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Communications Filters

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Section Overview Filter Features of the Blockset Group Delay of a Filter Filtering with Raised Cosine Filter Blocks Example: Using Raised Cosine Filters Selected Bibliography for Communications Filters

Section Overview

The Comm Filters library includes several blocks that you can use for filtering or pulse shaping (that is, either transmit filtering or receive filtering). These operations are necessary to control bandwidth, intersymbol interference, and signal-to-noise ratio.

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Filter Features of the Blockset

Filtering tasks supported in Communications Blockset include

• Filtering using a raised cosine filter. Raised cosine filters are very commonly used for pulse shaping and matched filtering. The schematic below illustrates two typical uses of raised cosine filters.

  

• Filtering using a Gaussian filter.

• Shaping a signal using ideal rectangular pulses.

• Implementing an integrate-and-dump operation or a windowed integrator. An integrate-and-dump operation is often used in a receiver model when the system's transmitter uses an ideal rectangular-pulse model. Integrate-and-dump can also be used in fiber optics and in spread-spectrum communication systems such as CDMA (code division multiple access) applications.

Other filtering capabilities are in Signal Processing Blockset, in the Filter Designs and Multirate Filters libraries.

For more background information about filters and pulse shaping, see the works listed in Selected Bibliography for Communications Filters.

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Group Delay of a Filter

The raised cosine and Gaussian filter blocks in this library implement realizable filters by delaying the peak response. This delay, known as the filter's group delay, is the length of time between the filter's initial response and its peak response. The filter blocks in this library have a Group delay parameter that is an integer representing the number of symbol periods.

For example, the square root raised cosine filter whose impulse response shown in the following figure uses a Group delay parameter of 4 in the filter block. In the figure, the initial impulse response is small and the peak impulse response occurs at the fourth symbol.

Implications of Delay for Simulations

A filter block's Group delay parameter value has implications for other parts of your model. For example, suppose you compare the symbol streams marked Symbols In and Symbols Out in the schematics in Filter Features of the Blockset by plotting or computing an error rate. Use one of these methods to make sure you are comparing symbols that truly correspond to each other:

• Use the Delay block in Signal Processing Blockset to delay the Symbols In signal, thus aligning it with the Symbols Out signal. Set the Delay parameter equal to the filter's Group delay parameter (or the sum of both values, if your model uses a pair of square root raised cosine filter blocks). This usage is illustrated in the following figure for the case of a pair of square root raised cosine filters.

  

• Use the Align Signals block to align the two signals.

• When using the Error Rate Calculation block to compare the two signals, increase the Receive delay parameter by the Group delay parameter value (or the sum of both values, if your model uses a pair of square root raised cosine filter blocks). The Receive delay parameter might include other delays as well, depending on the contents of your model.

For more information about how to manage delays in a model, see Computing Delays and Manipulating Delays.

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Filtering with Raised Cosine Filter Blocks

The Raised Cosine Transmit Filter and Raised Cosine Receive Filter blocks are designed for raised cosine filtering. Each block can apply a square root raised cosine filter or a normal raised cosine filter to a signal. You can vary the rolloff factor and group delay of the filter.

The Raised Cosine Transmit Filter and Raised Cosine Receive Filter blocks are tailored for use at the transmitter and receiver, respectively. In particular, the transmit filter outputs an upsampled signal, while the receive filter expects its input signal to be upsampled already. Also, the receive filter lets you choose whether to have the block downsample the filtered signal before sending it to the output port.

Both raised cosine filter blocks incur a propagation delay, described in Group Delay of a Filter.

Combining Two Square-Root Raised Cosine Filters

To split the filtering equally between the transmitter's filter and the receiver's filter, use a pair of square root raised cosine filters:

• Use a Raised Cosine Transmit Filter block at the transmitter, setting the Filter type parameter to Square root.

• Use a Raised Cosine Receive Filter block at the receiver, setting the Filter type parameter to Square root. In most cases, it is appropriate to set the Input samples per symbol parameter to match the transmit filter's Upsampling factor parameter.

In theory, the cascade of two square root raised cosine filters is equivalent to a single normal raised cosine filter. However, the limited impulse response of practical square root raised cosine filters causes a slight difference between the response of two cascaded square root raised cosine filters and the response of one raised cosine filter.

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Example: Using Raised Cosine Filters

This example illustrates a typical setup in which a transmitter uses a square root raised cosine filter to perform pulse shaping and the corresponding receiver uses a square root raised cosine filter as a matched filter. The example plots an eye diagram from the filtered received signal.

To open the completed model, click here in the MATLAB Help browser. To build the model, gather and configure these blocks:

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

  • Set M-ary number to 16.

  • Set Sample time to 1/100.

  • Select Frame-based outputs.

  • Set Samples per frame to 100.

• Rectangular QAM Modulator Baseband, in the AM sublibrary of the Digital Baseband sublibrary of Modulation

  • Set Normalization method to Peak Power.

  • Set Peak power to 1.

• Raised Cosine Transmit Filter, in the Comm Filters library

  • Set Group delay to 4.

• AWGN Channel, in the Channels library

  • Set Mode to Signal to noise ratio (SNR).

  • Set SNR to 40.

  • Set Input signal power to 0.0694. The power gain of square root raised cosine transmit filter is , where N represents the upsampling factor of the filter. The input signal power of filter is 0.5556. Because the Peak power of the 16-QAM Rectangular modulator is set to 1 Watt, it translates to an average power of 0.5556. Therefore, the output signal power of filter is .

• Raised Cosine Receive Filter, in the Comm Filters library

  • Set Group delay to 4.

  • Set Rolloff factor to 0.5.

  • Set Output mode to None.

• Discrete-Time Eye Diagram Scope, in the Comm Sinks library

  • Set Symbols per trace to 2.

  • Set Traces displayed to 100.

Connect the blocks as in the figure. Running the simulation produces the following eye diagram. The eye diagram has two widely opened "eyes" that indicate appropriate instants at which to sample the filtered signal before demodulating. This illustrates the absence of intersymbol interference at the sampling instants of the received waveform.

The large signal-to-noise ratio in this example produces a low-noise eye diagram, while the model still illustrates where the raised cosine filter blocks typically belong in relation to a channel block. If you decrease the SNR parameter in the AWGN Channel block, the eyes in the diagram are less open.

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Selected Bibliography for Communications Filters

[1] Proakis, John G., Digital Communications, 3rd ed., New York, McGraw-Hill, 1995.

[2] Rappaport, Theodore S., Wireless Communications: Principles and Practice, Upper Saddle River, NJ, Prentice Hall, 1996.

[3] Sklar, Bernard, Digital Communications: Fundamentals and Applications, Englewood Cliffs, NJ, Prentice Hall, 1988.

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Digital Modulation

Channels

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