Advanced Topics in Digital Communications at Universität Bremen

Flashcards and summaries for Advanced Topics in Digital Communications at the Universität Bremen

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Practical Meaning of the determinant?

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Important subspaces?

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Iterative Lösungen für lineare Gleichungssysteme?

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Exemplary flashcards for Advanced Topics in Digital Communications at the Universität Bremen on StudySmarter:

Porperties Inverse Matrix?

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LU Decomposition?

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Eigenvalues: Properties for hermitian matrices?

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Definition MIMO systems?

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Welche Multiple Access Schemes sind (nicht) orthogonal?

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Für wen erreichen orthogonale Signale ein Optimum?

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Was verursachen Nicht-orthogonale Signale und was kann man dagegen tun?

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Welche 2 MIMO Szenarien lassen sich unterscheiden?

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Welche Vorteile bietet der Einsatz von MIMO im Single-user Szenario?

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Exemplary flashcards for Advanced Topics in Digital Communications at the Universität Bremen on StudySmarter:

Advanced Topics in Digital Communications

Practical Meaning of the determinant?

  • If det A = 0 the matrix A is singular
  • det A equals volume of parallelepiped with edges given by rows (columns) of A
  • Gives formulas for the pivots used for solving linear equation systems

Advanced Topics in Digital Communications

Important subspaces?

  • Range (span, image)
  • Basis
  • Null space (kernel)

Advanced Topics in Digital Communications

Iterative Lösungen für lineare Gleichungssysteme?

  • Jacobi
  • Gauss-Seidel
  • Conjugate Gradient

Advanced Topics in Digital Communications

Porperties Inverse Matrix?

  • A⁻¹A = AA⁻¹ = I
  • Inverse exists only, if AX = I has a unique solution (A nonsingular)

Advanced Topics in Digital Communications

LU Decomposition?

  • Every invertible matrix A can be written as the product of a lower triangular matrix L and an upper triangluar matrix U: A = LU
  • Application: Solution of linear equation system Ax = LUx = b
  • Ly = b
  • Ux = y

Advanced Topics in Digital Communications

Eigenvalues: Properties for hermitian matrices?

  • All eigenvalues are real
  • Eigenvectors belonging to different eigenvalues are orthogonal
  • Algebraic and geometric multiplicities are identical
  • Consequence: all eigenvectors can be chosen to be mutually orthogonal

Advanced Topics in Digital Communications

Definition MIMO systems?

System with several input and output signals of same symbol rate T_s.

Advanced Topics in Digital Communications

Welche Multiple Access Schemes sind (nicht) orthogonal?

  1. Orthogonal: TDMA, FDMA
  2. Nicht orthogonal: CDMA, SDMA

Advanced Topics in Digital Communications

Für wen erreichen orthogonale Signale ein Optimum?

Für Single-user receiver.

Advanced Topics in Digital Communications

Was verursachen Nicht-orthogonale Signale und was kann man dagegen tun?

  • Verursachen Multiple Access Interferenzen
  • Ausgleich durch ausgeklügelte Signalverarbeitung

Advanced Topics in Digital Communications

Welche 2 MIMO Szenarien lassen sich unterscheiden?

  1. Multi-User Szenario
  2. Single-User Szenario

Advanced Topics in Digital Communications

Welche Vorteile bietet der Einsatz von MIMO im Single-user Szenario?

  • Erhöhte Datenrate durch Ausnutzen der Space Dimension, ohne die Bandbreite zu erweitern
  • Erhöhte Link reliability
  • Beamforming am Transmitter und Receiver

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