Bandwidth-Efficient Modulation

Bandwidth-Efficient Modulation Through Gaussian Minimum Shift Keying

Diana M. Johnson and Tien M. Nguyen

Using bandwidth-efficient modulation, communication satellites can transmit signals through a smaller frequency band. The Aerospace Corporation's research into one such technique has yielded tangible benefits for the military's protected communication satellites.

The recent proliferation of terrestrial and space-based communication systems has given rise to an increasingly critical problem—the lack of available frequency spectrum. One tool that satellite system designers can use to maximize the use of available spectrum is bandwidth-efficient modulation. This technique can enhance bandwidth efficiency while retaining reasonable power efficiency and implementation complexity. Because of the wide applicability of bandwidth-efficient modulation to most new satellite systems, The Aerospace Corporation has performed extensive research in this area. One recent application can be found in the Advanced Extremely High Frequency (AEHF) program.

With Gaussian minimum shift keying, the rectangular pulses representing input bits are converted into Gaussian shaped pulses. The resulting carrier signal is smooth in phase, and therefore requires less bandwidth to transmit. The configuration shown here uses a bandwidth–bit-time product of 1/5.

A successor to Milstar I and II, the AEHF program will form the basis of the military's next-generation protected communication system. Specifications called for a tenfold increase in capacity over the current Milstar system; however, early studies clearly indicated that the new downlink requirements could not be met within the existing frequency allocation simply by extending the Milstar design. The MILSATCOM (Military Satellite Communications) Joint Program Office at the Air Force Space and Missile Systems Center asked Aerospace to help investigate alternative signaling methods that would use the allotted bandwidth more efficiently.

Phase-Shift Modulation

Aerospace researchers began by characterizing traditional binary phase-shift keying and quarternary phase-shift keying—two commonly employed satellite signal-transmission techniques—in light of the new capacity requirements. Milstar currently uses differential phase-shift keying for its downlink. This method is similar to binary phase-shift keying and exhibits the same power spectral density, a measure of the distribution of signal power versus frequency.

Systems that transmit multiple signals within a given bandwidth have several options for sharing frequency resources. One technique, called frequency-division multiple access, assigns a carrier or channel to each signal, centered at a unique transmission frequency. Designers typically want to space these channels as closely as possible to increase the system capacity, but as the spacing gets too close, the power spectra start to overlap, and power from one channel spills into another. This phenomenon, known as adjacent channel interference, increases the probability of transmission errors, also known as the bit-error rate (see sidebar, Performance Measures for Digital Communication Systems).

	The power spectral density for Gaussian minimum shift keying is much more compact than that of differential phase-shift keying and does not exhibit the same pronounced sidelobes. In this example, the bandwidth–bit-time product is 1/6.
	Gaussian minimum shift keying waveforms with varying bandwidth–bit-time products are compared with binary and differential phase-shift keying. As the bandwidth–bit-time product decreases, the waveform spectra grows narrower.

The power spectral density of both binary and quarternary phase-shift keying is fairly broad, and when channels are packed together too tightly, the adjacent channel interference can be severe. In the case of the AEHF program, the channels would have to be spaced far apart to avoid large degradations from such interference. Researchers discovered that they simply could not fit enough channels within the allocated downlink frequency to meet the capacity requirement using standard binary, differential, or quarternary phase-shift keying. Other, more advanced modulation techniques would have to be found.

Gaussian Minimum Shift Keying

Aerospace had been studying a modulation technique known as Gaussian minimum shift keying for potential application in the Air Force Satellite Control Network and recognized that it might be a good candidate for the AEHF program.

Gaussian minimum shift keying is a form of continuous phase modulation, a technique that achieves smooth phase transitions between signal states, thereby reducing bandwidth requirements (see sidebar, Modulation Basics). With Gaussian minimum shift keying, input bits with rectangular (+1, -1) representation are converted to Gaussian (bell-shaped) pulses by a Gaussian filter before further smoothing by a frequency modulator. Also, in most cases, the Gaussian pulse is allowed to last longer than one bit time—the amount of time a binary 1 is in the "on" position. Consequently, the pulses overlap, giving rise to a phenomenon known as intersymbol interference. The extent of this overlap is determined by the product of the bandwidth of the Gaussian filter and the data-bit duration; the smaller the bandwidth–bit-time product, the more the data bits or pulses overlap.

