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# comm.RectangularQAMDemodulator System object

Package: comm

Demodulate using rectangular QAM signal constellation

## Description

The RectangularQAMDemodulator object demodulates a signal that was modulated using quadrature amplitude modulation with a constellation on a rectangular lattice.

To demodulate a signal that was modulated using quadrature amplitude modulation:

1. Define and set up your rectangular QAM demodulator object. See Construction.

2. Call step to demodulate the signal according to the properties of comm.RectangularQAMDemodulator. The behavior of step is specific to each object in the toolbox.

## Construction

H = comm.RectangularQAMDemodulator creates a demodulator System object™, H. This object demodulates the input signal using the rectangular quadrature amplitude modulation (QAM) method.

H = comm.RectangularQAMDemodulator(Name,Value) creates a rectangular QAM demodulator object, H, with each specified property set to the specified value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

H = comm.RectangularQAMDemodulator(M,Name,Value) creates a rectangular QAM demodulator object, H. This object has the ModulationOrder property set to M, and the other specified properties set to the specified values.

## Properties

 ModulationOrder Number of points in signal constellation Specify the number of points in the signal constellation as scalar value with a positive, integer power of two. The default is 16. PhaseOffset Phase offset of constellation Specify the phase offset of the signal constellation, in radians, as a real scalar value. The default is 0. BitOutput Output data as bits Specify whether the output consists of groups of bits or integer symbol values. When you set this property to true the step method outputs a column vector of bit values whose length equals log2(ModulationOrder) times the number of demodulated symbols. When you set this property to false, the step method outputs a column vector with a length equal to the input data vector. This vector contains integer symbol values between 0 and ModulationOrder-1. The default is false. SymbolMapping Constellation encoding Specify how the object maps an integer or group of log2(ModulationOrder) bits to the corresponding symbol as one of Binary | Gray | Custom. The default is Gray. When you set this property to Gray, the object uses a Gray-coded signal constellation. When you set this property to Binary, the object uses a natural binary-coded constellation. When you set this property to Custom, the object uses the signal constellation defined in the CustomSymbolMapping property. CustomSymbolMapping Custom constellation encoding Specify a custom constellation symbol mapping vector. The default is 0:15. This property is a row or column vector with a size of ModulationOrder and with unique integer values in the range [0, ModulationOrder-1]. The values must be of data type double. The first element of this vector corresponds to the top-leftmost point of the constellation, with subsequent elements running down column-wise, from left to right. The last element corresponds to the bottom-rightmost point. This property applies when you set the SymbolMapping property to Custom. NormalizationMethod Constellation normalization method Specify the method used to normalize the signal constellation as Minimum distance between symbols | Average power | Peak power. The default is Minimum distance between symbols. MinimumDistance Minimum distance between symbols Specify the distance between two nearest constellation points as a positive, real, numeric scalar value. The default is 2. This property applies when you set the NormalizationMethod property to Minimum distance between symbols. AveragePower Average power of constellation Specify the average power of the symbols in the constellation as a positive, real, numeric scalar value. The default is 1. This property applies when you set the NormalizationMethod property to Average power. PeakPower Peak power of constellation Specify the maximum power of the symbols in the constellation as a positive, real, numeric scalar value. The default is 1. This property applies when you set the NormalizationMethod property to Peak power. DecisionMethod Demodulation decision method Specify the decision method the object uses as Hard decision | Log-likelihood ratio | Approximate log-likelihood ratio. The default is Hard decision. When you set the BitOutput property to false the object always performs hard-decision demodulation. This property applies when you set the BitOutput property to true. VarianceSource Source of noise variance Specify the source of the noise variance as Property | Input port. The default is Property. This property applies when you set the BitOutput property to true and the DecisionMethod property to Log-likelihood ratio or Approximate log-likelihood ratio. Variance Noise variance Specify the variance of the noise as a positive, real scalar value. The default is 1. If this value is very small (i.e., SNR is very high), log-likelihood ratio (LLR) computations may yield Inf or -Inf. This result occurs because the LLR algorithm computes the exponential of very large or very small numbers using finite-precision arithmetic. In such cases, using approximate LLR is recommended because its algorithm does not compute exponentials. This property applies when you set the BitOutput property to true, the DecisionMethod property to Log-likelihood ratio or Approximate log-likelihood ratio, and the VarianceSource property to Property. This property is tunable. OutputDataType Data type of output Specify the output data type as Full precision | Smallest unsigned integer | double | single | int8 | uint8 | int16 | uint16 | int32 | uint32. The default is Full precision. This property applies only when you set the BitOutput property to false or when you set the BitOutput property to true and the DecisionMethod property to Hard decision. In this case, when the OutputDataType property is set to Full precision, and the input data type is single- or double-precision, the output data has the same data type as the input. When the input data is of a fixed-point type, the output data type behaves as if you had set the OutputDataType property to Smallest unsigned integer. When you set the BitOutput property to true and the DecisionMethod property to Hard Decision, then logical data type becomes a valid option. When you set the BitOutput property to true and the DecisionMethod property to Log-likelihood ratio or Approximate log-likelihood ratio, the output data type is the same as that of the input. In this case, that data type can only be single- or double-precision.

## Methods

 clone Create rectangular QAM demodulator object with same property values constellation Calculate or plot ideal signal constellation getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs from step method isLocked Locked status for input attributes and nontunable properties release Allow property value and input characteristics changes step Demodulate using rectangular QAM method

## Examples

expand all

### Modulate and Demodulate Data Using 16-QAM

This example shows how to modulate and demodulate data using 16-QAM modulation.

Create rectangular QAM modulator and demodulator objects with the modulation order set to 16.

```hMod = comm.RectangularQAMModulator('ModulationOrder',16);
hDemod = comm.RectangularQAMDemodulator('ModulationOrder',16);
```

Create an AWGN channel object.

```hAWGN = comm.AWGNChannel('EbNo',2,'BitsPerSymbol',4);
```

To track the number of errors, create an error rate counter object.

```hError = comm.ErrorRate;
```

Set the random number generator to its default state to ensure repeatability.

```rng default
```

Generate random data symbols and apply 16-QAM modulation.

```dataIn = randi([0 15],10000,1);
txSig = step(hMod,dataIn);
```

Pass the modulated data through the AWGN channel.

```rxSig = step(hAWGN,txSig);
```

Display the noisy constellation using the scatterplot function.

```scatterplot(rxSig)
```

```dataOut = step(hDemod,rxSig);
```

Using the step function of hError, calculate the error statistics.

```errorStats = step(hError,dataIn,dataOut);
```

Display the error statistics, where you can observe that 8 errors were recorded in 10,000 transmitted symbols.

```fprintf('\nError rate = %f\nNumber of errors = %d\nNumber of symbols = %d\n', ...
errorStats)
```
```Error rate = 0.000800
Number of errors = 8
Number of symbols = 10000
```

## Algorithms

This object implements the algorithm, inputs, and outputs described on the Rectangular QAM Demodulator Baseband block reference page. The object properties correspond to the block parameters.