Unwrapping wireless signals
Applying the right signal-calculation algorithms and techniques can compensate for AWG wraparound artifacts and can also save memory.
Joan Mercadé, Arbitrary Resources -- Test & Measurement World, 12/1/2006 2:00:00 AM
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READ OTHER DEC./JAN. ARTICLES: Contents, Dec. 2006/Jan. 2007 SIDEBAR: Impairment effects in various domains |
Arbitrary waveform generators (AWGs) have become the standard signal sources for baseband and IF signals in wireless test applications. The increasing sampling speed, bandwidth, and linearity of available instruments are opening the door to direct RF generation. Although the instruments can generate high-quality signals, wraparound artifacts can ruin the final results. By using the right signal-calculation algorithms and techniques, you can eliminate wraparound problems while saving precious generation memory.
AWGs can create virtually any modulation scheme, including multicarrier, dissimilar signals with linear and nonlinear impairments. Some use firmware or external software to calculate the required samples according to user requests. The calculation software, unlike a real transmitter, need not calculate samples in real time, as samples are stored in the generation memory and played back at the required sampling speed during generation.
Current AWGs provide enough signal quality and sampling speed to generate highly accurate signals capable of testing the most demanding wireless devices. Although current implementations provide flexible signal generation, including long record lengths and intelligent segment sequencing, the only way to create arbitrarily long signals, including continuous generation, is by repeating or sequencing finite-duration waveforms. This is a classic AWG limitation that results in an unwanted side effect on the signal: the so-called ¡°wraparound artifact.¡±
Wraparound causes and effects
Wraparound artifacts (Figure 1) are caused by the discontinuity between both ends of a given waveform being repeated in a loop or, in a more general case, between the end and the beginning of two consecutive waveforms in a sequence. It is important to understand that AWGs can link signal segments without any gap or glitch related to the sampling period as samples are converted seamlessly regardless of their location.
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Figure 1. (Top left) This VSA display shows the effects of the wraparound artifacts on the signal. (Lower left) The spectrogram displays regular spectral-growth episodes, right at the connection between waveform segments. The constellation display (top right) and the eye diagram (bottom right) show how wraparound affects all the aspects of a digitally modulated signal. |
The effect of wraparound artifacts may be negligible in many time-domain tests as users can restrict their measurements made on the device under test (DUT) to areas away from the transition between signal segments. The usage of synchronization signals provided by the generators makes this approach easy to implement in most test cases.
Even if the measurements are performed at the right moments in time, however, the intersegment transients can affect the behavior of the DUT. For example, in a serial-data transmission test, the clock-recovery circuits in a DUT can lose their lock if a transient results in truncated symbols or illegal line coding. Depending on the length of the data and the time taken by the DUT to lock the clock again, test results will not be valid as they will not reflect steady-state behavior.
Wireless test can be even more demanding. Wireless tests occur in many domains consecutively or simultaneously: time, frequency, modulation, channel-coding, and protocol. In many wireless-test situations, measurements cannot be easily restricted to signal areas away from the wraparound transients. (See ¡°Impairment effects in various domains,¡± for an explanation of how wraparound artifacts can hinder wireless measurements.)
Solving the problem
There are two basic ways to handle the wraparound problem: hide the symptoms or eliminate the causes.
For some wireless signals, just hiding the side effects of wraparound may be sufficient. The prime method for doing this is transient editing.
The idea is quite simple. Because discontinuity between the end and the beginning of consecutive signal segments is the main cause of impairments, editing the transition area so that both ends match as perfectly as possible could help solve the problem. This can be accomplished by manual editing or in a semiautomatic way through filtering or smoothing. Filtering is applied to the border sections of the waveforms to bring about a smooth transition (Figure 2). This methodology can attenuate, or even eliminate, the spectral-growth impairment to the level required by adjacent channel power ratio (ACPR) measurements.
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Figure 2. Transient smoothing can help reduce some of the side effects of wraparound, especially spectral growth. a) This display shows the result of looping a waveform with a discontinuity in its derivative at time 0. b) This display shows the same signal after transient smoothing, with no apparent discontinuities. |
Unfortunately, transient editing does not solve any of the other impairments, and in most cases the overall situation worsens. Any measurement of modulation quality must be performed away from the wraparound transient, which requires you to use time-gated measurements. Furthermore, DUTs must have enough time to settle between these transients. Time-gated measurements also require the use of measurement-synchronization signals to mark the distortion-free areas of the signal. Some AWGs offer such signals in the form of trigger or user-editable marker outputs.
