System and method for wideband spectral estimation using joint space-time array manifold vectors

Embodiments of systems and method for determining a joint space-time spectral estimate (P) for a wideband spectrum are generally described herein. To determine a joint space-time spectral estimate (P) for a wideband spectrum, a random time delay may be applied to received signals for each channel of a plurality of receive channels to generate time-delayed signals for each receive channel. The time-delayed signals may be sampled for each receive channel to generate time-delayed samples and form array manifold vectors based on the random time delays and position of each antenna element in an array of antenna elements. An inverse (Q) of the joint-space time spectral estimate (P) may be determined by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples. The joint space-time spectral estimate (P) may comprise spatial and temporal properties of the wideband spectrum.

TECHNICAL FIELD

Embodiments pertain to signal identification in a wideband spectrum. Some embodiments pertain to determining angle-of-arrival (AOA), frequency and bandwidth characteristics of the identified signals.

BACKGROUND

One issue with conventional wideband spectral estimation techniques is that they necessarily have to channelize input data prior to performing spatial-spectral estimation. This is because the array manifold vectors are defined at a specific signal frequency which creates errors when the signal frequency is not equal to the frequency used in the array manifold vector for the spatial-spectral estimation technique. Furthermore, wideband signals that extend through channels have challenges as they are processed in separate channels and have to be stitched back together or reconciled prior to reporting angle of arrival.

Thus, there are general needs for improved wideband spectral estimation.

DETAILED DESCRIPTION

Embodiments disclosed herein utilize the joint space-time relationship of electromagnetic waves to define array manifold vectors in 4-dimensional space and overcome the lack of sample diversity in the z-dimension for planar arrays by introducing a known random time delay in each channel of the receiving array. Some embodiments perform 4-dimensional processing of incoming electromagnetic waves. Some embodiments perform Latin hypercube sampling of the k-space to determine array manifold vectors. Some embodiments perform randomized channel-to-channel delays prior to the formation of the covariance matrix utilized in spectral-estimation techniques. These embodiments are discussed in more detail below.

FIG.1is a functional diagram of a system for performing a joint space-time spectral estimate in accordance with some embodiments. In accordance with embodiments, system100is configured for joint space-time spectral estimation. In these embodiments, the system100may include processing circuitry106and memory110. In these embodiments, to determine a joint space-time spectral estimate (P) for a wideband spectrum, the processing circuitry106may apply a random time delay (tn)107to received signals101for each channel of a plurality of receive channels to generate time-delayed signals105for each receive channel. In these embodiments, the processing circuitry106may also sample the time-delayed signals105for each receive channel to generate time-delayed samples (Xn), and form array manifold vectors based on the random time delays and position of each antenna element102in the array of antenna elements. The processing circuitry106may also determine an inverse (Q) of the joint-space time spectral estimate (P)109by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples (Xn). The joint space-time spectral estimate (P)109may comprise spatial and temporal properties of the wideband spectrum.

In some embodiments, the processing circuitry106may form the array manifold vectors in k-space (i.e., wave number space), each manifold vector having a length (m) corresponding with a number of channels.

In some embodiments, each receive channel may comprise a same wideband frequency spectrum. Each receive channel may be associated with one antenna element102of the array of antenna elements. For each receive channel, one of the random time delays may be applied to the received signals of the associated receive channel.

In some embodiments, the processing circuitry106may compute the inverse (Q) of the joint-space time spectral estimate (P) by projecting the array manifold vectors through the mixing matrix (M) yields. In some embodiments, the processing circuitry106may invert the inverse (Q) of the joint-space time spectral estimate (P) to obtain the joint-space time spectral estimate (P)109.

In some embodiments, the processing circuitry106may form a sample covariance matrix (Sxx) from the time-delayed samples (Xn) and invert the sample covariance matrix to form the mixing matrix (M). In these embodiments, the sample covariance matrix (Sxx) may be an N×N Hermitian matrix.

In some embodiments, the processing circuitry106may identify signals (seeFIGS.3A and3B) within the wideband spectrum based on the joint-space time spectral estimate (P)109. In some embodiments, the processing circuitry106may determine an angle-of-arrival (AOA) and determine frequency and bandwidth characteristics of the identified signals based on the joint-space time spectral estimate (P)109.

In some embodiments, the system may further comprise delay circuitry104. The delay circuitry104may comprise a discrete time delay unit (TDU)114for each receive channel. Each of the TDUs may be configured to delay signals within one of the receive channels by the random time delay (tn) for that receive channel. In some embodiments, the discrete delay times are randomly set using control words to yield different delay times, although the scope of the embodiments is not limited in this respect.

In some embodiments, each array manifold vector (Vn) is computed using the following equation:
vn=ej(kTpn−K·clightτn)

where pnrepresents position vectors corresponding to a position of an element, k represents the k-space vectors, K is the wavenumber, and tnrepresents the random time delay applied to a receive channel.

In some embodiments, the memory110may store the random time delay (τn) for each receive channel.

FIG.2is a procedure for performing a joint space-time spectral estimate in accordance with some embodiments. In accordance with embodiments, operation202may comprise applying a random time delay (tn) to received signals101(FIG.1) for each channel of a plurality of receive channels to generate time-delayed signals105(FIG.1) for each receive channel. Operation204may include sampling the time-delayed signals105for each receive channel to generate time-delayed samples (Xn). Operation206may include forming array manifold vectors based on the random time delays and position of each antenna102(FIG.1) element in an array of antenna elements. Operation212may comprise determining an inverse (Q) of the joint-space time spectral estimate (P)109by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples (Xn). In these embodiments, the joint space-time spectral estimate (P) comprises spatial and temporal properties of the wideband spectrum.

In these embodiments, the inverse (Q) of the joint-space time spectral estimate (P) may be computed in operation212by projecting the array manifold vectors through the mixing matrix (M) yields and operation214may comprise inverting the inverse (Q) of the joint-space time spectral estimate (P) to obtain the joint-space time spectral estimate (P).

In some embodiments, operation208may comprise forming a sample covariance matrix (Sxx) from the time-delayed samples (Xn) and operation210may comprise inverting the sample covariance matrix to form the mixing matrix (M).

In some embodiments, operations208,210,212and214may form the high-resolution spectrum as described by J. Capon, “High-resolution frequency-wavenumber spectrum analysis,”Proc IEEE, vol 57, pp 1408-1418, August 1969, although the scope of the embodiments is not limited in this respect.

FIG.3Aillustrates the spatial properties of identified signals in accordance with some embodiments.

FIG.3Billustrates the frequency properties of the identified signals ofFIG.3A, in accordance with some embodiments.

FIG.4illustrates wave propagation in accordance with some embodiments. As illustrated inFIG.4, an incident electromagnetic wave (normal vector n) may be incident on an antenna array of individual elements. The joint space-time definition for electromagnetic wave propagation may be written as follows:
e(r,t)≅E·ej(kTr-ωt)

At an array whose location is at r at time t the signal at channel n can be expressed as:
en(r,t)≅E·ej(kTpn−ωτn)ej(kTr-ωt)≅E·ej(kTpn−ωτn)ejϕ

In these embodiments, the array manifold vector can be re-written as:
vn(r,t)=ej(kTpn−ωτn)

In these embodiments, the time delay, tn, (seeFIG.4) is randomized at every channel and the array response in four-dimensions can be examined.

Accordingly, a joint-space time spectral estimate (P)109may be determined by projecting the array manifold vectors through a mixing matrix (M) which is based on time-delayed samples (Xn) of the received signals.