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The Tuneable Pipelined Frequency Transform—A New Filter-Bank Technique

Building upon the Pipelined Frequency Transform (PFT ) architecture, we have developed a new filter-bank technique that allows asymmetrical-band splitting of a given spectrum of frequencies. A few applications require that an input signal be separated into a number of different frequency channels. If these channels are of equal width and equally spaced, you can use techniques such as the Fast Fourier Transform (FFT) or RF Engine's proprietary Pipelined Frequency Transform (PFT).

For the general case of frequency bands of different width, unevenly distributed across the spectrum, then the most common solution is to employ a number of Digital Down Converters (DDCs), each responsible for an individual channel. The Tuneable Pipelined Frequency Transform (TPFT) provides similar functionality to a stack of DDCs. TPFT gives the user freedom to specify channels by center frequency and bandwidth, define filter characteristics, and reconfigure to another frequency plan as required. Furthermore, you can also directly apply spectral-shaping masks onto the outputs within the architecture itself. This article will provide a description of the TPFT architecture and will highlight the advantages of this technique over competing solutions.

General Description of the Tuneable PFT (TPFT)

The pipelined architecture employed by the PFT serves well for the purpose of extracting different size frequency bands: at each PFT stage, the spectrum is separated into bands which are half as wide as those from the previous stage, and positioned as illustrated in Figure 1 .


Figure 1:  Frequency separation of a standard PFT

Due to the PFT cascaded architecture (Figure 2 ), intermediate outputs are readily available. It is possible, by means of modifying the PFT architecture, not only to extract frequency bands of the desired size, but also to ensure these bands are centered at any given frequency.


Figure 2:  Schematic view of TPFT typical architecture

This level of tuneability is achieved in two stages. First, the signals are coarsely tuned within the PFT stages, then fine tuned by a complex converter whose Local Oscillator (LO) is a Numerically Controlled Oscillator (NCO) driven by the routing engine (a schematic of these subsystems is shown in Figures 3 and 4 ).

The approach chosen here is to provide coarse tuning within the PFT stages, doing so by means of LO values chosen from the following set:

Wider filters are used to ensure that the entire spectrum is covered and carried forward to the next stages. The filter passband has been extended by 50%, while maintaining the same stopband characteristics. Note that the wider filter allows us to include the same frequencies as the standard PFT, independent of the LO value used, with the added benefit of ensuring the center of any carrier within the bin would not be further than Fx/16 from the bin's center.


Figure 3:  Schematic of a Complex Down-Converter for TPFT

The main advantage of performing the tuning operation in two steps is the reduction of size, for a given frequency resolution, of the LUT used for fine-tuning. The fine-tuning mixing process only needs to shift frequencies by a maximum of Fsbin /16 Hz instead of the full Fsbin /4 Hz. This, in practice, translates to a four-fold LUT size saving for a given frequency resolution.

The benefit of such a reduction in LUT size can be best appreciated with a numerical example. Assume both a DDC and the TPFT have to extract a 100 kHz channel from an input bandwidth of ~80 MHz, with a frequency resolution of 10 Hz. The size of the LUT used in the DDC NCO would be 8e6 , while a 10-stage TPFT would achieve this resolution with a 1.25e3 -valued LUT. The reduction in LUT size is ~1e4 orders of magnitude. Note that the frequency resolution is relative to the stage considered and is given by Fxresolution = (Fx/16) / LUTsize , where Fx is the sample rate of every bin out of stage x.


Figure 4:  Schematic of a fine-tuning complex-frequency converter used in the TPFT

After fine-tuning takes place, we use a polyphase Finite Impulse Response (FIR) filter to extract only the required bandwidth for each signal (Figure 5 ). You can also use this final filtering stage for independent spectral shaping/masking of each output bin.


Figure 5:  Example of a polyphase shaping filter for two-channel shaping: one channel is filtered by filter h(n), the other by filter k(n)

As the sample rate of every band out of the TPFT is a power-of-two fraction of the input sample rate, it is possible to interleave all outputs from different stages within one output stream running at the full system rate. Furthermore, so long as the sum of the all-bands sample rate does not exceed the system rate, all of these can be accommodated in one output stream. For those familiar with the wavelet transform, the samples are interleaved in a similar manner to the one used for the output of a discrete wavelet transform.