Measured data showing growth of sidelobes in the power spectral density of offset quarternary phase-shift keying. The pink curve indicates performance through a standard (linear) amplifier, while the green curve shows the poorer performance though a saturated (nonlinear) amplifier.

The resulting carrier signal is very smooth in phase—particularly in comparison to waveforms generated through standard binary or quarternary phase-shift keying. This is important because signals with smooth phase transitions require less bandwidth to transmit. On the other hand, this very smooth phase makes the receiver's job much harder. With Gaussian minimum shift keying, there are no well-defined phase transitions to detect for bit synchronization, and the energy from each bit is mixed with the energy from several other bits. The transmitter output looks nothing like the data input, and on the receiver side, a special demodulator of increased complexity is needed to extract the data bits. For the receiver to achieve a given bit-error rate, the transmitter must generate more power to overcome the receiver noise in the presence of the intersymbol interference. In other words, the Gaussian minimum shift keying waveform is usually less power-efficient than more traditional waveforms such as binary phase-shift keying and requires a more complex receiver, but this potential reduction in power efficiency and increase in receiver complexity could be rewarded with a very significant enhancement of bandwidth efficiency. So, with Gaussian minimum shift keying, there is a trade-off between bandwidth efficiency and power efficiency.

Gaussian minimum shift keying is not new—the technique has been used extensively in Europe for cell-phone applications with a bandwidth–bit-time product of 0.3. But system designs using very small bandwidth–bit-time products such as 1/5 or 1/8 are new—and challenging. Aerospace became interested in these smaller bandwidth–bit-time products because of their narrow bandwidth occupancy and the rapid roll-off of their power spectra. These two factors strongly influence the ability to pack many different channels into a limited amount of bandwidth. The Gaussian minimum shift keying waveform exhibits a steep power spectrum and therefore coexists well with adjacent channels in a frequency-division multiple-access system.

This graph shows the measured power spectral density for Gaussian minimum shift keying when passed though a standard (linear) and saturated (nonlinear) power amplifier. Even in scenarios involving saturated amplifiers, the technique does not give rise to significant sidelobes. In this example, the bandwidth–bit-time product is 0.125, and the data rate is 1 megabit per second.

Feasibility Testing

When Aerospace first proposed the use of Gaussian minimum shift keying for the AEHF program, the milsatcom community reacted with considerable skepticism. By all accounts, much work still needed to be done. In particular, researchers needed to figure out how to demodulate Gaussian minimum shift keying waveforms having small bandwidth–bit-time products. Also, they had to devise a method to acquire and track the frequency, phase, and bit timing of the Gaussian signals. Other unknowns included how closely channels could be spaced and how the technique would perform in the real world, with imperfect time and frequency synchronization. The milsatcom technical community was also concerned about the implementation complexity of the demodulator, and had to be convinced that the risk was acceptable. In addition, researchers needed to investigate how Gaussian minimum shift keying performed under special operating environments associated with AEHF satellites, such as jamming. Backward compatibility with existing Milstar terminals was also an important consideration.

Demodulation

As a first step, Aerospace researchers developed a demodulator algorithm specifically optimized for Gaussian minimum shift keying signals. The algorithm was initially created and validated using commercial modeling software and was later translated into C, a programming language that runs very fast on a personal computer, to shorten the simulation times.

	Aerospace developed a demodulator algorithm specifically optimized for Gaussian minimum shift keying signals. The program was first compiled in C for simulation purposes, then subjected to breadboard testing. The predicted results are closely matched. Bandwidth–bit-time product is 0.2.
	In demonstrating the effectiveness of Gaussian minimum shift keying, Aerospace developed the tracking loops needed to maintain time, frequency, and phase synchronization. As shown here, the simulations exhibited negligible degradation on demodulator bit-error rate, when compared to ideal synchronization.

Optimizing the demodulator was not an easy task. Receiver noise is inevitable, and because noise is a random process, designers in general can only seek to maximize the probability that a demodulator will correctly discern the value of each bit that is transmitted. Moreover, to compensate for the intentional intersymbol interference introduced by the Gaussian minimum shift keying modulation process, the optimal receiver would have to look at sequences of bits, not individual bits, to decide what data were sent. Ultimately, Aerospace developed a demodulator, called a Maximum Likelihood Sequence Estimator, that receives a signal in white Gaussian noise and outputs an estimate of the most likely data sequence transmitted.

