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CNA 7.2 (Génération des codes de Walsh–Hadamard)
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CNA 7.2 (Génération des codes de Walsh–Hadamard)

Introduction to CDMA and Walsh-Hadamard Codes

Overview of Digital Transmission

  • The video introduces a series focused on digital transmissions, specifically exploring essential elements of CDMA systems.
  • It highlights the importance of Walsh-Hadamard codes in asynchronous CDMA transmissions, particularly in WCDMA downlink scenarios.

Importance of Orthogonality

  • The orthogonality of Walsh-Hadamard codes is emphasized as crucial for minimizing user interference in CDMA systems.
  • The generation process of these codes from Hadamard matrices is outlined, showcasing their recursive structure.

Generating Hadamard Matrices

Construction Process

  • Starting with a basic matrix H1 containing a single coefficient (1), larger matrices are constructed recursively.
  • For any n x n matrix hn, the next size matrix H2N can be formed by assembling four blocks: hn and its sign-inverted version.

Example Construction

  • An example illustrates how to derive the first non-trivial matrix H2 from H1 using the recursive rule.
  • This results in a 2x2 matrix where each row represents unique Walsh codes necessary for CDMA systems.

Orthogonality and User Separation

Key Properties

  • Each line in the Hadamard matrix serves as an independent vector composed solely of +1 and -1 values.
  • When calculating dot products between different lines, the result is always zero, confirming their orthogonal nature.

Practical Implications

  • This orthogonality allows multiple users to transmit simultaneously without interference as long as synchronization is maintained.

Conclusion and Future Topics

Summary of Key Insights

  • The video concludes by summarizing how Walsh-Hadamard codes are generated and their significance in ensuring user separation within synchronous CDMA systems.

Next Steps

  • Upcoming videos will explore hierarchical families of CDMA codes, starting with variable spreading factor (VSF), which maintains orthogonality while allowing dynamic adjustment of data rates.
Video description

nous allons explorer ensemble l’un des éléments essentiels des systèmes CDMA : la génération des codes d’étalement de Walsh–Hadamard. Ces codes parfaitement orthogonaux construits à partir des matrices d'Hadamard. Ils sont au cœur des transmissions CDMA synchrones, notamment dans le downlink du WCDMA, où leur orthogonalité permet de minimiser les interférences entre utilisateurs.