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Communications EW, part 7 - Bandwidth Required for Digital Signals

Posted on: Sunday, 28 December 2003, 06:00 CST

The frequency spread of digitally modulated radio-frequency (RF) signals has a characteristic shape that depends on the bit rate of the transmitted data. The higher the data rate, the greater the frequency bandwidth required for its transmission.

The Digital-Modulation Frequency Spectrum

Figure 1 is a photograph of the display of a spectrum analyzer receiving a digitally modulated RF signal. It shows the transmitted RF spectrum of the main lobe of a binary-phase-shift-keyed (BPSK) signal between the two nulls at the edges of the picture as it would be displayed on the analyzer. The carrier frequency is at the center of the display, and the characteristic nulls at the edges of the main lobe are clearly shown.

This signal has a Sin X/X frequency pattern. As shown in Figure 2, the main lobe is "twice the bit rate" wide (converted to RF at 1 Hz per bps). The frequency side lobes are half as wide as the main lobe and roll off with frequency distance from the main lobe. Only the main lobe and first side lobes are shown in this figure. The bandwidth of a digital signal is often taken to be between the frequencies at which the main lobe energy is 3-dB below the peak value (at the carrier frequency). However, the shape of the received bits depends on the transmission of higher- frequency components, so more transmission bandwidth may be required.

Spectrum-Expanding Signal Features

It is normally necessary to add synchronizing, address, and parity bits to the digital bit stream, in addition to the basic data carried. These extra bits are called the overhead and are often 10% to 20% of the transmitted signal. The bandwidth of the transmitted signal is determined by the actual transmitted-bit rate, including these extra bits.

It is sometimes appropriate to encode digital data in error- detection and correction (EDC) codes that allow bit errors introduced during transmission to be corrected in the receiver. A typical such code is the 31/15 Reed Solomon code used in the widely employed Link 16 system. This code transmits 31 bytes for each 15 bytes of data passed. Thus, the transmitted-bit rate is more than doubled - proportionally increasing the required transmission bandwidth.

Frequency-Efficient Modulations

Last month we discussed amplitude- shift-keyed (ASK), binary- phase-shiftkeyed (BPSK) and quadriture-phaseshift-keyed (QPSK) modulations (see "Communications EW, Part 6 - RF Modulations for Digital Signals," JED, November 2003, p. 64). These were described only in terms of the way that the modulated signal carries "one" and "zero" values. The modulation is presumed to move very quickly between the two values, which causes significant higher-frequency components to appear in the modulation. This, in turn, causes the side lobes of the frequency spectrum to carry significant energy.

Table 1 : Comparison of the frequency-spread digital-modulation waveforms.

Figure 3 shows two modulations designed to reduce the higher- frequency components, allowing a higher-quality signal to be carried in less bandwidth. The two waveforms shown in the time domain are sinusoidal-shift keying and minimum-shift keying. The sinusoidalshift keying moves the signal between binary values sinusoidally, and the minimum-shift keying moves it along a minimum- energy curve.

Table 1 compares the frequency spreading of the minimum-shift- keyed signal with that of other digital- modulation waveforms. This data comes from an excellent textbook by Robert Dixon, entitled Spread Spectrum Systems with Commercial Applications (ISBN 0-471- 5934297). Note that the 3-dB bandwidth of BPSK, ASK, and QPSK signals is 88% of the clock rate - compared with twice the clock rate for the null-to- null bandwidth of the main lobe. For MSK signals, you will note that the null- to-null and 3-dB bandwidths are only 75% of that for conventionally modulated signals carrying the same data rate. You will further note that the power in the side lobes is significantly reduced.

Impact of Bandwidth on EW

There are several ways that the bandwidth of transmitted digital signals impacts electronic warfare (EW). The most obvious is that the receiver band- width is a major determinant of sensitivity. Sensitivity is the minimum signal that the receiver can receive and still do its job. Sensitivity is the sum of kTB, the receiver- noise figure, and the required signal-to- noise ratio (SNR). In the atmosphere, kTB (the thermal noise in the receiver) is calculated by the following formula:

Fig. 1 The frequency spectrum of a digitally modulated FR signal has a characteristics shape dictated by the bit rate.

Fig. 2 The null-to-null frequency bandwidth of a typical digitally modulated signal is twice the bit rate, converted at 1 Hz per bit per second.

Fig. 3 There are frequency-effecient digital modulations that move between one and zero modulation values in a way that reduces the level of higherfrequency components.

kTB = -114 dBm + 10 log (bandwidth/ 1 MHz)

Thus, wider bandwidth, by reducing the sensitivity, requires additional transmitter power to provide adequate communications over any given operating range.

When receiving a hostile signal (in an electronic-support or electronic- intelligence system), the sensitivity determines the range from which adequate interception and emitter location can be accomplished.

Another, more subtle effect has to do with low-probability-of- intercept (LPI) features used to protect communications systems. LPI features involve the deliberate spreading of the transmitted frequency's bandwidth. The greater the LPI- spreading factor, the harder it is to intercept, locate, or jam the signal. Since high- data-rate digital signals occupy large bandwidths, it is difficult to achieve large LPI-spreading ratios before running into limitations in the bandwidth of amplifiers and antennas.

Error-detection codes (EDCs) reduce the impact of certain types of jamming on digital signals. Although an error-correction code can improve the SNR in a communications receiver, the extra bandwidth required for the code will, in general, hurt performance more than the EDC/SNR improvement will help it. However, when there is some specific error-inducing element in the communications situation - typically either jamming or a severe impact from even low bit-error rates - EDC can be used to great advantage. We will be discussing these codes and their impact on communications jamming in more detail a little later in this series.

What's Next

For the next two or three months, we'll discuss communications jamming. For your comments and suggestions, Dave Adamy can be reached at dave@lynxpub.com.

Copyright Horizon House Publications, Inc. Dec 2003

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