In developing the demodulator, Aerospace researchers also discovered that by preparing or "preprocessing" the data through a specialized algorithm known as the precoding algorithm, the demodulator performance could be improved. As a result, the transmission power requirements could be reduced by 2 to 2.5 decibels. Simulations using this precoding algorithm and the Maximum Likelihood Sequence Estimator demonstrated that, assuming ideal synchronization, the power performance of Gaussian minimum shift keying is superior to differential phase-shift keying by 0.5 to 1 decibel at the bit-error rate required for the AEHF program.

More recently, Aerospace improved on the Gaussian minimum shift keying demodulator with the development of a so-called soft-decision demodulator. While the Maximum Likelihood Sequence Estimator provides only hard yes-no decisions (was a 1 sent or not?), the soft-output demodulator yields both the bit decision and a reliability measure of that decision (there's a 90 percent likelihood that a 1 was sent). The use of this soft-output demodulator enables soft-decision decoding, which provides an additional 2.5-decibel power advantage over hard-decision decoding (see related article, "Forward Error Correction Coding").

Tracking and Acquisition

Having simulated the performance of the Gaussian minimum shift keying signals with ideal transmitter and receiver synchronization, Aerospace researchers then designed the tracking loops needed to maintain time, frequency, and phase synchronization. Using a mathematical model of the received signal, they derived timing-error and phase-error information using the received random data and designed tracking algorithms to track and correct these errors. The tracking algorithms were validated in C-code simulations and were found to have negligible degradation on demodulator bit-error rate, when compared to ideal synchronization.

The measured power spectral density for Gaussian minimum shift keying. The yellow curve shows the performance calculation derived from the C-code computation. The orange curve shows the results from a breadboard test (the noise floor is higher because of the test-equipment limitations). In this example, the bandwidth–bit-time product is 0.2, and the data rate is 1 megabit per second.

Researchers then implemented a signal-frequency acquisition scheme that allows acquisition of the Gaussian minimum shift keying signal within a relatively wide window of frequency uncertainty. A series of C-code simulations demonstrated that its residual frequency error could be easily handled by the phase-tracking algorithm. It should also be noted that although both the signal-acquisition and tracking functions are needed for a stand-alone application of the Gaussian minimum shift keying signal, the AEHF system would only need phase tracking at the satellite payload because the signal timing and frequency of the transmitting terminal are already synchronized to the satellite while operating in communication mode.

Next, Aerospace assessed the jamming vulnerability of the demodulator with its attendant phase-tracking algorithm. Simulations were conducted using jammers that were representative of any anticipated threat. Results showed that none of the jammers had a serious effect on demodulator performance. In addition, the issue of backward compatibility with existing Milstar terminals was addressed. Aerospace verified, by simulation and analysis, that a properly designed Gaussian minimum shift keying downlink could be tracked and demodulated, with acceptable degradation, by existing Milstar terminals designed for differential phase-shift keying signals.

Prototyping

After the simulation stage, Aerospace researchers moved on to the prototyping stage. Field-programmable gate arrays (customizable integrated circuits that are commonly used in hardware development) were combined with components such as analog-to-digital and digital-to-analog converters to create a laboratory prototype of the modulator and demodulator, with signal acquisition and tracking functions. Radio-frequency components were added to convert the signal up and down as needed, and a high-power amplifier was inserted to demonstrate how Gaussian minimum shift keying performed through a saturated power amplifier. This prototype modem allowed Aerospace and the larger milsatcom community to confirm the simulation results, obtain hardware complexity estimates, and gain confidence in Gaussian minimum shift keying as a viable option for both the downlinks and high-data-rate uplinks of the AEHF system.

This schematic diagram shows the prototype Gaussian minimum shift keying modulator/demodulator test configuration, with time and phase tracking.

Conclusion

Aerospace has worked closely with the AEHF contractors and other agencies to transfer knowledge and experience about Gaussian minimum shift keying—particularly for signals with small bandwidth–bit-time products. Extensive simulations and analyses performed by Aerospace and the larger milsatcom community have confirmed that the technique is suitable for the AEHF program and that the proposed downlink waveform can in fact meet the new system requirements with acceptable implementation complexity and risk. As a result, the AEHF program has adopted the Gaussian minimum shift keying technique for both of its high-data-rate uplink and downlink components.

Acknowledgment

The authors would like to thank Dr. Gee Lui for his guidance and assistance in preparing this article.