When time-gated measurements are impossible or undesirable and the available generation time window at the target AWG is not enough to generate the required signal in a single pass, the only practical solution is to eliminate the wraparound problem. As the basic reason for wraparound is the repetition or the sequencing of inconsistent signals, an obvious solution would be to use a real-time generation architecture. After all, real-world transmitters, in which the carrier is modulated by nonrepetitive data and in which baseband filtering is performed in real time, do not show this problem.
But real-time generators also have limitations. In addition to being costly, they have a complex architecture that differs completely from the standard, scenario-based, AWG architecture. Also, real-time generators use DSPs to calculate the I and Q baseband samples in real time, so processing power is an issue. And all the calculations are performed by a program run by the DSP, so any modulation scheme must be supported by the instrument.
Sampling speed and signal quality are influenced by the processing power as they limit the oversampling capacity and the maximum symbol rate supported by the instrument. The quality of the signal may also be affected by the impulse response truncation required by implementation of the baseband digital filter. In addition, users are restricted to using the built-in signal standards and impairments instead of being able to create their own signals, as they can with conventional AWGs.
An alternative approach to using a real-time generator is to design the AWG¡¯s signals in such a way that the wraparound artifacts are completely eliminated. In such an environment, signals can be repeated or sequenced without any glitch during the waveform-to-waveform transitions just as in real transmitters when transmitting live traffic. Designing signals that meet these requirements is not as difficult as it may seem, at least at the basic layers of the protocol stack, but the signals do need to meet some requirements:
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The number of symbols in the signal must be an integer. Some modulation schemes may have additional requirements. The p/4 differential quadrature phase-shift keyed (DQPSK) scheme, as an example, requires the number of symbols to be an even number.
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For IF/RF signals, the number of carrier cycles must be an integer as well.
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For multicarrier signals, all the components must meet the two above conditions.
These conditions seem to impose restrictions to the values for carrier frequency and symbol rates, but if you carefully select the number of symbols, record length, and sampling speed, you can minimize frequency errors, especially when long record lengths are involved. In addition, in order to have glitch-free signals, you must perform baseband filtering seamlessly between the symbols at the end of the current waveform and at the beginning of the next.
For continuous repetition of any waveform, you must use the end symbols and the ones at the beginning in the convolution process with the baseband filter just as if they were part of the same sequence. You can accomplish this by applying an operation called circular convolution (Figure 3).
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Figure 3. Circular convolution is the key to obtaining self-consistent signals that can be looped seamlessly. |
A similar approach, although more complex, can be applied to dissimilar waveforms in a sequence. The final result will be a waveform or set of waveforms that can be sequenced seamlessly without any wraparound impairments in the time, frequency, or modulation domains.
Although this methodology gives a general solution for baseband signals and for quadrature modulated IF/RF carriers, it is not enough to guarantee good results with frequency-shift keying (FSK) modulated carriers. FSK, including Gaussian minimum-shift keying (GMSK), will need an extra step to obtain a glitch-free signal, because even if all the previous conditions are met and circular convolution is applied to the modulating signal, the initial and final phase will differ.
Fortunately, there is a solution to this issue: adding a linear twist to the phase of the carrier. This ¡°phase twisting¡± process is equivalent to modifying the carrier frequency. As the range for the phase difference is ¡Àp, a simple calculation gives a maximum frequency error of ¡À1/(2TW), where TW is the duration of the waveform segment. For a 100-Msamples/s, 10-Msample waveform, the worst-case error will be 5 Hz.
Going up in the protocol stack
In some cases, random data may be adequate, as it is the best payload for general-purpose time, frequency, and modulation domain testing. In other situations, though, a signal must convey framing, synchronization, or protocol information. So, even if the signal meets the basic wraparound, artifact-free conditions, you may need to take additional steps in order to avoid glitches at the required levels of channel coding or at the protocol layer.
A good example may be CATV DVB-C digital signals. To test the error level with a standard analysis tool, you must use a test signal with all the required channel coding, because errors are typically measured by using the error protection information carried by signal channel coding. This includes framing, block-error-correction (Reed-Solomon code) insertion, data interleaving, scrambling, and differential coding.
