What is intersymbol interference — and why should I care about it?

Real-world digital signals and their channels are characterized by complex equations that lead to improved link performance.

When engineers think or talk about digital signals, there’s often the sense that these are nice rectangular pulses with right-angle squared-off corners, but that’s only in the ideal world. In the real world, signal challenges begin with how “perfect” these waveforms are, although they can come quite close.

However, the much bigger challenge for digital signals is when the digital waveforms’ pulses are transmitted via cable, fiber, or air, whether it is for a relatively short interchip or interboard link, or a long-distance multikilometer optical fiber path. These waveforms are distorted and “smeared” primarily due to bandwidth limitations, and their energy is dispersed in time. The spreading of the pulse energy then overlaps with the energy of subsequent pulses, a phenomenon known as intersymbol interference (ISI), as shown in Figure 1.

There are negative consequences of ISI. First, some of the energy that was used to create the original pulse is wasted. Even if that is not a concern, the spread energy of the original signal means there is less for the desired signals, which reduces the signal-to-noise ratio (SNR) at the receiver. When it is sampled to determine whether it was a one or a zero (or other digital code, as in multilevel signals), the reduced SNR increases the chance of a misinterpretation and so increases the bit error rate (BER).

For these reasons, ISI and what to do about it have been studied since the early days of analog signals, with much of the work done at Bell Labs in the 1930s through 1960s (see the seminal work by R. W. Lucky; J. Salz; and E. J. Weldon, “Principles of Data Communications”). For perspective, recognize that when the first trans-Atlantic telegraph cable was laid in the late 1800s, ISI was not yet recognized, and signaling rates were on the order of about 10 bits/minute!

ISI is analyzed and must be understood in both time and frequency domains. As with all insight and analysis related to signal theory, the math gets extremely complicated as it deals with signals spaces, convolution, and more; those who are interested can look at the many available references.

ISI, bandwidth, sampling rate, and more

Fortunately, it’s not difficult to gain a qualitative understanding of ISI, the resultant problems it induces, and possible solutions to minimize both ISI and its impact. Understanding begins with the relationship among the various factors and parameters.

For a wideband channel where the channel bandwidth (BW) is greater than half the symbol rate (Rs) (BW>Rs/2), most of the signal’s power is retained in the original pulse. A small fraction of the higher-frequency components is filtered out; however, the resultant distortion is relatively minor and generally acceptable for most practical communication systems, as shown in Figure 2.

In contrast, when the channel bandwidth equals one-half the symbol rate (BW= Rs/2), the channel has just sufficient bandwidth to pass the main lobe of the signal’s spectrum, seen in Figure 3. At the same time, all of the side lobes are filtered out, and the received signal’s quality depends on the precise timing at the receiver. While distortion appears to be minimal, any timing errors can significantly impact the signal recovery and BER.

The most challenging case is when the channel bandwidth is less than Rs/2, as even the main lobe of the signal’s spectrum is partially attenuated (BW<Rs/2). This results in significant intersymbol interference, as the signal’s shape is increasingly distorted and there is a significant amount of overlap between consecutive symbols, shown in Figure 4. This is detrimental to the accurate, correct, and error-free recovery of symbols.

Observing ISI

Both the frequency and time domains provide insight into ISI. In the frequency domain, a power spectral density (PSD) graph illustrates the “splatter” of energy resulting from band-limiting and distortion.

The well-known eye diagram (eye pattern) in the time domain is more revealing, as seen in Figure 5. This diagram shows the effects of overlapping one bit’s energy into adjacent bit periods; in most cases, the optimum sampling point is at the middle of the eye, where the option is at its widest. A wide-open eye means that there is little or no ISI, while a closed eye means that there is a bit of overlap.

Note that the eye diagram also shows the effects of additive noise, which is a non-ISI problem; noise usually manifests as jitter around the zero-crossing points of the eye, rather than closing of the eye.

Minimizing ISI itself — or its effects

While the best course from an engineering perspective would be to improve the channel characteristics or reduce the channel bit rate, those are unlikely solutions. The former approach is often not possible, while the latter is not desirable or acceptable.

Fortunately, there are alternatives that can reduce the impact of ISI and improve the error rate. Some of these are analog techniques that are now implemented digitally using software or hardware, while others are inherently digital.

Raised cosine pulse shaping: Minimizing the effects of ISI begins with pulse shaping of the transmitted pulse. Using a pulse with square corners requires a larger (in fact, infinite) bandwidth, and any spectral energy that does not fit within the channel bandwidth contributes to ISI. The solution is to shape that pulse to maximize the energy that the channel passes.

This problem was studied for many years by researchers such as Harry Nyquist (yes, also the developer of the famous eponymous criteria for analog-signal sampling and reconstruction). The Bell Labs researchers were able to show that the optimum shape for that initial pulse was the raised cosine, which ensures that the spectrum is bandlimited while minimizing ISI at the sampling instants, shown in Figure 6. it has an adjustable bandwidth that is controlled by the “roll-off” factor.

