# DFECDR

Decision feedback equalizer (DFE) with clock and data recovery (CDR)

**Library:**SerDes Toolbox / Datapath Blocks

## Description

The DFECDR block adaptively processes a sample-by-sample input signal or analytically processes an impulse response vector input signal to remove distortions at post cursor taps.

The DFE modifies baseband signals to minimize the intersymbol interference (ISI) at the clock sampling times. The DFE samples data at each clock sample time and adjusts the amplitude of the waveform by a correction voltage.

For impulse response processing, the hula-hoop algorithm is used to find the clock
sampling locations. The zero-forcing algorithm is then used to determine the
*N* correction factors necessary to have no ISI at the *N*
subsequent sampling locations, where *N* is the number of DFE taps.

For sample-by-sample processing, the clock recovery is accomplished by a first order phase
tracking model. The bang-bang phase detector utilizes the unequalized edge samples and
equalized data samples to determine the optimum sampling location. The DFE correction voltage
for the *N*-th tap is adaptively found by finding a voltage that compensates
for any correlation between two data samples spaced by *N* symbol times. This
requires a data pattern that is uncorrelated with the channel ISI for correct adaptive
behavior.

## Ports

### Input

`WaveIn`

— Input baseband signal

scalar | vector

Input baseband signal. The input signal can be a sample-by-sample signal specified as a scalar, or an impulse response vector signal.

**Data Types: **`double`

### Output

`WaveOut`

— Estimated channel output

scalar | vector

Estimated channel output. If the input signal is a sample-by-sample signal specified as a scalar, the output is also scalar. If the input signal is an impulse response vector signal, the output is also a vector.

**Data Types: **`double`

## Parameters

### DFE

`Mode`

— DFE operating mode

`Adapt`

(default) | `Off`

| `Fixed`

DFE operating mode:

`Off`

— DFECDR is bypassed and the input waveform remains unchanged.`Fixed`

— DFECDR applies the input DFE tap weights specified in**Initial tap weights (V)**to the input waveform.`Adapt`

— The Init subsystem calls to the DFECDR System object™. The DFECDR System object finds the optimum DFE tap values for the best eye height opening for statistical analysis. During time domain simulation, DFECDR uses the adapted values as the starting point and applies them to the input waveform. For more information about the Init subsystem, see Statistical Analysis in SerDes Systems.

#### Programmatic Use

Use

`get_param(gcb,'Mode')`

to view the current DFECDR**Mode**.Use

`set_param(gcb,'Mode',value)`

to set DFECDR to a specific**Mode**.

`Initial tap weights (V)`

— Initial DFE tap weights

`[0 0 0 0]`

(default) | row vector

Initial DFE tap weights, specified as a row vector in volts. The length of the vector specifies the number of DFE taps. The vector element value specifies the strength of the tap at that element position. Setting a vector element value to zero only initializes the tap.

You can use a valid MATLAB expression to evaluate the **Initial tap
weights (V)** row vector.

**Example: **`set_param(gcb,'TapWeights',"zeros(1,100)")`

creates a
DFE with 100 taps.

#### Programmatic Use

Use

`get_param(gcb,'TapWeights')`

to view the current value of DFECDR**Initial tap weights (V)**.Use

`set_param(gcb,'TapWeights',value)`

to set DFECDR to a specific**Initial tap weights (V)**vector value.

**Data Types: **`double`

`Adaptive gain`

— Controls DFE tap weight update rate

`9.6e-5`

(default) | positive real scalar

Controls DFE tap weight update rate, specified as a unitless positive real scalar.
Increasing the value of **Adaptive gain** leads to a faster
convergence of DFE adaptation at the expense of more noise in DFE tap values.

#### Programmatic Use

Use

`get_param(gcb,'EqualizationGain')`

to view the current DFECDR**Adaptive gain**value.Use

`set_param(gcb,'EqualizationGain',value)`

to set DFECDR to a specific value of**Adaptive gain**.

**Data Types: **`double`

`Adaptive step size (V)`

— DFE adaptive step resolution

`1e-06`

(default) | nonnegative real scalar | nonnegative real-valued row vector

DFE adaptive step resolution, specified as a nonnegative real scalar or a
nonnegative real-valued row vector in volts. Specify as a scalar to apply to all the
DFE taps or as a vector that has the same length as the **Initial tap weights
(V)**.

**Adaptive step size (V)** specifies the minimum DFE tap change
from one time step to the next to mimic hardware limitations. Setting
**Adaptive step size (V)** to `0`

yields DFE tap
values without any resolution limitation.

#### Programmatic Use

Use

`get_param(gcb,'EqualizationStep')`

to view the current DFECDR**Adaptive step size (V)**value.Use

`set_param(gcb,'EqualizationStep',value)`

to set DFECDR to a specific value of**Adaptive step size (V)**.

**Data Types: **`double`

`Minimum DFE tap value (V)`

— Minimum value of adapted taps

`-1`

(default) | real scalar | real-valued row vector

Minimum value of the adapted taps, specified as a real scalar or a real-valued row
vector in volts. Specify as a scalar to apply to all the DFE taps or as a vector that
has the same length as the **Initial tap weights (V)**.

#### Programmatic Use

Use

`get_param(gcb,'MinimumTap')`

to view the current DFECDR**Minimum DFE tap value (V)**value.Use

`set_param(gcb,'MinimumTap',value)`

to set DFECDR to a specific value of**Minimum DFE tap value (V)**.

