I first ran across David Messerschmitt’s work in his paper “Interstellar Communication: The Case for Spread Spectrum,” and was delighted to meet him in person at Starship Congress in Dallas last summer. Dr. Messerschmitt has been working on communications methods designed for interstellar distances for some time now, with results that are changing the paradigm for how such signals would be transmitted, and hence what SETI scientists should be looking for. At the SETI Institute he is proposing the expansion of the types of signals being searched for in the new Allen Telescope Array. His rich discussion on these matters follows.
By way of background, Messerschmitt is the Roger A. Strauch Professor Emeritus of Electrical Engineering and Computer Sciences at the University of California at Berkeley. For the past five years he has collaborated with the SETI institute and other SETI researchers in the study of the new domain of “broadband SETI”, hoping to influence the direction of SETI observation programs as well as future METI transmission efforts. He is the co-author of Software Ecosystem: Understanding an Indispensable Technology and Industry (MIT Press, 2003), author of Understanding Networked Applications (Morgan-Kaufmann, 1999), and co-author of a widely used textbook Digital Communications (Kluwer, 1993). Prior to 1977 he was with AT&T Bell Laboratories as a researcher in digital communications. He is a Fellow of the IEEE, a Member of the National Academy of Engineering, and a recipient of the IEEE Alexander Graham Bell Medal recognizing “exceptional contributions to the advancement of communication sciences and engineering.”
by David G. Messerschmitt
We all know that generating sufficient energy is a key to interstellar travel. Could energy also be a key to successful interstellar communication?
One manifestation of the Fermi paradox is our lack of success in detecting artificial signals originating outside our solar system, despite five decades of SETI observations at radio wavelengths. This could be because our search is incomplete, or because such signals do not exist, or because we haven’t looked for the right kind of signal. Here we explore the third possibility.
A small (but enthusiastic and growing) cadre of researchers is proposing that energy may be the key to unlocking new signal structures more appropriate for interstellar communication, yet not visible to current and past searches. Terrestrial communication may be a poor example for interstellar communication, because it emphasizes minimization of bandwidth at the expense of greater radiated energy. This prioritization is due to an artificial scarcity of spectrum created by regulatory authorities, who divide the spectrum among various uses. If interstellar communication were to reverse these priorities, then the resulting signals would be very different from the familiar signals we have been searching for.
Starships vs. civilizations
There are two distinct applications of interstellar communication: communication with starships and communication with extraterrestrial civilizations. These two applications invoke very different requirements, and thus should be addressed independently.
Starship communication. Starship communication will be two-way, and the two ends can be designed as a unit. We will communicate control information to a starship, and return performance parameters and scientific data. Effectiveness in the control function is enhanced if the round-trip delay is minimized. The only parameter of this round-trip delay over which we have influence is the time it takes to transmit and receive each message, and our only handle to reduce this is a higher information rate. High information rates also allow more scientific information to be collected and returned to Earth. The accuracy of control and the integrity of scientific data demands reliability, or a low error rate.
Communication with a civilization. In our preliminary phase where we are not even sure other civilizations exist, communication with a civilization (or they with us) will be one way, and the transmitter and receiver must be designed independently. This lack of coordination in design is a difficult challenge. It also implies that discovery of the signal by a receiver, absent any prior information about its structure, is a critical issue.
We (or they) are likely to carefully compose a message revealing something about our (or their) culture and state of knowledge. Composition of such a message should be a careful deliberative process, and changes to that message will probably occur infrequently, on timeframes of years or decades. Because we (or they) don’t know when and where such a message will be received, we (or they) are forced to transmit the message repeatedly. In this case, reliable reception (low error rate) for each instance of the message need not be a requirement because the receiving civilization can monitor multiple repetitions and stitch them together over time to recover a reliable rendition. In one-way communication, there is no possibility of eliminating errors entirely, but very low rates of error can be achieved. For example, if an average of one out of a thousand bits is in error for a single reception, after observing and combining five (seven) replicas of a message only one out of 100 megabits (28 gigabits) will still be in error.
Message transmission time is also not critical. Even after two-way communication is established, transmission time won’t be a big component of the round-trip delay in comparison to large one-way propagation delays. For example, at a rate of one bit per second, we can transmit 40 megabyles of message data per decade, and a decade is not particularly significant in the context of a delay of centuries or millennia required for speed-of-light propagation alone.
