Communications Toolbox™ provides sinks and display devices that facilitate analysis of communication system performance. You can implement devices using either System objects, blocks, or functions.

You can use blocks or functions to generate random data to simulate a signal source. In addition, you can use Simulink blocks such as the Random Number block as a data source. You can open the Random Data Sources sublibrary by double-clicking its icon (found in the Comm Sources library of the main Communications Toolbox block library).

The `randsrc`

function generates random matrices whose entries are
chosen independently from an alphabet that you specify, with a distribution that you
specify. A special case generates bipolar matrices.

For example, the command below generates a 5-by-4 matrix whose entries are independently chosen and uniformly distributed in the set {1,3,5}. (Your results might vary because these are random numbers.)

a = randsrc(5,4,[1,3,5]) a = 3 5 1 5 1 5 3 3 1 3 3 1 1 1 3 5 3 1 1 3

If you want 1 to be twice as likely to occur as either 3 or 5, use the command below
to prescribe the skewed distribution. The third input argument has two rows, one of which
indicates the possible values of `b`

and the other indicates the
probability of each value.

b = randsrc(5,4,[1,3,5; .5,.25,.25]) b = 3 3 5 1 1 1 1 1 1 5 1 1 1 3 1 3 3 1 3 1

In MATLAB, the `randi`

function generates random integer matrices
whose entries are in a range that you specify. A special case generates random binary
matrices.

For example, the command below generates a 5-by-4 matrix containing random integers between 2 and 10.

c = randi([2,10],5,4) c = 2 4 4 6 4 5 10 5 9 7 10 8 5 5 2 3 10 3 4 10

If your desired range is [0,10] instead of [2,10], you can use either of the commands below. They produce different numerical results, but use the same distribution.

d = randi([0,10],5,4); e = randi([0 10],5,4);

In Simulink^{®}, the Random Integer Generator and Poisson
Integer Generator blocks both generate vectors containing random nonnegative
integers. The Random Integer Generator block uses a uniform distribution on a bounded
range that you specify in the block mask. The Poisson Integer Generator block uses a
Poisson distribution to determine its output. In particular, the output can include any
nonnegative integer.

In MATLAB^{®}, the `randerr`

function generates matrices whose entries
are either 0 or 1. However, its options are different from those of
`randi`

, because `randerr`

is meant for testing
error-control coding. For example, the command below generates a 5-by-4 binary matrix,
where each row contains exactly one 1.

f = randerr(5,4) f = 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0

You might use such a command to perturb a binary code that consists of five four-bit
codewords. Adding the random matrix `f`

to your code matrix (modulo 2)
introduces exactly one error into each codeword.

On the other hand, to perturb each codeword by introducing one error with probability 0.4 and two errors with probability 0.6, use the command below instead.

```
% Each row has one '1' with probability 0.4, otherwise two '1's
g = randerr(5,4,[1,2; 0.4,0.6])
g =
0 1 1 0
0 1 0 0
0 0 1 1
1 0 1 0
0 1 1 0
```

The probability matrix that is the third argument of `randerr`

affects only the *number* of 1s in each row, not their
placement.

As another application, you can generate an equiprobable binary 100-element column
vector using any of the commands below. The three commands produce different numerical
outputs, but use the same *distribution*. The third input arguments
vary according to each function's particular way of specifying its behavior.

binarymatrix1 = randsrc(100,1,[0 1]); % Possible values are 0,1. binarymatrix2 = randi([0 1],100,1); % Two possible values binarymatrix3 = randerr(100,1,[0 1;.5 .5]); % No 1s, or one 1

In Simulink, the Bernoulli Binary Generator block generates random bits and is suitable for representing sources. The block considers each element of the signal to be an independent Bernoulli random variable. Also, different elements need not be identically distributed.

Construct noise generator blocks in Simulink to simulate communication links.

You can construct random noise generators to simulate channel noise by using the MATLAB Function block with random number generating functions. Construct different types of channel noise by using the following combinations.

