Statistical mode if you are interested in accurate simulations down to low BERs. Choose bit-by-bit simulation if you are interested in the response of your system to a specific bit sequence in the TX or crosstalk channel.

In bit-by-bit simulation, DFE/FFE RX equalizers can operate in adaptive mode. Adaptive DFE/FFE are not available in statistical simulation (you can still use DFE/FFE in optimized or any other fixed-tap mode). To look at low-BER statistics with adaptive DFE/FFE, run bit-by-bit simulation and save DFE taps. You can then run statistical simulations by reading in the taps computed at the last time point of a bit-by-bit simulation.

Note that, with the exception of the Waveform measurement, which is available in bit-by-bit only, all Eye_Probe measurements are available in both channel simulation modes, including bathtub and contour plots. Statistical simulation offers more accurate results faster when you wish to calculate BERs down to low levels.

##### References

1. Anthony Sanders, Mike Resso, John D.Ambrosia. *Channel Compliance Testing Utilizing Novel Statistical Eye Methodology*, DesignCon 2004.