At interstellar distances of hundreds or thousands of light years, there are additional impairments to overcome at radio wavelengths, in the form of interstellar dispersion and scattering due to clouds of partially ionized gases. Fortunately these impairments have been discovered and “reverse engineered” by pulsar astronomers and astrophysicists, so that we can design our signals taking these impairments into account, even though there is no possibility of experimentation.
Propagation losses are proportional to distance-squared, so large antennas and/or large radiated energies are necessary to deliver sufficient signal flux at the receiver. This places energy as a considerable economic factor, manifested either in the cost of massive antennas or in energy utility costs.
The remainder of this article addresses communication with civilizations rather than starships.
Compatibility without coordination
Even though one civilization is designing a transmitter and the other a receiver, the only hope of compatibility is for each to design an end-to-end system. That way, each fully contemplates and accounts for the challenges of the other. Even then there remains a lot of design freedom and a world (and maybe a galaxy) full of clever ideas, with many possibilities. I believe there is no hope of finding common ground unless a) we (and they) keep things very simple, b) we (and they) fall back on fundamental principles, and c) we (and they) base the design on physical characteristics of the medium observable by both of us. This “implicit coordination” strategy is illustrated in Fig. 1. Let’s briefly review all three elements of this three-pronged strategy.
The simplicity argument is perhaps the most interesting. It postulates that complexity is an obstacle to finding common ground in the absence of coordination. Similar to Occam’s razor in philosophy, it can be stated as “the simplest design that meets the needs and requirements of interstellar communication is the best design”. Stated in a negative way, as designers we should avoid any gratuitous requirements that increase the complexity of the solution and fail to produce substantive advantage.
Regarding fundamental principles, thanks to some amazing theorems due to Claude Shannon in 1948, communications is blessed with mathematically provable fundamental limits on our ability to communicate. Those limits, as well as ways of approaching them, depend on the nature of impairments introduced in the physical environment. Since 1948, communications has been dominated by an unceasing effort to approach those fundamental limits, and with good success based on advancing technology and conceptual advances. If both the transmitter and receiver designers seek to approach fundamental limits, they will arrive at similar design principles even as they glean the performance advantages that result.
We also have to presume that other civilizations have observed the interstellar medium, and arrived at similar models of impairments to radio propagation originating there. As we will see, both the energy requirements and interstellar impairments are helpful, because they drastically narrow the characteristics of signals that make sense.
Prioritizing energy simplifies the design
Ordinarily it is notoriously difficult and complex to approach the Shannon limit, and that complexity would be the enemy of uncoordinated design. However, if we ask “limit with respect to what?”, there are two resources that govern the information rate that can be achieved and the reliability with which that information can be extracted from the signal. These are the bandwidth which is occupied by the signal and the “size” of the signal, usually quantified by its energy. Most complexity arises from forcing a limit on bandwidth. If any constraint on bandwidth is avoided, the solution becomes much simpler.
Harry Jones of NASA observed in a paper published in 1995 that there is a large window of microwave frequencies over which the interstellar medium and atmosphere are relatively transparent. Why not, Jones asked, make use of this wide bandwidth, assuming there are other benefits to be gained? In other words, we can argue than any bandwidth constraint is a gratuitous requirement in the context of interstellar communication. Removing that constraint does simplify the design. But another important benefit emphasized by Jones is reducing the signal energy that must be delivered to the receiver. At the altar of Occam’s razor, constraining bandwidth to be narrow causes harm (an increase in required signal energy) with no identifiable advantage. Peter Fridman of the Netherlands Institute for Radio Astronomy recently published a paper following up with a specific end-to-end characterization of the energy requirements using techniques similar to Jones’s proposal.
I would add to Jones’s argument that the information rates are likely to be low, which implies a small bandwidth to start with. For example, starting at one bit per second, the minimum bandwidth is about one Hz. A million-fold increase in bandwidth is still only a megahertz, which is tiny when compared to the available microwave window. Even a billion-fold increase should be quite feasible with our technology.
Why, you may be asking, does increasing bandwidth allow the delivered energy to be smaller? After all, a wide bandwidth allows more total noise into the receiver. The reason has to do with the geometry of higher dimensional Euclidean spaces, since permitting more bandwidth allows more degrees of freedom in the signal, and a higher dimensional space has a greater volume in which to position signals farther apart and thus less likely to be confused by noise. I suggest you use this example to motivate your kids to pay better attention in geometry class.