Distribution | Block | Function |
---|---|---|

Gaussian | MATLAB Function | `randn` |

Rayleigh | MATLAB Function | `randn` |

Rician | MATLAB Function | `randn` |

Uniform on a bounded interval | MATLAB Function | `rand` |

See Random Noise Generators for an example of how Rayleigh and Rician distributed noise is created.

In MATLAB, the `wgn`

function generates random matrices using a white
Gaussian noise distribution. You specify the power of the noise in either dBW (decibels
relative to a watt), dBm, or linear units. You can generate either real or complex
noise.

For example, the command below generates a column vector of length 50 containing real white Gaussian noise whose power is 2 dBW. The function assumes that the load impedance is 1 ohm.

y1 = wgn(50,1,2);

To generate complex white Gaussian noise whose power is 2 watts, across a load of 60 ohms, use either of the commands below.

y2 = wgn(50,1,2,60,'complex','linear'); y3 = wgn(50,1,2,60,'linear','complex');

To send a signal through an additive white Gaussian noise channel, use the `awgn`

function. See AWGN Channel for more information.

You can use blocks in the Sequence Generators sublibrary of the Communications Sources library to generate sequences for spreading or synchronization in a communication system. You can open the Sequence Generators sublibrary by double-clicking its icon in the main Communications Toolbox block library.

Blocks in the Sequence Generators sublibrary generate

The following table lists the blocks that generate pseudorandom or pseudonoise (PN) sequences. The applications of these sequences range from multiple-access spread spectrum communication systems to ranging, synchronization, and data scrambling.

Sequence | Block |
---|---|

Gold sequences | Gold Sequence Generator |

Kasami sequences | Kasami Sequence Generator |

PN sequences | PN Sequence Generator |

All three blocks use shift registers to generate pseudorandom sequences. The following is a schematic diagram of a typical shift register.

All *r* registers in the generator update their values at each time
step according to the value of the incoming arrow to the shift register. The adders
perform addition modulo 2. The shift register can be described by a binary polynomial in
*z*,
g_{r}*z*^{r} +
g_{r-1}*z*^{r-1} + ... +
g_{0}. The coefficient g_{i} is 1 if there is a
connection from the ith shift register to the adder, and 0 otherwise.

The Kasami Sequence Generator block and the PN Sequence Generator block use this
polynomial description for their **Generator polynomial** parameter,
while the Gold Sequence Generator block uses it for the **Preferred polynomial
[1]** and **Preferred polynomial [2]** parameters.

The lower half of the preceding diagram shows how the output sequence can be shifted by a positive integer d, by delaying the output for d units of time. This is accomplished by a single connection along the dth arrow in the lower half of the diagram.

The Barker Code Generator block generates Barker codes to perform synchronization. Barker codes are subsets of PN sequences. They are short codes, with a length at most 13, which are low-correlation sidelobes. A correlation sidelobe is the correlation of a codeword with a time-shifted version of itself.

Orthogonal codes are used for spreading to benefit from their perfect correlation properties. When used in multi-user spread spectrum systems, where the receiver is perfectly synchronized with the transmitter, the despreading operation is ideal.

Code | Block |
---|---|

Hadamard codes | Hadamard Code Generator |

OVSF codes | OVSF Code Generator |

Walsh codes | Walsh Code Generator |

The Comm Sinks block library contains scopes for viewing three types of signal plots:

The following table lists the blocks and the plots they generate.

Block Name | Plots |
---|---|

Eye Diagram | Eye diagram of a signal |

Constellation Diagram | Constellation diagram and signal trajectory of a signal |

An eye diagram is a simple and convenient tool for studying the effects of intersymbol interference and other channel impairments in digital transmission. When this software product constructs an eye diagram, it plots the received signal against time on a fixed-interval axis. At the end of the fixed interval, it wraps around to the beginning of the time axis. As a result, the diagram consists of many overlapping curves. One way to use an eye diagram is to look for the place where the eye is most widely opened, and use that point as the decision point when demapping a demodulated signal to recover a digital message.