**Data Types: **`double`

`Maximum DFE tap value (V)`

— Maximum value of adapted taps

`1`

(default) | nonnegative real scalar | nonnegative real-valued row vector

Maximum value of the adapted taps, specified as a nonnegative real scalar or a
nonnegative real-valued row vector in volts. Specify as a scalar to apply to all the
DFE taps or as a vector that has the same length as the **Initial tap weights
(V)**.

#### Programmatic Use

Use

`get_param(gcb,'MaximumTap')`

to view the current DFECDR**Maximum DFE tap value (V)**value.Use

`set_param(gcb,'MaximumTap',value)`

to set DFECDR to a specific value of**Maximum DFE tap value (V)**.

**Data Types: **`double`

`2x tap weights`

— Multiply DFE tap weights by a factor of two

off (default) | on

Select to multiply the DFE tap weights by a factor of two.

The output of the slicer in the DFECDR block from the SerDes Toolbox™ is [-0.5 0.5]. But some industry applications require the slicer output
to be [-1 1]. **2x tap weights** allows you to quickly double the DFE
tap weights to change the slicer reference.

### CDR

`Phase offset (symbol time)`

— Manual clock phase offset

`0`

(default) | real scalar in the range [−0.5, 0.5]

Manual clock phase offset to move the recovered clock phase, specified as a real
scalar in the range [-0.5, 0.5] in the fraction of symbol time. **Phase offset
(symbol time)** is used to manually shift the clock probability
distribution function (PDF) for a better bit error rate (BER).

#### Programmatic Use

Use

`get_param(gcb,'PhaseOffset')`

to view the current DFECDR**Phase offset (symbol time)**value.Use

`set_param(gcb,'PhaseOffset',value)`

to set DFECDR to a specific value of**Phase offset (symbol time)**.

**Data Types: **`double`

`Reference offset (ppm)`

— Reference clock offset impairment

`0`

(default) | real scalar in the range [−300, 300]

Reference clock offset impairment, specified as a real scalar in the range [−300,
300] in parts per million (ppm). **Reference offset (ppm)** is the
deviation between transmitter oscillator frequency and receiver oscillator
frequency.

#### Programmatic Use

Use

`get_param(gcb,'ReferenceOffset')`

to view the current DFECDR**Reference offset (ppm)**value.Use

`set_param(gcb,'ReferenceOffset',value)`

to set DFECDR to a specific value of**Reference offset (ppm)**.

**Data Types: **`double`

`Early/late count threshold`

— Early or late CDR count threshold to trigger phase update

`16`

(default) | positive real integer ≥5

Early or late CDR count threshold to trigger a phase update, specified as a
unitless positive real integer ≥5. Increasing the value of **Early/late count
threshold** provides a more stable output clock phase at the expense of
convergence speed. Because the bit decisions are made at the clock phase output, a
more stable clock phase has a better bit error rate (BER).

**Early/late count threshold** also controls the bandwidth of the
CDR, which is approximately calculated by using the equation:

$$\text{Bandwidth}=\frac{1}{\text{Symboltime}\xb7\text{Early/latethresholdcount}\xb7\text{Step}}$$

#### Programmatic Use

Use

`get_param(gcb,'Count')`

to view the current DFECDR**Early/late count threshold**value.Use

`set_param(gcb,'Count',value)`

to set DFECDR to a specific value of**Early/late count threshold**.

**Data Types: **`double`

`Step (symbol time)`

— Clock phase resolution

`0.0078`

(default) | real scalar

Clock phase resolution of the recovered clock, specified as a real scalar in
fraction of symbol time. **Step (symbol time)** is the inverse of the
number of phase adjustments in the CDR. If the CDR has 128 steps of phase adjustment,
the **Step (symbol time)** value is 1/128.

#### Programmatic Use

Use

`get_param(gcb,'ClockStep')`

to view the current DFECDR**Step (symbol time)**value.Use

`set_param(gcb,'ClockStep',value)`

to set DFECDR to a specific value of**Step (symbol time)**.

**Data Types: **`double`

`Sensitivity (V)`

— Sampling latch metastability voltage

`0`

(default) | real scalar

Sampling latch metastability voltage, specified as a real scalar in volts. If the
data sample voltage lies within the region of (±**Sensitivity (V)**),
there is a 50% probability of bit error.

#### Programmatic Use

Use

`get_param(gcb,'Sensitivity')`

to view the current DFECDR**Sensitivity (V)**value.Use

`set_param(gcb,'Sensitivity',value)`

to set DFECDR to a specific value of**Sensitivity (V)**.

**Data Types: **`double`

**IBIS-AMI parameters**

`Mode`

— Include Mode parameter in IBIS-AMI model

on (default) | off

Select to include **Mode** as a parameter in the IBIS-AMI file.
If you deselect **Mode**, it is removed from the AMI files,
effectively hard-coding **Mode** to its current value.

`Tap weights`

— Include Tap weights parameter in IBIS-AMI model

on (default) | off

Select to include **Tap weights** as a parameter in the IBIS-AMI
file. If you deselect **Tap weights**, it is removed from the AMI
files, effectively hard-coding **Tap weights** to its current
value.

`Phase Offset`

— Include Phase Offset parameter in IBIS-AMI model

on (default) | off

Select to include **Phase Offset** as a parameter in the IBIS-AMI
file. If you deselect **Phase Offset**, it is removed from the AMI
files, effectively hard-coding **Phase Offset** to its current
value.

`Reference offset`

— Include Reference offset parameter in IBIS-AMI model

on (default) | off

Select to include **Reference offset** as a parameter in the
IBIS-AMI file. If you deselect **Reference offset**, it is removed
from the AMI files, effectively hard-coding **Reference offset** to
its current value.

**Introduced in R2019a**

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