Fortunately, at this testing level, the contents of the payload are irrelevant. The minimum self-consistent data chunk for that kind of signal is 1632 (204x8) bytes long and includes eight complete error-protected packets along with the required synchronization and scrambling. The minimum symbol sequence that can accommodate a consistent data sequence depends, though, on the modulation scheme.
For QAM16 (4 bits/symbol), QAM64 (6 bits/symbol), and QAM256 (8 bits/symbol), the data sequence can be accommodated in an integer number of symbols. For QAM32 (5 bits/symbol) and QAM128 (7 bits/symbol), there is no way a single sequence can be accommodated in an integer number of symbols. If the sequence is truncated, it will lose its proper channel coding, and it will be meaningless for any receiver or analysis instrument. In other words, there will be a wraparound artifact at the channel-coding layer.
The solution is to require that the symbol length be a multiple of 5x1632 bytes or 7x1632 bytes for QAM32 or QAM128, respectively. But meeting this condition does not come without a cost: The sequence will need five or seven times more generation memory, which eventually may overflow the available size at the target instrument. Is that enough? The answer, unfortunately, is no. Differential modulation adds a new source of signal inconsistency.
In differentially modulated QAM signals, the two most-significant bits (MSBs) of the symbols control the relative phase jump from the previous quadrant. The remaining bits are mapped using Grey coding to the symbol location in the current quadrant so a rotationally invariant modulation is obtained.
The problem is that the last modulation state in the current waveform and the initial modulation state in the beginning of the next one may be inconsistent, even if the rest of the information is properly coded and filtered. As a result, the bit sequence will be improperly decoded, and the signal will be meaningless again.
There are several solutions for this problem. The most obvious one is to carefully select the data to ensure consistency at this level. Although this solution works, it does impose limitations on the acceptable data, and this may be inconvenient in some situations.
Another solution may be to repeat the same data sequence four times (in some cases, two repetitions may be enough). It is easy to find out that this will always create a consistent sequence no matter what data was used in the original sequence. Again, this solution comes at the expense of an increase in the record-length requirements for the AWG.
Phase twister
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Figure 4. Phase twisting may be used to solve some specific wraparound problems related to signal consistency at the channel coding or protocol levels while saving precious waveform memory. TW equals the time window. |
If the previous solution does not work because there is not enough generation memory available, then there is another solution: twisting the phase (Figure 4). This solution is very similar to the FSK modulation where some linear phase shift must be added to every sample to compensate for the phase difference between the end and the beginning of the waveform.
For differentially modulated signals, the phase difference between the required phase at the beginning of the next waveform to play back and its actual value can be any multiple of p/2. If the signal phase is rotated in the same direction and magnitude as the error during the complete record, the result will be a wraparound-artifact-free signal without any glitch at the differential modulation level.
For baseband signals, the I and Q components at the output of a two-channel AWG will no longer be the original I and Q components but their projections on these axes with the added rotation. As in FSK-modulated signals, this is equivalent to slightly increasing or decreasing (depending on the rotation direction) the carrier frequency.
But things become strange: Circular convolution stops working and discontinuities will show up. For example, if the difference of phase to compensate is p/2, the I component will rotate 90¡ã counterclockwise, and at the end of the record it will be, in fact, aligned with the Q component at the beginning. Similarly, the Q component at the end will be facing the ¨CI component at the beginning.
The solution consists in simply applying the same calculation method, but in this example, the I component of the end symbols will be convolved along with the Q component of the initial symbols, and the Q component of the end symbols will be convolved along with the inverted I component of the initial symbols. Circular convolution takes the shape of a helix instead. This approach may be used in some other situations, such as accommodating an odd number of symbols in a p/4 DQPSK modulated signal.
| FOR FURTHER READING |
| Mercad¨¦, Joan, ¡°Ruling the Waves,¡± Evaluation Engineering, July 2004. www.evaluationengineering.com/archive/articles/0704/0704rulingwaves.asp. |
| Strassberg, Dan, ¡°Making Waves: Eight Years Later, Details Still Matter,¡± EDN, September 14, 2006. pp. 46¨C57. www.edn.com/article/CA6368440.html. |
| ¡°XYZ of Signal Sources,¡± Tektronix, Publication No. 76-W-16672-3. www.tek.com/Measurement/programs/301889X312609. |
| See also en.wikipedia.org/wiki/Circular_convolution for more information on Circular Convolution. |
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