J. Scott Goldstein

Reduced-rank chip-level MMSE equalization for the 3G CDMA forward link with code-multiplexed pilot

This paper deals with synchronous direct-sequence code-division multiple access (CDMA) transmission using orthogonal channel codes in frequency selective multipath, motivated by the forward link in 3G CDMA systems. The chip-level minimum mean square error (MMSE) estimate of the (multiuser) synchronous sum signal transmitted by the base, followed by a correlate and sum, has been shown to perform very well in saturated systems compared to a Rake receiver. In this paper, we present the reduced-rank, chip-level MMSE estimation based on the multistage nested Wiener filter (MSNWF). We show that, for the case of a known channel, only a small number of stages of the MSNWF is needed to achieve near full-rank MSE performance over a practical single-to-noise ratio (SNR) range. This holds true even for an edge-of-cell scenario, where two base stations are contributing near equal-power signals, as well as for the single base station case. We then utilize the code-multiplexed pilot channel to train the MSNWF coefficients and show that adaptive MSNWF operating in a very low rank subspace performs slightly better than full-rank recursive least square (RLS) and significantly better than least mean square (LMS). An important advantage of the MSNWF is that it can be implemented in a lattice structure, which involves significantly less computation than RLS. We also present structured MMSE equalizers that exploit the estimate of the multipath arrival times and the underlying channel structure to project the data vector onto a much lower dimensional subspace. Specifically, due to the sparseness of high-speed CDMA multipath channels, the channel vector lies in the subspace spanned by a small number of columns of the pulse shaping filter convolution matrix. We demonstrate that the performance of these structured low-rank equalizers is much superior to unstructured equalizers in terms of convergence speed and error rates.

Robust rank selection for the Multistage Wiener Filter

The Multistage Wiener Filter (MWF) is an adaptive processing technique that has the ability to outperform the full rank Wiener solution in a low sample support environment. However, this requires knowledge of the appropriate rank in order to enjoy these advantages. In this paper we show that the addition of a diagonal loading-like quantity to the Multistage Wiener Filter will add significant robustness to the rank selection process. Since the MWF is most often implemented without the formation of a sample covariance matrix, diagonal loading cannot be added in the usual sense. In this paper we describe an alternate technique called “error loading” for augmenting the filter. The incorporation of error loading is shown to provide the rank selection robustness that we desire.

Reduced rank matrix multistage wiener filter with applications in MMSE joint multiuser detection for DS-CDMA

A generalized statistical signal processing framework developed in [2] is utilized for interference suppression for Joint Multiuser Detection (MUD). Previous work on the efficient correlations subtractive architecture form of the reduced rank multistage Wiener filter (CSA-MWF) is extended by considering the multiple signal constraint case. The reduced rank algorithm is not based on an eigen-decomposition, which requires the signal subspace rank to be greater than or equal to the number of signals present in the system. The solution meets or exceeds full rank MMSE at a significantly reduced rank. System performance is characterized for a highly loaded synchronous DS-CDMA system in the presence of multi path. The bit error rate (BER) performance of the Joint CSA-MWF (JCSA-MWF) is compared to MMSE and RAKE receivers.

A low complexity receiver for space-time coded CDMA systems

A novel receiver for space-time coded systems based on the reduced rank multistage Wiener filter (MWF) is presented. It is shown that this receiver has a complexity that is only a linear function of the processing gain (N), the number of transmit antennas (Lt), and the rank (D) of the MWF. The complexity of the equivalent MMSE solution is a function of (N Lt)3. It is also demonstrated by numerical simulation that this receiver meets MMSE performance at a significantly lower rank. The MMSE implementation is derived and performance is evaluated for highly loaded synchronous CDMA systems in flat fading.

Multistage anti-spoof GPS interference correlator (MAGIC)

With the proliferation of GPS jammers and spoofers, commercial GPS receivers need robust anti-jam (AJ)/anti-spoofing (AS) solutions to ensure the future integrity of precision navigation and timing (PNT) solutions. The AJ/AS challenge is perhaps greatest when confronting the size, weight, power (SWaP) constraints of commercial applications that typically have GPS receivers with single antenna configurations and limited intrinsic AJ/AS capability. This article focuses on a newly developed single antenna AJ/AS solution known as MAGIC. Our approach applies a reduced-rank MMSE based C/A code correlator for single antenna GPS receivers that replaces a standard C/A code correlator for enhanced AJ/AS capability.

A COTS based asynchronous distributed array processor utilizing reduced-rank STAP

Distributed array processing has been a topic of interest due to its added advantage of sensor placement and processing gain for leveraging transmit/receive beamforming configurations. However, having independent local oscillators at each sensor presents a synchronization challenge for a distributed array. We explore the use of reduced-rank signal processing and Signals-of-Opportunity (SOOs) to maintain better-distributed sensor coherency while performing Space-time Adaptive Processing (STAP) when GPS is unavailable for local sensor oscillator synchronization. Reduced-rank signal processing requires fewer samples for STAP convergence, thereby allowing less stringent coherency constraints on the distributed array processor. Less stringent coherency constraints enables the use of SOOs as timing reference beacons in the field of view, thereby eliminating the need to have a dedicated transmitter for sensor synchronization. We explore these concepts utilizing COTS Software Defined Radios (SDRs) providing data to an asynchronous distributed array processor (ADAP). The SDRs are setup to simultaneously sample the SOO and the Signal-of-Interest (SOI) to enable the distributed array processor to achieve both sensor synchronization and reduced-rank STAP on the SOI. Results are presented utilizing FM HD radio towers as both SOOs and SOIs, but our approach can easily be extended to a variety of other signals such as TV, cellular tower, and satellite signals just to name a few.

Adaptive Noise Waveform Design for Radar

This paper introduces an adaptive radar waveform technique where a standard LFM waveform is used as an initial seed. The seed waveform is changed using a phase-only adaptive technique to minimize the resulting waveforms power in specific areas associated with in-band and adjacent-band spectral regions. Adjacent-band power minimization reduces interference to other spectral users, while in-band power minimization improves the waveform performance in matching interference environments. The resulting waveform retains a constant modulus which is valuable for practical transmitters, yet exhibits a variable degree of phase noise. Results are shown for three levels of computational convergence in the power minimization process. Ambiguity functions are plotted for each waveform to illustrate waveform performance characteristics such as radar resolution, target ambiguities, sidelobe response, and Doppler tolerance.