Prior to interleaving, every stage's output stream is buffered in a circular manner; hence all bin outputs are available at any given time. For each stage buffer, an address table and counter are kept, so the correct bin can be extracted when its time slot on the interleaved output stream becomes available. The order by which intermediate stages are interleaved onto the output stream is stored together with the information required for accessing the correct sample within each of the stages buffers. A schematic of this subsystem is shown in Figure 6 .

The interleaved-output sample streams are not necessarily at the exact sampling rate for baseband demodulation. For different bandwidth channels that follow a similar bandwidth pattern (such as, a power-of-two step size), this can be addressed by adjusting the system rate. The general case requires a multi-rate section operating on each channel independently, and we are currently studying a solution for this scenario.


Figure 6:  Schematic of the output interleaver architecture

Tunability Requirements

There are frequency-splitting plans that require the fine-tuning components of the TPFT to be duplicated. Typically, this happens when a large number of desired frequency spans are just about large enough for extraction within a given stage. As this implies that the effective sample rate for each of those bins is greater than the twice oversampled rate, either or both of the following will happen:

  • The output stream rate is insufficient for all channels required
  • Some of the adjacent carriers becomes unreachable.

Figure 7 shows an example of such a situation.


Figure 7:  An example of closely packed carriers of width slightly greater than the minimum required for extraction out of Stage 3 (St3). The net result is that some of these carriers will not be extracted and a contiguous portion of the spectrum is completely out of reach.

In order to deal with this problem, two adjacent carriers of total bandwidth Bw (where Fx < Bw < 1.5Fx) are extracted from a given bin. The issue of using more bandwidth than the one normally available in one bin is overcome by fine tuning both carriers separately, thus resulting in a two output streams, both running at the bin sample rate. A schematic of such a subsystem is shown in Figure 8 .


Figure 8:  Illustration of two carriers extracted from one bin

In those situations where no assumption can be made on the channels required for extraction, the fine-tuning components need to be duplicated, as illustrated in Figure 9 .


Figure 9:  Schematic of fully customizable TPFT

However, the situation just illustrated is perhaps extreme: in most real-life situations guard-bands separate adjacent carriers. Furthermore, the first and last 10~15% of the spectrum are typically unusable. Any anti-aliasing filter at the front-end of the PFT would need to have a zero-transition band to make 100% of the spectrum usable or, alternatively, for the given bandwidth, the sample rate would need to be increased by a factor of 120%.

The trade-off between hardware complexity (single- or double-fine-tuning subsystem) and flexibility in terms of guaranteeing full spectrum coverage for any given set of signals is application dependent and needs to be assessed on a case-by-case basis. A final decision as to whether or not to use two output streams is dependent on the balance between reducing hardware complexity and the typical bandwidth occupancy of the application in which the TPFT is used.

Frequency Reconfiguration

Perhaps the most important feature of the TPFT is its ability to be reconfigured in real time to output different user-defined frequency bands. The total output delay due to reconfiguration depends mainly on the filters used within each stage, as these need to fill up with new values before they output reliable information. As a guide, the delay due to reconfiguration effects for a 10-stage TPFT varies typically between 5000 to 15,000 clock cycles (25 µs to 75 µs at a system clock rate of 204.8 MHz). Furthermore, you must also consider the physical interface to the hardware, as this dictates the time for the new parameters to be updated into the registers.

Although it is possible to manually change the TPFT parameters to achieve tuneability onto a band, this process can be completely automated. We have implemented an algorithm to perform automatic routing onto carriers of interest, as well as calculating other parameters necessary for the TPFT to function. The user is left with the sole task of selecting the frequency plan of interest and the type of shaping to be applied onto the output (Figure 10 ).


Figure 10:  Screen-shot of GUI software: four BPSK modulated signals of various bandwidth are extracted from one wide-band input

NOTE: flat pass-band shaping filters are used in this example, thus the signal's sidelobes fall within the filters' transition band and still show significant power spectral density above the noise floor.

Software Demonstrator

In Figure 10 , an input signal is loaded from either an ASCII file or from our demonstrator board. Sampling rate and input bitwidth are then selected and the input spectrum shown on the bottom half of the screen. The two grey-shadowed opposite ends of the spectrum represent the aliased frequencies, on which the TPFT cannot operate. The amount of aliased spectrum is user-defined (the default value is ~10% of the total bandwidth) and can be modified to represent any front-end filter rolloff.

