Hermitian Transform-Based Differencing Approach for Angle Estimation for Bistatic MIMO Radar Under Unknown Colored Noise Field

Hu, Jurong; Baidoo, Evans; Ying, Tian; Bao, Zhejing

doi:10.1109/access.2020.3007547

Cited by 4 publications

(5 citation statements)

References 22 publications

(47 reference statements)

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“…In Equation (13), the alteration of the significant elements occurs in the imaginary part of the observed measurement signal. Clearly, there exist invariances between the two transformed signal matrices; hence, by utilizing the covariance invariance approach [38, 39], a new measurement matrix can be obtained, which can be expressed as

\begin{array}{l} \bar{bold-italicC} = ({bold-italicC}_{0} - {bold-italicC}_{1}) \\ = (T^{- 1} bold-italicA \overset{´}{bold-italicS} A^{H} bold-italicT + T^{- 1} Q_{0} bold-italicT) - (j bold-italicTA \overset{´}{bold-italicS} A^{H} T^{- 1} + j bold-italicT Q_{0} T^{- 1}) \\ \begin{array}{l} left & = [TA, {bold-italicT}^{- 1} A] false[\begin{matrix} left \\ left \overset{´}{bold-italicS} & left 0 \\ left 0 & left - \overset{´}{j S} \end{matrix} false] {[bold-italicTA, T^{- 1} bold-italicA]}^{H}, \end{array} \end{array}

where

\overset{´}{bold-italicS}

denotes the estimated signal covariance matrix, and

\bar{bold-italicC}

is the resultant noise‐free covariance matrix. As observed from Equation (14), the components of

\bar{bold-italicC}

denotes a Hermitian conjugate matrix due to the imaginary factor applied, and the elements corresponding to the

{σ_{m n}^{2}}_{m n = 1}^{M N}

locations in

{bold-italicR}_{y} ...

…”

Section: Proposed Inverse Transformation Based Enhanced Capon Methodsmentioning

confidence: 99%

“…In Equation ( 13), the alteration of the significant elements occurs in the imaginary part of the observed measurement signal. Clearly, there exist invariances between the two transformed signal matrices; hence, by utilizing the covariance invariance approach [38,39], a new measurement matrix can be obtained, which can be expressed as…”

Section: Inverse Transformation-based Nonuniform Noise Elimination Te...mentioning

confidence: 99%

“…On the derivation of the Cramér–Rao Bound (CRB), based on the received data signal in Equation (6), the stochastic CRB to determine the angle estimates for the partly calibrated subarray‐based MIMO radar under non‐uniform noise effect can be derived by following the entries for the

(4 K P - 2 K) \times (4 K P - 2 K)

equation of the CRB matrix as [18, 38, 42].

\begin{array}{l} left & {[bold-italicCR B^{- 1} (Ψ)]}_{i, j} = 2 P R e {trace (B \frac{\partial \tilde{bold-italicA}}{\partial {normalΨ}_{i}} {bold-italicP}_{\overset{A}{true}}^{⊥} \frac{\partial \tilde{bold-italicA}}{\partial {normalΨ}_{j}})}, \end{array}

where

i, j

are the entries and

Ψ = {[\emptyset^{T}, θ^{T}, φ_{2}^{T}, …, φ_{L}^{T}, ψ_{2}^{T}, …, ψ_{L}^{T}, q^{T}]}^{T}

.…”

Section: Analysis Of the Algorithmmentioning

confidence: 99%

“…On the derivation of the Cramér-Rao Bound (CRB), based on the received data signal in Equation ( 6), the stochastic CRB to determine the angle estimates for the partly calibrated subarray-based MIMO radar under non-uniform noise effect can be derived by following the entries for the ð4KP−2KÞ � ð4KP−2KÞ equation of the CRB matrix as [18,38,42].…”

Section: Analysis Of the Algorithmmentioning

confidence: 99%

“…The stochastic CRB to determine the angle estimates for the partly calibrated subarray-based MIMO radar under nonuniform noise effect can be derived as [18,38,42].…”

