Documentation

# M-PAM Demodulator Baseband

Demodulate PAM-modulated data

## Library

AM, in Digital Baseband sublibrary of Modulation

## Description

The M-PAM Demodulator Baseband block demodulates a signal that was modulated using M-ary pulse amplitude modulation. The input is a baseband representation of the modulated signal.

The signal constellation has M points, where M is the M-ary number parameter. M must be an even integer. The block scales the signal constellation based on how you set the Normalization method parameter. For details on the constellation and its scaling, see the reference page for the M-PAM Modulator Baseband block.

This block accepts a scalar or column vector input signal. For information about the data types each block port supports, see Supported Data Types.

### Note

All values of power assume a nominal impedance of 1 ohm.

### Integer-Valued Signals and Binary-Valued Signals

When you set the Output type parameter to `Integer`, the block outputs integer values between `0` and M-`1`. M represents the M-ary number block parameter.

When you set the Output type parameter to `Bit`, the block outputs binary-valued signals that represent integers. The block represents each integer using a group of K = log2(M) bits, where K represents the number of bits per symbol. The output vector length must be an integer multiple of K.

The Constellation ordering parameter indicates how the block assigns binary words to points of the signal constellation. More details are on the reference page for the M-PAM Modulator Baseband block.

## Algorithm

The demodulator algorithm maps received input signal constellation values to M-ary integer symbol indices between 0 and M-1 and then maps these demodulated symbol indices to formatted output values.

The integer symbol index computation is performed by first scaling the real part of the input signal constellation (possibly with noise) by a denormalization factor derived from the Normalization method and related parameters. This denormalized value is added to M-1 to translate it into an approximate range between 0 and 2 x (M-1) plus noise. The resulting value is then rescaled via a divide-by-two (or, equivalently, a right-shift by one bit for fixed-point operation) to obtain a range approximately between 0 and M-1 (plus noise). The noisy index value is rounded to the nearest integer and clipped, via saturation, to the exact range of [0 M-1]. Finally, based on other block parameters, the integer index is mapped to a symbol value that is formatted and cast to the selected Output data type.

The following figures contains signal flow diagrams for floating-point and fixed-point algorithm operation. The floating-point diagrams apply when the input signal data type is `double` or `single`. The fixed-point diagrams apply when the input signal is a signed fixed-point data type. Note that the diagram is simplified when using normalized constellations (i.e., denormalization factor is 1).

Signal-Flow Diagrams with Denormalization Factor Equal to 1

Signal-Flow Diagrams with Nonunity Denormalization Factor

## Parameters

M-ary number

The number of points in the signal constellation. It must be an even integer.

Output type

Determines whether the output consists of integers or groups of bits. If this parameter is set to `Bit`, then the M-ary number parameter must be 2K for some positive integer K.

Constellation ordering

Determines how the block maps each integer to a group of output bits.

Normalization method

Determines how the block scales the signal constellation. Choices are `Min. distance between symbols`, `Average Power`, and ```Peak Power```.

Minimum distance

The distance between two nearest constellation points. This field appears only when Normalization method is set to `Min. distance between symbols`.

Average power, referenced to 1 ohm (watts)

The average power of the symbols in the constellation, referenced to 1 ohm. This field appears only when Normalization method is set to `Average Power`.

Peak power, referenced to 1 ohm (watts)

The maximum power of the symbols in the constellation, referenced to 1 ohm. This field appears only when Normalization method is set to `Peak Power`.

Output

When the parameter is set to ```'Inherit via internal rule'``` (default setting), the block will inherit the output data type from the input port. The output data type will be the same as the input data type if the input is of type `single` or `double`. Otherwise, the output data type will be as if this parameter is set to ```'Smallest unsigned integer'```.

When the parameter is set to ```'Smallest unsigned integer'```, the output data type is selected based on the settings used in the Hardware Implementation pane of the Configuration Parameters dialog box of the model. If `ASIC/FPGA` is selected in the Hardware Implementation pane, the output data type is the ideal minimum size, i.e., `ufix(1)` for bit outputs, and `ufix(ceil(log2(M)))` for integer outputs. For all other selections, it is an unsigned integer with the smallest available word length large enough to fit the ideal minimum size, usually corresponding to the size of a char (e.g., `uint8`).

For integer outputs, this parameter can be set to ```Smallest unsigned integer```, `int8`, `uint8`, `int16`, `uint16`, `int32`, `uint32`, `single`, and `double`. For bit outputs, the options are `Smallest unsigned integer`, `int8`, `uint8`, `int16`, `uint16`, `int32`, `uint32`, `boolean`, `single`, or `double`.

Denormalization factor

This parameter applies when a fixed-point input is not normalized. It can be set to `Same word length as input` or ```Specify word length```, in which case a field is enabled for user input. A best-precision fraction length is always used.

Product output

This parameter only applies when the input is a fixed-point signal and there is a nonunity (not equal to 1) denormalized factor. It can be set to `Inherit via internal rule` or ```Specify word length```, which enables a field for user input.

Setting to `Inherit via internal rule` computes the full-precision product word length and fraction length. Internal Rule for Product Data Types (DSP System Toolbox) in DSP System Toolbox™ User's Guide describes the full-precision Product output internal rule.

Setting to `Specify word length` allows you to define the word length. The block computes a best-precision fraction length based on the word length specified and the pre-computed worst-case (min/max) real world value Product output result. The worst-case Product output result is precomputed by multiplying the denormalized factor with the worst-case (min/max) input signal range, purely based on the input signal data type.

The block uses the Rounding method when the result of a fixed-point calculation does not map exactly to a number representable by the data type and scaling storing the result. For more information, see Rounding Modes (DSP System Toolbox) or Rounding Mode: Simplest (Fixed-Point Designer).

Sum

This parameter only applies when the input is a fixed-point signal. It can be set to `Inherit via internal rule`, ```Same as product output```, or `Specify word length`, in which case a field is enabled for user input

Setting `Inherit via internal rule` computes the full-precision sum word length and fraction length, based on the two inputs to the Sum in the fixed-point Hard Decision Algorithm signal flow diagram. The rule is the same as the fixed-point inherit rule of the internal Accumulator data type parameter in the Simulink® Sum block.

Setting `Specify word length` allows you to define the word length. A best precision fraction length is computed based on the word length specified in the pre-computed maximum range necessary for the demodulated algorithm to produce accurate results. The signed fixed-point data type that has the best precision fully contains the values in the range 2 * (M-1) for the specified word length.

Setting to `Same as product output` allows the Sum data type to be the same as the Product output data type (when Product output is used). If the Product output is not used, then this setting will be ignored and the `Inherit via internal rule` Sum setting will be used.

## Supported Data Types

PortSupported Data Types

Input

• Double-precision floating point

• Single-precision floating point

• Signed fixed-point

Output

• Double-precision floating point

• Single-precision floating point

• Boolean when Output type is `Bit`

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

• ufix(1) in ASIC/FPGA when Output type is `Bit`

• $ufix\left(⌈{\mathrm{log}}_{2}M⌉\right)$ in ASIC/FPGA when Output type is `Integer`

## Pair Block

M-PAM Modulator Baseband