You can then select the frequency bands of interest directly on the spectrum plot itself or by entering their coordinates. Finally, you can apply different shaping filters onto each individual channel. At this point, the model can be started: on the basis of the channels selected, the number of necessary stages is determined and the TPFT tree is automatically routed. The input stream is then passed through the TPFT itself. The output samples of each channel are stored and their spectra displayed on-screen.

System Architecture

Figure 11 shows a schematic of the main building blocks of a TPFT system.


Figure 11:  Schematic view of a complete TPFT system. The m-processor to configure the architecture to a frequency plan can either be a PC or a dedicated solution

The graphical interface, shown in Figure 10 , provides full controls for the engine. This is to be provided by RFEL, thus eliminating the need to generate a custom interface to the hardware, which in turn minimizes customer risk and cost.

You can perform the processing of the routing of the TPFT onto a specified frequency plan either on a general purpose PC, or embed the processing into the hardware. The latter, for instance, can be performed via any of the System-On-Programmable-Chip (SoPC) devices commercially available (for example, the Xilinx Virtex-II Pro).

A designer can easily accommodate the TPFT engine within a modern FPGA device such as a Xilinx Virtex-II or an Altera Stratix, as well as develop it as an ASIC. Additional memory might be required for larger transforms, mainly due to the increase in memory bandwidth needs of later stages. Finally, a Digital Half-Band Filter (DHBF) might also be incorporated to perform real-to-complex conversion of an already digitized signal.

Comparison of the TPFT with Conventional Digital Down-Converters

Standard DDCs are probably the most common solution in those applications where you need only a limited number of channels. However, as the number of channels increases, it becomes apparent that the linear growth in component count for by a stack of DDCs can be outperformed by an interleaving structure such as the TPFT. The growth in logic-component count due to an increased number of channels within a TPFT is proportional to log2 ; thus there would be a threshold point after which DDCs are inefficient when compared to the TPFT (Figure 12 ). In reality, the TPFT memory requirements increase exponentially with the number of stages, until the memory becomes the principal constraint. We envision that you can implement as many as 16 stages (up to 65,536 different channels) using external memory with an FPGA or ASIC solution.


Figure 12:  Amount of logic required by DDC/TPFT for a given number of channels

As an example, a TPFT design could extract 25 channels, each ~1MHz in bandwidth, from a wideband input of 100 MHz with a six-stage engine. This, depending on filter requirements, would typically fit on a Xilinx Virtex-II 3000.

TPFT Application Example

In satellite communications, the allocation of frequencies within the available spectrum will change with the bandwidth requirements of the various operators. It is possible that, at a particular time, the channel configuration of Figure 13a would be used. As the operators' requirements change, the new configuration of Figure 13b might now be employed. Using a TPFT allows switching on the new frequency plan with minimal delays and without changes in the hardware. If a stack of DDCs were used instead, the reconfiguration process would still have the typical delay due to filter settling time, yet would now require 10 more DDCs. As the number of channels grows, the use of DDCs becomes more and more impractical when compared to the TPFT.


Figure 13:  Two possible frequency plans for a wide-band satellite-radio link

Conclusions

Hopefully, this article has demonstrated that for a plurality of simultaneous channels, the TPFT architecture provides significant advantages over more conventional methods of frequency splitting, such as complex down-converters, or even less flexible frequency transforms such as the Discrete Fourier Transform (DFT) and similar techniques.

Overall, the TPFT fills the gap between the comparatively inflexible FFT or PFT approaches and the use of DDCs, which is extremely flexible but becomes increasingly inefficient above a certain number of channels. The TPFT provides a highly flexible and efficient means of frequency channelization, fully reconfigurable within its hardware frame.

About the Author

John Lillington, Founder, CEO and CTO of RF Engines, has had over thirty years' experience in radio-frequency and digital-signal-processing design work. He has held senior design positions with Raytheon in the U.S., BAE Systems (formerly Plessey) and Thales (formerly EMI) in Europe, and has run a highly successful design consulting business for over 20 years. John is the architect of the PFT product family. He has a BSc from the University of London, U.K., and an MSc from the University of Birmingham, U.K.

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