Section: Experiments Seven: Resolution Probability Against Snr In Uni...mentioning

confidence: 99%

See 4 more Smart Citations

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

Baidoo

Bao

2021

IET Radar Sonar & Navi

Self Cite

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Uniformly distributed white noise is often the desirable noise assumption for partly calibrated subarray-based radar systems. However, this assumption may practically not always be guaranteed. In this study, the angle estimation problem of the partly calibrated multi-subarray-based bistatic multiple-input multiple-output radar, where intersubarray calibration errors and non-uniform noise coexist, is considered. In addition, an inverse transformation-based enhanced Capon method is proposed to adapt to such a challenging situation. First, the noise-free covariance matrix of each subarray is obtained by formulating an imaginary selecting matrix following a covariance matrix invariance approach which performs an inverse transformation of the matrix. Thus, the noise identities at the different antennas of the subarray are estimated as nuisance parameters at the expense of the target signals. Second, assuming that the calibration within each subarray is well configured such that the steering vector of a subarray is known, knowledge is required of the intersubarray calibration mismatches. To this, a highresolution Capon estimator which applies a combination of root and local searching orientation of the antenna arrays is implemented. The proposed approach resolves the intersubarray calibration errors and ultimately leads to obtaining the joint direction of departure and direction of arrival estimation of the target. Evidence of the proposed algorithm's validity and effectiveness over existing methods is demonstrated in numerical simulations under varying conditions.

show abstract

\begin{array}{l} \bar{bold-italicC} = ({bold-italicC}_{0} - {bold-italicC}_{1}) \\ = (T^{- 1} bold-italicA \overset{´}{bold-italicS} A^{H} bold-italicT + T^{- 1} Q_{0} bold-italicT) - (j bold-italicTA \overset{´}{bold-italicS} A^{H} T^{- 1} + j bold-italicT Q_{0} T^{- 1}) \\ \begin{array}{l} left & = [TA, {bold-italicT}^{- 1} A] false[\begin{matrix} left \\ left \overset{´}{bold-italicS} & left 0 \\ left 0 & left - \overset{´}{j S} \end{matrix} false] {[bold-italicTA, T^{- 1} bold-italicA]}^{H}, \end{array} \end{array}

where

\overset{´}{bold-italicS}

denotes the estimated signal covariance matrix, and

\bar{bold-italicC}

is the resultant noise‐free covariance matrix. As observed from Equation (14), the components of

\bar{bold-italicC}

denotes a Hermitian conjugate matrix due to the imaginary factor applied, and the elements corresponding to the

{σ_{m n}^{2}}_{m n = 1}^{M N}

locations in

{bold-italicR}_{y} ...

…”

Section: Proposed Inverse Transformation Based Enhanced Capon Methodsmentioning

confidence: 99%

“…In Equation ( 13), the alteration of the significant elements occurs in the imaginary part of the observed measurement signal. Clearly, there exist invariances between the two transformed signal matrices; hence, by utilizing the covariance invariance approach [38,39], a new measurement matrix can be obtained, which can be expressed as…”

Section: Inverse Transformation-based Nonuniform Noise Elimination Te...mentioning

confidence: 99%

(4 K P - 2 K) \times (4 K P - 2 K)

equation of the CRB matrix as [18, 38, 42].

\begin{array}{l} left & {[bold-italicCR B^{- 1} (Ψ)]}_{i, j} = 2 P R e {trace (B \frac{\partial \tilde{bold-italicA}}{\partial {normalΨ}_{i}} {bold-italicP}_{\overset{A}{true}}^{⊥} \frac{\partial \tilde{bold-italicA}}{\partial {normalΨ}_{j}})}, \end{array}

where

i, j

are the entries and

Ψ = {[\emptyset^{T}, θ^{T}, φ_{2}^{T}, …, φ_{L}^{T}, ψ_{2}^{T}, …, ψ_{L}^{T}, q^{T}]}^{T}

.…”

Section: Analysis Of the Algorithmmentioning

confidence: 99%

Section: Analysis Of the Algorithmmentioning

confidence: 99%

“…The stochastic CRB to determine the angle estimates for the partly calibrated subarray-based MIMO radar under nonuniform noise effect can be derived as [18,38,42].…”

Section: Experiments Seven: Resolution Probability Against Snr In Uni...mentioning

confidence: 99%

See 3 more Smart Citations

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

Baidoo

Bao

2021

IET Radar Sonar & Navi

Self Cite

View full text Add to dashboard Cite

show abstract

Dynamic subspace angle estimation method for bistatic MIMO radar with system imperfections

Baidoo

Bao

et al. 2022

Digital Signal Processing

View full text Add to dashboard Cite

Joint DOD and DOA estimation using tensor reconstruction based sparse representation approach for bistatic MIMO radar with unknown noise effect

Baidoo

Zeng

et al. 2021

Signal Processing

View full text Add to dashboard Cite

Hermitian Transform-Based Differencing Approach for Angle Estimation for Bistatic MIMO Radar Under Unknown Colored Noise Field

Cited by 4 publications

References 22 publications

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

Dynamic subspace angle estimation method for bistatic MIMO radar with system imperfections

Joint DOD and DOA estimation using tensor reconstruction based sparse representation approach for bistatic MIMO radar with unknown noise effect

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