Building Blocks: Frequency-Hopping — CDMA's Lost Relative
Code division multiple access (CDMA) has become a household engineering word. However, before everyone jumped on the spread-spectrum bandwagon, there were two technologies receiving significant attention.
By Rob Howald
Either directly or
indirectly, several of my columns over the past few years have been spent discussing asymmetric digital subscriber line (ADSL) technology (high-speed data over twisted pair). During the many years of ADSL development, there have been U-turns, tangents, and improvement proposals. As a result, ADSL technology options and development are commonly discussed under the umbrella of xDSL. It is cute and catchy. And, perhaps because I’m an X-files fan, I see it as an appropriate title for a technology whose
progress over its lifetime can best be described as mysterious. I see this same mysterious road being staked out now for spread spectrum with the CDMA acronym. There once was a time when CDMA meant enough by itself. As wireless technology quickly matured, spawning commercial CDMA usage, system designers searched for an edge. Once, new communications acronyms implied a completely new technology advance, not a new marketing brainstorm. But that time is now long gone. Therefore, I am preparing for the
inevitable deluge of X-CDMAs. In the meantime, it is useful to understand CDMA’s relative, frequency-hopping spread spectrum.
CDMA in 200 words
In a “Building Blocks” column last year called “Spreading the Word,” (
Communication Systems Design
, September 1997, pp.20-25), the basic concepts of CDMA were introduced. The article dealt almost exclusively with direct sequence spread spectrum (DS-SS). Briefly, DS-SS spreads a signal’s bandwidth by “multiplying” a
data stream by a pseudorandom (PN) code (thus code division multiple access). The PN code looks random to the outside world. However, it is actually periodic, with a bit sequence (known as a chip) determined by a logical mathematical relationship and known only to the transmitter and receiver. A profusion of information is available on how to design these codes with the required properties to make CDMA work best. (Apparently, people study these things deeply.) Because the multiplication by a higher rate
stream spreads the signal in the frequency domain, and the receive operation (RX) does the opposite, the RX operation is known as despreading. Meanwhile, a narrowband interferer gets multiplied only at the receiver. The interferer is thus spread into a noise-like impairment, often generating only a minor signal-to-noise (SNR) degradation (as opposed to a major link impairment). Equations and numbers are involved, but this is the basic idea.
FH-SS 101
This month, we will branch out into another
major form of spread spectrum. (Due to length constraints, it was only skimmed in the previous piece.) That technology is called frequency-hopping spread spectrum (FH-SS).
The underlying concept of FH-SS is understood by thinking of the idea in a very simple way. We have spoken on multiple occasions about frequency domain multiple access (FDMA) systems, whereby many individually modulated carriers share a common allocated spectrum. Each carrier can communicate simultaneously by using only its given,
pre-assigned bandwidth. Another idea I have emphasized repeatedly is the rapid growth of really crummy channels. These channels are actually a conspiracy by us communication systems designer types to provide a reason to develop new, complicated signaling techniques that nobody understands, but that can save the world (oops, there’s that X-files conspiracy stuff sneaking in again). Several of the channels are indeed crummy, or more technically speaking, shoddy, in the form of narrowband interference (as
mentioned earlier for DS-CDMA). CDMA turns this interference into a broadband noise-like impairment. This approach to mitigation is sometimes referred to as averaging, in contrast to the FH-SS approach, which uses avoidance. Consider a simple frequency agile modulator to understand avoidance. Under crummy, shoddy, or even shabby channel conditions, a simple modem technique used to assure reliable transport creates frequency agility. Frequency agility is a fancy way of saying that a modem can change its
transmit frequency to a location in the allocated spectrum that is unused and clean. If the spectrum is full, then the modem is out of luck. Frequency agile systems, however, often have spare channels as a matter of course, because they anticipate that they might encounter bad channels.
FH-SS implements a solution to such channels on a larger and more impressive scale. However, instead of passively waiting for a defective channel, FH-SS takes a pro-active approach. It changes transmission frequency constantly,
and in some design cases, changes many times per symbol (fast-hopping). By contrast, slow-hopping would correspond to remaining on one frequency of the sequence for many symbols in a row. Some very good reasons to consider FH-SS are synchronization, frequency programmability, and dynamic range issues.
PN codes and FH
The PN code described earlier is not exclusive to DS-SS. The FH-SS signal hops all over the allocated spread spectrum bandwidth. But, like the DS-SS system, there has to be some
periodicity to it in order to recover the original transmission. The PN code in FH-SS, rather than multiplying the data sequence, is used to select an address for the frequency tuning word of the synthesizer. Many frequency synthesizer design details could fit here, but let’s just suffice to say that the periodicity of the code is used to give the receiver a priori knowledge of the frequency pattern. It is merely (but by no means simply) a matter of synchronizing the hopping patterns. The easiest way to
visualize the transmit processing with the PN code is to imagine a shift register when we say PN code generator. To envision a synthesizer interface, think of the shift register’s parallel outputs feeding a memory IC, whose output is a frequency tuning word, input to a direct digital synthesizer. This description coarsely shows how a frequency-hopping synthesizer is commanded in a periodic fashion from a PN code.
Frequency synthesizers
Frequency synthesizers come in many types. One of
the key design trade-offs is, as previously mentioned, whether to hop quickly (say, ten times per symbol) or slowly (many symbols per hop). The next section, which dips into the analysis, tells this story in numbers. From the viewpoint of not letting practical concerns get in the way of good theory, it is easy to conclude that the faster the frequency hopping, the better. Faster frequency hopping is also more difficult, however (thus adopting the no pain, no gain principle). We can assume this higher degree
of difficulty by recognizing what happens when a hopped signal plunks itself down on top of an interferer. For that hop, the information is assumed to be wrong 50% of the time. If that hop includes several symbols in a row — look out. If the hop is one-tenth of one symbol, maybe we can plow through it. Thus, the added strength of rapid hopping. This all-or-nothing scenario is what ensures that FH-SS will need to use forward error correction (FEC) for added robustness against errors that we know will
periodically arise.