The Eye Diagram block produces eye diagrams. This block processes discrete-time signals and periodically draws a line to indicate a decision, according to a mask parameter.

Examples appear in View a Sinusoid and View a Modulated Signal.

A constellation diagram of a signal plots the signal's value at its decision points. In the best case, the decision points should be at times when the eye of the signal's eye diagram is the most widely open.

The Constellation Diagram block produces a constellation diagram from discrete-time signals. An example appears in View a Sinusoid.

A signal trajectory is a continuous plot of a signal over time. A signal trajectory differs from a scatter plot in that the latter displays points on the signal trajectory at discrete intervals of time.

The Constellation Diagram block produces signal
trajectories. The Constellation Diagram block produces signal trajectories
when the `ShowTrajectory`

property is set to true. A signal trajectory
connects all points of the input signal, irrespective of the specified decimation factor
(`Samples per symbol`

)

The following model produces a constellation diagram and an eye diagram from a complex sinusoidal signal. Because the decision time interval is almost, but not exactly, an integer multiple of the period of the sinusoid, the eye diagram exhibits drift over time. More specifically, successive traces in the eye diagram and successive points in the scatter diagram are near each other but do not overlap.

To open the model, enter
`doc_eyediagram`

at the MATLAB command line. To build the model, gather and configure these blocks:

Sine Wave, in the Sources library of the DSP System Toolbox™ (

*not*the Sine Wave block in the Simulink Sources library)Set

**Frequency**to`.502`

.Set

**Output complexity**to`Complex`

.Set

**Sample time**to`1/16`

.

Constellation Diagram, in the Comm Sinks library

On the

**Constellation Properties**panel, set**Samples per symbol**to`16`

.

Eye Diagram, in the Comm Sinks library

On the

**Plotting Properties**panel, set**Samples per symbol**to`16`

.On the

**Figure Properties**panel, set**Scope position**to`figposition([42.5 55 35 35]);`

.

Connect the blocks as shown in the preceding figure. From the model window's
**Simulation** menu, choose **Model Configuration
parameters**. In the **Configuration Parameters** dialog box,
set **Stop time** to `250`

. Running the model produces the
following scatter diagram plot.

The points of the scatter plot lie on a circle of radius 1. Note that the points fade as
time passes. This is because the box next to **Color fading** is checked
under **Rendering Properties**, which causes the scope to render points
more dimly the more time that passes after they are plotted. If you clear this box, you see
a full circle of points.

The Constellation Diagram block displays a circular trajectory.

In the eye diagram, the upper set of traces represents the real part of the signal and the lower set of traces represents the imaginary part of the signal.

This multipart example creates an eye diagram, scatter plot, and signal trajectory plot for a modulated signal. It examines the plots one by one in these sections:

The following model modulates a random signal using QPSK, filters the signal with a raised cosine filter, and creates an eye diagram from the filtered signal.

To open the model, enter
`doc_signaldisplays`

at the MATLAB command line. To build the model, gather and configure the following
blocks:

Random Integer Generator, in the Random Data Sources sublibrary of the Comm Sources library

Set

**M-ary number**to`4`

.Set

**Sample time**to`0.01`

.

QPSK Modulator Baseband, in PM in the Digital Baseband sublibrary of the Modulation library of Communications Toolbox, with default parameters

AWGN Channel, in the Channels library of Communications Toolbox, with the following changes to the default parameter settings:

Set

**Mode**to`Signal-to-noise ratio (SNR)`

.Set

**SNR (dB)**to`15`

.

Raised Cosine Transmit Filter, in the Comm Filters library

Set

**Filter shape**to`Normal`

.Set

**Rolloff factor**to`0.5`

.Set

**Filter span in symbols**to`6`

.Set

**Output samples per symbol**to`8`

.Set

**Input processing**to`Elements as channels (sample based)`

.