Another requirement that we have argued is gratuitous is high reliability in the extraction of information from the signal. Achieving very low bit error rates can be achieved by error-control coding schemes, but these add considerable complexity and are unnecessary when the receiver has multiple replicas of a message to work with. Further, allowing higher error rates further reduces the energy requirement.
The minimum delivered energy
For a message, the absolute minimum energy that must be delivered to the receiver baseband processing while still recovering information from that signal can be inferred from the Shannon limit. The cosmic background noise is the ultimate limiting factor, after all other impairments are eliminated by technological means. In particular the minimum energy must be larger than the product of three factors: (1) the power spectral density of the cosmic background radiation, (2) the number of bits in the message, and (3) the natural logarithm of two.
Even at this lower limit, the energy requirements are substantial. For example, at a carrier frequency of 5 GHz at least eight photons must arrive at the receiver baseband processing for each bit of information. Between two Arecibo antennas with 100% efficiency at 1000 light years, this corresponds to a radiated energy of 0.4 watt-hours for each bit in our message, or 3.7 megawatt-hours per megabyte. To Earthlings today, this would create a utility bill of roughly $400 per megabyte. (This energy and cost scale quadratically with distance.) This doesn’t take into account various non-idealities (like antenna inefficiency, noise in the receiver, etc.) or any gap to the fundamental limit due to using practical modulation techniques. You can increase the energy by an order of magnitude or two for these effects. This energy and cost per message is multiplied by repeated transmission of the message in multiple directions simultaneously (perhaps thousands!), allowing that the transmitter may not know in advance where the message will be monitored. Pretty soon there will be real money involved, at least at our Earthly energy prices.
Two aspects of the fundamental limit are worth noting. First, we didn’t mention bandwidth. In fact, the stated fundamental limit assumes that bandwidth is unconstrained. If we do constrain bandwidth and start to reduce it, then the requirement on delivered energy increases, and rapidly at that. Thus both simplicity and minimizing energy consumption or reducing antenna area at the transmitter are aligned with using a large bandwidth in relation to the information rate. Second, this minimum energy per message does not depend on the rate at which the message is transmitted and received. Reducing the transmission time for the message (by increasing the information rate) does not affect the total energy, but does increase the average power correspondingly. Thus there is an economic incentive to slow down the information rate and increase the message transmission time, which should be quite okay.
What do energy-limited signals actually look like?
A question of considerable importance is the degree to which we can or cannot infer enough characteristics of a signal to significantly constrain the design space. Combined with Occam’s razor and jointly observable physical effects, the structure of an energy-limited transmitted signal is narrowed considerably.
Based on models of the interstellar medium developed in pulsar astronomy, I have shown that there is an “interstellar coherence hole” consisting of an upper bound on the time duration and bandwidth of a waveform such that the waveform is for all practical purposes unaffected by these impairments. Further, I have shown that structuring a signal around simple on-off patterns of energy, where each “bundle” of energy is based on a waveform that falls within the interstellar coherence hole, does not compromise our ability to approach the fundamental limit. In this fashion, the transmit signal can be designed to completely circumvent impairments, without a compromise in energy. (This is the reason that the fundamental limit stated above is determined by noise, and noise alone.) Both the transmitter and receiver can observe the impairments and thereby arrive at similar estimates of the coherence hole parameters.
The interstellar medium and motion are not completely removed from the picture by this simple trick, because they still announce their presence through scintillation, which is a fluctuation of arriving signal flux similar to the twinkling of the stars (radio engineers call this same phenomenon “fading”). Fortunately we know of ways to counter scintillation without affecting the energy requirement, because it does not affect the average signal flux. The minimum energy required for reliable communication in the presence of noise and fading was established by Robert Kennedy of MIT (a professor sharing a name with a famous politician) in 1964. My recent contribution has been to extend his models and results to the interstellar case.
Signals designed to minimize delivered energy based on these energy bundles have a very different character from what we are accustomed to in terrestrial radio communication. This is an advantage in itself, because another big challenge I haven’t yet mentioned is confusion with artificial signals of terrestrial or near-space origin. This is less of a problem if the signals (local and interstellar) are quite distinctive.