With this knowledge, I can’t overemphasize enough the impact direct digital synthesizer (DDS) technology has had on FH-SS’ ability to achieve the benefits of fast-hopping synthesizers. In the not-so-distant past, fast hopping required at least two programmable phase-locked loops (PLLs). When it was desired to switch frequencies, one would be loaded, allowed to settle, and switched to, once the other PLL had settled. Design trade-offs between spurious performance, PLL bandwidth,
auxiliary acquisition circuitry, and hopping speed were sometimes torture, and a box often seemed to require a nuclear reactor to power it adequately. Frequency synthesizers are still not a complete pushover, particularly beyond the maximum output frequency capability of today’s DDSs. But, synthesizers have made a major FH-SS problem much more bearable.
Avoidance
The processing gain (PG), referred to in last year’s column as the ratio of spread bandwidth (BW) to signal BW, takes on a
different look for FH-SS. In FH-SS, the PG boils down to a hit-or-miss operation. Most of the time, transmission will be interference-free, under the practical assumption that your code has not been broken and synthesizer replicated. Broken code may require the most smarts, because codes are combined and changed regularly in high-security architectures. However, another “advantage” of FH-SS is that frequency synthesizers can be a real pain to create — and are thus a major hassle for any
deliberate troublemaker. (These synthesizers used to be even more difficult to make then they are now. However, as described, advances in DDS have made fine resolution, rapid switching, and rapid settling a practical reality at reasonable cost.)
The nature of avoidance forces two important considerations upon us. First, it is impractical to implement coherent modulations when the frequency changes (generally, not phase-coherently) ten times in the middle of a symbol. Simple solutions like frequency shift
keying (FSK) are used to deal with this problem. Each hopping tone, for example, is actually one of two tones close together — one for a logic zero and another for a one. This example would leave one extra bit to augment the PN code and tune the synthesizer. However, there is some loss of capacity, due to the use of a less efficient underlying modulation.
The second item to note when discussing avoidance is that, unlike DS-SS, it isn’t useful to do performance analysis via SNR and S/I
calculations to determine processing gain. Instead, the hit-or-miss situation created by a narrowband interference requires a look at probabilities of channel hits and of symbol errors.
Performance
DS-SS had an easy fundamental idea. The PG was simply the ratio of spread BW to information BW. It was a straightforward process to determine which chip rate was necessary to achieve a certain adequate SNR under additive white Gaussian noise (AWGN) and interference combined. As mentioned earlier, FH-SS
requires a different approach. Still, it can be boiled down to some pretty simple ideas:
- Assume a fast-hopping system, because we know this would be a more desirable link
- Assume there are l hops for every information symbol
- Assume there are K total frequencies possible from the synthesizer
- Assume Df between adjacent synthesizer frequencies (thus, total bandwidth (
BW) Kf
)
- Assume information signal
BW f
.
The basic PG expression used
for DS-SS would yield, for FH-SS:
PG =
l
K.
Whereas PG directly associates with S/I and SNR for DS-SS due to interference averaging, this is not the case with FH-SS. Instead, interference rejection occurs because the signal hops near to an interferer only a small fraction of the time (avoidance as opposed to averaging). When the interference and the signal coincide, interference is assumed to be overwhelming for analysis purposes. Average SNR is basically meaningless, therefore, and
error probability is more useful. The statistical nature of this scenario leads us down the binomial path. These calculations may involve long lost mathematical residue from your formal education days, but your calculator handles it easily. Assume there are N 2 narrowband interferers.
1
Then, the binary FSK error probability is:
Pb = S
n=0,1,2
b(2, n) b(M-2, 2-n)
S
n
/ b(M, 2),
where
b(A, B) = A!/B!(A-B)!
This approach to FH-SS analysis
is much more fruitful. By assuming 50% error rate for each coincidence of signal and interference, we would require on the order of 10 million or so frequencies to achieve a good bit error rate (BER) (1e-7) with only a single interferer, without error correction. This example shows why FEC and FH-SS make for a happy marriage.
DS vs. FH
Assembling a list of pros and cons of the DS and FH technologies is worthwhile (see Table 1). However, it should also be realized that combinations of these
technologies, and others, can be used to fit the circumstances most relevant to the spread spectrum application at hand.
Conclusion
Spread spectrum systems have roots in military applications. The techniques used are ideal for secure communications in hostile environments. Such systems fall under my heading of “favorite pairs in the acronym world:” ECM = electronic counter measures and ECCM = electronic counter-counter measures. In the last 20 years or so, spread spectrum, and in
particular DS-SS, has taken off in the commercial arena. Since the early 1980s, it has been one of the most popular topics of study and technical publication. FH-SS still takes second fiddle to DS-SS, and is likely to continue to do so in commercial settings. Some obvious reasons for this are:
- FH-SS’ hardware complexity can’t compete with DS-SS’ low-cost targets in commercial quantities
- A push towards highest capacity channels (and thereby coherent communication links)
- The commercial band interference and lower spectral density of DS-SS.
At one time, an exorbitant hardware complexity price was paid for FH-SS. The development and rapid progress of DDS has lowered the value of DS-SS systems, particularly those looking to push very high chip rates.
Rob Howald is a staff engineer in the transmission network systems group at General Instrument in Hatboro, PA. He has a BSEE and an MSEE from Villanova Univer- sity, and received his PhD from Drexel
University. He can be reached at
rhowald@gi.com.
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