Eye Diagram, in the Comm Sinks library

Set

**Samples per symbol**to`8`

.Set

**Symbols per trace**to`3`

. This specifies the number of symbols that are displayed in each trace of the eye diagram. A*trace*is any one of the individual lines in the eye diagram.Set

**Traces displayed**to`3`

.Set

**New traces per display**to`1`

. This specifies the number of new traces that appear each time the diagram is refreshed. The number of traces that remain in the diagram from one refresh to the next is**Traces displayed**minus**New traces per display**.On the

**Rendering Properties**panel, set**Markers**to`+`

to indicate the points plotted at each sample. The default value of**Markers**is empty, which indicates no marker.On the

**Figure Properties**panel, set**Eye diagram to display**to`In-phase only`

.

When you run the model, the Eye Diagram displays the following diagram. Your exact image varies depending on when you pause or stop the simulation.

Three traces are displayed. Traces 2 and 3 are faded because **Color
fading** under **Rendering Properties** is selected. This
causes traces to be displayed less brightly the older they are. In this picture, Trace 1
is the most recent and Trace 3 is the oldest. Because **New traces per
display** is set to `1`

, only Trace 1 is appearing for the
first time. Traces 2 and 3 also appear in the previous display.

Because **Symbols per trace** is set to `3`

, each
trace contains three symbols, and because **Samples per trace** is set to
`8`

, each symbol contains eight samples. Note that trace 1 contains 24
points, which is the product of **Symbols per trace** and
**Samples per symbol**. However, traces 2 and 3 contain 25 points each.
The last point in trace 2, at the right border of the scope, represents the same sample as
the first point in trace 1, at the left border of the scope. Similarly, the last point in
trace 3 represents the same sample as the first point in trace 2. These duplicate points
indicate where the traces would meet if they were displayed side by side, as illustrated
in the following picture.

You can view a more realistic eye diagram by changing the value of **Traces
displayed** to `40`

and clearing the **Markers
**field.

When the **Offset** parameter is set to `0`

, the
plotting starts at the center of the first symbol, so that the open part of the eye
diagram is in the middle of the plot for most points.

The following model creates a scatter plot of the same signal considered in Eye Diagram of a Modulated Signal.

To build the model, follow the instructions in Eye Diagram of a Modulated Signal but replace the Eye Diagram block with the following block:

Constellation Diagram, in the Communications Toolbox/Comm Sinks library

Set

**Samples per symbol**to`2`

Set

**Offset**to`0`

. This specifies the number of samples to skip before plotting the first point.Set

**Symbols to display**to`40`

.

When you run the simulation, the Constellation Diagram block displays the following plot.

The plot displays 30 points. Because **Color fading** under
**Rendering Properties** is selected, points are displayed less
brightly the older they are.

The following model creates a signal trajectory plot of the same signal considered in Eye Diagram of a Modulated Signal.

To build the model, follow the instructions in Eye Diagram of a Modulated Signal but replace the Eye Diagram block with the following block:

Constellation Diagram , in the Communications Toolbox/Comm Sinks library

Set

**Samples per symbol**to`8`

.Set

**Symbols to display**to`40`

. This specifies the number of symbols displayed in the signal trajectory. The total number of points displayed is the product of**Samples per symbol**and**Symbols to display**.

When you run the model, the Constellation Diagram displays a trajectory like the one below.

The plot displays 40 symbols. Because **Color fading** under
**Rendering Properties** is selected, symbols are displayed less
brightly the older they are.

See Constellation Diagram of a Modulated Signal to compare the preceding signal trajectory to the scatter plot of the same signal. The Constellation Diagram block connects the points displayed by the Constellation Diagram block to display the signal trajectory.

If you increase **Symbols to display** to `100`

, the
model produces a signal trajectory like the one below. The total number of points
displayed at any instant is 800, which is the product of the parameters **Samples
per symbol** and **Symbols to display**.