Fredric J. Harris

Digital receivers and transmitters using polyphase filter banks for wireless communications

Provides a tutorial overview of multichannel wireless digital receivers and the relationships between channel bandwidth, channel separation, and channel sample rate. The overview makes liberal use of figures to support the underlying mathematics. A multichannel digital receiver simultaneously down-converts a set of frequency-division-multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver, these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase M-path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple baseband aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator.

Configurable logic for digital communications: some signal processing perspectives

For the past two decades software programmable digital signal processors and ASICs have provided hardware solutions for signal processing system designers. A new option has become available: field programmable gate arrays. FPGA-based DSP platforms allow the designer to realize a data path that exactly matches the required processing, while at the same time maintaining the flexibility of a software approach. This article presents an overview of some FPGA DSP applications. Several filter designs are presented, and the use of CORDIC arithmetic for constructing an FPGA carrier recovery loop is outlined. In addition to presenting design examples that can be realized using present-generation devices and tools, we take a brief look at how the dynamic reconfiguration aspect of certain FPGAs could be exploited in future-generation communication technologies.

Multirate digital filters for symbol timing synchronization in software defined radios

This paper describes the use of a polyphase filterbank to perform the interpolations required for symbol timing synchronization in a sampled-data receiver. The polyphase filterbank possesses advantages over architectures based on separate matched and interpolation filters. Interpolations are realized by filterbank index selection and a separate interpolating filter following the matched filter is not required. Maximum likelihood timing synchronization techniques can be easily incorporated into the polyphase filter bank in a natural way. An M-stage polyphase filterbank with input data sampled at approximately N samples/symbol can be used in a loop that operates at MN samples/symbol, N samples/symbol, or 1 sample/symbol. When operating at 1 sample/symbol, auxiliary control must also be included to adjust the clocking of data into the filter bank to account for small differences in the sample clock and N times the data clock. Examples are presented to illustrate loop performance and control.

Performance and design of Farrow filter used for arbitrary resampling

The Farrow filter (1988) is a multirate filter structure which offers the option of continuously adjustable resample ratio. This paper presents a derivation of the method proposed by Farrow, and demonstrates the performance and complexity of resampling filters using his technique. The paper also develops some important system options made available to the designer as spin-offs of the derivation.

Non-Maximally Decimated Analysis/Synthesis Filter Banks: Applications in Wideband Digital Filtering

We present a new class of highly effective and low complexity digital filters for processing very wideband signals. Digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval. We will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate. The digital filtering will be shown to include various tasks such as linear/non-linear phase finite impulse response (FIR) filtering, fractional delay filter among others. The proposed technique utilizes the framework of non-maximally decimated filter banks (NMDFBs) with perfect reconstruction (PR) property, which makes the filter bank design simpler and more flexible. Compact representation for the generalized DFT based NMDFBs as well as its efficient polyphase implementation will be provided. The digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks. We will show this embedded intermediate processing elements can achieve spectral shaping/signal manipulation task, which is a generalization of the concept of manipulating a digital filter in the frequency domain. We also analyze both analytically and experimentally, the spectral shaping accuracy based on different design strategies.

Highly adjustable multirate digital filters based on fast convolution

FFT-IFFT configuration, or more generally a forward-inverse orthogonal transform pair, offers a way to implement a digital filter whose frequency-domain characteristics can be straightforwardly tuned by adjusting the complex gains of the frequency bins. Using filter banks (FBs) for the transform pair, sharp transition bands can be obtained for low-pass/bandpass/highpass type filter designs. However, FBs suffer from relatively high implementation complexity. Fast convolution based multirate FBs constitute and alternative approach which is able to reach high spectral containment together with high flexibility and conceptual simplicity. In this paper we consider a fast convolution based highly tunable analysis FB configuration and show that nearly perfect-reconstruction FB systems can be implemented using this approach. Further, the channel filters of the analysis FB are easily configurable for different bandwidths, center frequencies and output sampling rates.

Implementation considerations and limitations for dynamic range enhanced analog to digital converters

The authors review the operation of single and cascade oversampled noise-feedback converters operating with multilevel ADCs (analog/digital converters). Attention is given to techniques for improving the accuracy and the dynamic range of ADCs by operating a reduced resolution quantizer in a feedback loop. These techniques are seen to be special cases of noise-feedback coding in which the loop operates at sample rates far in excess of the signal bandwidth and uses spectral noise shaping to shift in-band quantizing noise power to out-of-band spectral positions. It is noted that implementing these techniques at very high sample rates (10/sup 8/ samples per second) with combinations of analog and digital subsystems offers a number of challenging signal processing problems. It is shown that the mix of analog and digital segments and the ADC-DAC (digital/analog converter) delays have significant deleterious effects on the loop performance.<<ETX>>

Design and implementation of efficient resampling filters using polyphase recursive all-pass filters

Computationally efficient resampling filters are formed from sets of recursive all-pass subfilters operating in a polyphase structure. These subfilters, exhibiting unity magnitude response, have phase shifts which add constructively in the passband(s) and destructively in the stopband(s). The computational burden for these filters is one-fifth to one-tenth that of conventional resampling filters. The primary advantage of these structures is the relatively low workload per output point. A secondary advantage is the low sensitivity to finite arithmetic and the lack of bit growth in internal states. Disadvantages include the nonuniform phase response of the filter, as well as the newness of the idea and the difficulty in determining coefficients for the filter.<<ETX>>

Vector Signal Analyzer Implemented as a Synthetic Instrument

Synthetic instruments (SIs) use the substantial signal processing assets of a field-programmable gate array (FPGA) to perform the multiple tasks of targeted digital signal processing (DSP)-based instruments. The topic of this paper is vector signal analysis from which time-dependent amplitude and phase is extracted from the input time signal. With access to the time-varying amplitude-phase profiles of the input signal, the vector signal analyzer can present many of the quality measures of a modulation process. These include estimates of undesired attributes such as modulator distortion, phase noise, clock jitter, I -Q imbalance, intersymbol interference, and others. This is where the SI is asked to become a smart software-defined radio (SDR), performing all the tasks of a DSP radio receiver and reporting small variations between the observed modulated signal parameters and those of an ideal modulated signal. Various quality measures (e.g., the size of errors) have value in quantifying and probing performance boundaries of communication systems.

On Detecting White Space Spectra for Spectral Scavenging in Cognitive Radios

A primary task performed by a Cognitive Radio is that of spectral estimation to locate the segments in a spectral span that contain white zones, spans that contains noise only, or grey zones, spans that contain signals with significant intervals of off-time. The identification of spectral regions containing noise only spectra, as opposed to regions containing signals with low spectral density, is surprising difficult. The estimator must deal with questions of transform length, window selection, window length, window overlap, and ensemble averaging options. This paper describes the impact of each selection option and presents the architecture of the optimal spectral estimator.