A typical example of an energy-limited signal is illustrated in Fig. 2. The idea behind energy-limited communication is to embed energy in the locations of energy bundles, rather than other (energy-wasting but bandwidth-conserving) parameters like magnitude or phase. In the example of Fig. 2, each rectangle includes 2048 locations where an energy bundle might occur (256 frequencies and 8 time locations), but an actual energy bundle arrives in only one of these locations. When the receiver observes this unique location, eleven bits of information have been conveyed from transmitter to receiver (because 211 = 2048). This location-based scheme is energy-efficient because a single energy bundle conveys eleven bits.
The singular characteristic of Fig. 2 is energy located in discrete but sparse locations in time and frequency. Each bundle has to be sufficiently energetic to overwhelm the noise at the receiver, so that its location can be detected reliably. This is pretty much how a lighthouse works: Discrete flashes of light are each energetic enough to overcome loss and noise, but they are sparse in time (in any one direction) to conserve energy. This is also how optical SETI is usually conceived, because optical designers usually don’t concern themselves with bandwidth either. Energy-limited radio communication thus resembles optical, except that the individual “pulses” of energy must be consciously chosen to avoid dispersive impairments at radio wavelengths.
This scheme (which is called frequency-division keying combined with pulse-position modulation) is extremely simple compared to the complicated bandwidth-limited designs we typically see terrestrially and in near space, and yet (as long as we don’t attempt to violate the minimum energy requirement) it can achieve an error probability approaching zero as the number of locations grows. (Some additional measures are needed to account for scintillation, although I won’t discuss this further.) We can’t do better than this in terms of the delivered energy, and neither can another civilization, no matter how advanced their technology. This scheme does consume voluminous bandwidth, especially as we attempt to approach the fundamental limit, and Ian S. Morrison of the Australian Centre for Astrobiology is actively looking for simple approaches to achieve similar ends with less bandwidth.
What do “they” know about energy-limited communication?
Our own psyche is blinded by bandwidth-limited communication based on our experience with terrestrial wireless. Some might reasonably argue that “they” must surely suffer the same myopic view and gravitate toward bandwidth conservation. I disagree, for several reasons.
Because energy-limited communication is simpler than bandwidth-limited communication, the basic design methodology was well understood much earlier, back in the 1950’s and 1960’s. It was the 1990’s before bandwidth-limited communication was equally well understood.
Have you ever wondered why the modulation techniques used in optical communications are usually so distinctive from radio? One of the main differences is this bandwidth- vs energy-limited issue. Bandwidth has never been considered a limiting resource at the shorter optical wavelengths, and thus minimizing energy rather than bandwidth has been emphasized. We have considerable practical experience with energy-limited communication, albeit mostly at optical wavelengths.
If another civilization has more plentiful and cheaper energy sources or a bigger budget than us, there are plenty of beneficial ways to consume more energy other than being deliberately inefficient. They could increase message length, or reduce the message transmission time, or transmit in more directions simultaneously, or transmit a signal that can be received at greater distances.
Based on our Earthly experience, it is reasonable to expect that both a transmitting and receiving civilization would be acutely aware of energy-limited communication and I expect that they would choose to exploit it for interstellar communication.
Communication isn’t possible until the receiver discovers the signal in the first place. Discovery of an energy-limited signal as illustrated in Fig. 2 is easy in one respect, since the signal is sparse in both time and frequency (making it relatively easy to distinguish from natural phenomenon as well as artificial signals of terrestrial origin) and individual energy bundles are energetic (making them easier to detect reliably). Discovery is hard in another respect, since due to that same sparsity we must be patient and conduct multiple observations in any particular range of frequencies to confidently rule out the presence of a signal with this character.
Criticisms of this approach
What are some possible shortcomings or criticisms of this approach? None of us have yet studied possible issues in design of a high-power radio transmitter generating a signal of this type. Some say that bandwidth does need to be conserved, for some reason such as interference with terrestrial services. Others say that we should expect a “beacon”, which is a signal designed to attract attention, but simplified because it carries no information. Others say that an extraterrestrial signal might be deliberately disguised to look identical to typical terrestrial signals (and hence emphasize narrow bandwidth rather low energy) so that it might be discovered accidently.
What do you think? In your comments to this post, the Centauri Dreams community can be helpful in critiquing and second guessing my assumptions and conclusions. If you want to delve further into this, I have posted a report at http://arxiv.org/abs/1305.4684 that includes references to the foundational work.