Finite sample identifiability of multiple constant modulus sources

Leshem, Amir; Petrochilos, Nicolas; Veen, Alle-Jan van der

doi:10.1109/tit.2003.815791

Cited by 14 publications

(11 citation statements)

References 9 publications

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“…As mentioned earlier, although bilinear decomposition is not unique in general, bilinear decomposition under FA/CM constraints can be unique [9], [15], [17]. We show that the necessary and sufficient condition for unique bilinear decomposition under CM constraints is strikingly similar to the one for uniqueness of certain CP models.…”

supporting

confidence: 69%

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Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints

Jiang

Sidiropoulos

2004

IEEE Trans. Signal Process.

161

157

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Abstract-CANDECOMP/PARAFAC (CP) analysis is an extension of low-rank matrix decomposition to higher-way arrays, which are also referred to as tensors. CP extends and unifies several array signal processing tools and has found applications ranging from multidimensional harmonic retrieval and angle-carrier estimation to blind multiuser detection. The uniqueness of CP decomposition is not fully understood yet, despite its theoretical and practical significance. Toward this end, we first revisit Kruskal's Permutation Lemma, which is a cornerstone result in the area, using an accessible basic linear algebra and induction approach. The new proof highlights the nature and limits of the identification process. We then derive two equivalent necessary and sufficient uniqueness conditions for the case where one of the component matrices involved in the decomposition is full column rank. These new conditions explain a curious example provided recently in a previous paper by Sidiropoulos, who showed that Kruskal's condition is in general sufficient but not necessary for uniqueness and that uniqueness depends on the particular joint pattern of zeros in the (possibly pretransformed) component matrices. As another interesting application of the Permutation Lemma, we derive a similar necessary and sufficient condition for unique bilinear factorization under constant modulus (CM) constraints, thus providing an interesting link to (and unification with) CP.

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confidence: 69%

“…Therefore, Kruskal's Permutation Lemma can again be taken as the cornerstone for uniqueness. Earlier work on the identification of bilinear mixtures under CM constraints [9], [15] . The necessary and sufficient condition for unique bilinear decomposition under CM constraints can now be stated:…”

Section: Letmentioning

confidence: 99%

Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints

Jiang

Sidiropoulos

2004

IEEE Trans. Signal Process.

161

157

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“…The proposition implies that for sufficiently large AE there are no other solutions than Û ¥ ½ ¡ ¡ ¡ , so that the problem is identifiable. Experience with similar algorithms indicate that È is already of maximal rank once it is tall, i.e., AE ¿ is sufficient in practice [29], [30]. This is because it is very unlikely that a random square or tall matrix has a kernel unless there is a structural reason for it.…”

Section: B Mda: Manchester Decoding Algorithmmentioning

confidence: 99%

Algebraic Algorithms to Separate Overlapping Secondary Surveillance Radar Replies

Petrochilos

Veen

2007

IEEE Trans. Signal Process.

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Abstract-The Secondary Surveillance Radar (SSR) is a transponder system used in air traffic control. Due to growing traffic densities, it is increasingly likely that a ground station receives a mixture of responses of various aircraft, partly overlapping in frequency and time. Currently such "collisions" are disregarded, at a loss of system performance and reliability. In this article, we propose to equip the ground station with an antenna array, and investigate techniques to blindly separate such a mixture based on source waveform properties. At base-band, a received SSR signal consists of a binary sequence with alphabet ¼ ½ , modulated by a complex exponential due to the residual carrier frequency. We present three algebraic algorithms to compute the separating beamformers by taking into account the particular modulation format of the received signal. The CramerRao Bound is derived, extensive simulations are presented, and an experimental platform has been built to collect measurement data and demonstrate the algorithms.

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“…Fortunately, the matrix formulation admits a simple least square solution to (14) and non-linear mapping solution to (15):…”

Section: Fir Zero-forcing Equalizer For Isi Mimo Channels For Isi Mimomentioning

confidence: 99%

A recursive QR approach to adaptive equalization of time-varying MIMO channels

Kung

Zhang

Myers

2005

Communications in Information and Systems

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Abstract. This paper presents a novel adaptive equalization algorithm for time-varying MIMO systems with ISI channel conditions. The algorithm avoids channel estimation before equalization and leads to a direct QR-based procedure for updating the equalizer coefficients to track the timevarying channel characteristics. Our approach does not require precise channel estimation and needs relatively few pilot symbols for satisfactory equalization. The theoretical foundations of the proposed algorithm are rooted in signal recovery results derived from the generalized Bezout identity and the finite alphabet property inherent in digital communication schemes. Concerning the convergence behavior of the algorithm, we address the following three issues: existence of fixed points, exclusiveness of fixed points, and robustness under noise disturbance and parameter selection. The equalizer demonstrates promising capability in achieving low symbol error rates for a very broad range of SNRs. Simulation results are presented confirming that this approach outperforms the more traditional recursive least squares (RLS) adaptive equalizer for this application and rivals the performance of MMSE equalizers requiring channel knowledge.

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Finite sample identifiability of multiple constant modulus sources

Cited by 14 publications

References 9 publications

Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints

Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints

Algebraic Algorithms to Separate Overlapping Secondary Surveillance Radar Replies

A recursive QR approach to adaptive equalization of time-varying MIMO channels

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