The key parameters of the raised cosine, such as roll-up rate, can be adjusted to match the channel characteristics and performance tradeoffs.

The raised cosine filter for pulse shaping is not just another low-pass filter. In the time domain, the filter has a zero response at time intervals T so that a given symbol’s pulse response will add to the signal energy at the sampling times of the neighboring symbols. It should also minimize the height of the lobes of the impulse (time) response, and have it decay quickly, to reduce the sensitivity to ISI if the receiver doesn’t sample at precisely the ideal time for each symbol.

As the roll-off time increases (curve D in Figure 6), the impulse response goes to zero very quickly, and the lobes of the filter impulse response are very small. However, they have a frequency spectrum that is excessively wide. A better compromise would be a roll-off factor somewhere between 0.25 and 0.5. In that case, the impulse response decays relatively quickly, with small lobes, while still maintaining a reasonable bandwidth.

The receiver filter: An important issue is the design of a receiver filter that optimizes SNR and thus receiver performance. Signal-theory analysis provided the answer to this as well, showing that what is called a “matched filter” is optimum. By definition, a matched filter provides an output that maximizes the output peak power-to-mean-noise power ratio. The matched filter is the optimal linear filter for maximizing the SNR in the presence of additive stochastic noise.

What are the key characteristics of the matched filter? The output of the matched filter is given by correlating a known delayed signal called a template with an unknown signal to detect the presence of the template in the unknown signal. The impulse response of the ideal matched filter, assuming white (uncorrelated) noise, should be a time-reversed complex-conjugate scaled version of the signal that the system is trying to recover. (That’s all we can say about this without getting into a very deep analytical discussion.)

Pre-distortion: if you know the characteristics of the channel and how it distorts the signal path, it may make sense to “pre-empt” the problem using complementary pulse shaping of the transmitted signal itself. For example, if the channel does not have a flat response up to its bandwidth limit but instead has an attenuation “valley” within the bandwidth range, designers can add some signal boost at the transmitted side to those attenuated frequencies. Ideally, the result will be a signal with flat bandwidth when it emerges at the other end of the channel.

Equalization: this is the complement of pre-distortion. Instead of pre-distorting the transmitted signal, equalizers are used at the receiver to counteract the effects of the band-limited channel by reversing the distortion.

Error-Correcting Codes and Forward Error Correction (FEC): These techniques can help recover lost or distorted bits caused by ISI. Among the widely used ones are Viterbi coding, developed in 1967 by Andrew J. Viterbi. In this approach, the raw data to be transmitted is encoded using a convolutional code or trellis code. At the receiving end, the data has noise and distortion along with ISI. The decoder counteracts these error-inducing problems by using maximum likelihood decoding. By doing so, it leverages “knowledge” of the coding scheme to determine with high probability what the next most likely bit would be and so decreases the bit error rate. This decoding can be performed in hardware or software, depending on the data rate and the usual tradeoffs in cost, power, and speed between hardware and software.

Finally, adaptive pre-distortion and equalization schemes are used to minimize ISI. These advanced versions dynamically adjust transmitter and receiver parameters and waveforms based on channel conditions. This is necessary since the reality is that channel performance parameters and deficiencies are usually not static, but rather vary with time, temperature, motion, interference sources, and other factors. This dynamic time-varying approach is particularly necessary for wireless channels, where numerous factors can impact the channel while it is in use.  Adaptive techniques are used extensively in modems of various types.

Summary

ISI is a problem that has been recognized since the earliest days of communications, beginning with telegraph lines and even the trans-Atlantic telegraph cable. Solutions to the problem have evolved as data speeds have increased, demanding ever-higher channel bandwidths, while the use of simple wires as channel media has expanded to include coaxial cables, waveguides, optical links, and, of course, wireless links.

Many of these ISI solutions are based on advanced signal-theory analysis, which first characterized the root causes of the problems and then helped develop approaches for minimizing them. The result has been higher SNR and lower BER, even as speeds increased by many orders of magnitude.

References

Intersymbol interference, Wikipedia
Intersymbol interference, Southern Illinois University Edwardsville
Understanding Inter-Symbol Interference (ISI) in Communication Systems, Rahsoft
Intersymbol interference, Science Direct
Intersymbol interference and equalization, Cambridge University Press
The effects of Inter Symbol Interference (ISI) and FIR Pulse Shaping Filters: A survey, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering
Raised Cosine Filter, Science Direct
Raised Cosine Pulse, Science Direct
Raised Cosine Pulse and Eye Diagram, Simon Fraser University
Equations for the Raised Cosine and Square-Root Raised Cosine Shapes, Purdue University
Raised-cosine filter, Wikipedia
The care and feeding of digital, pulse-shaping filters, RF Design
Raised Cosine Pulse, University of Texas
Matched filter, Wikipedia
Matched Filtering, University of Texas
Matched filter, ElProCus

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