walsh code

Walsh Hadamard codes

Walsh-sequences have the advantage to be orthogonal, in this way we should get rid of any multi-access interference. There are however a number of drawbacks:

• The codes do not have a single, narrow autocorrelation peak. As a consequence code-synchronization becomes difficult.
• The spreading is not very efficient: the energy is only spread over a small number of discrete frequency-components.
  
• Although the full-sequence cross-correlation is identically zero, this does not hold for partial-sequence cross-correlation function. The consequence is that the advantage of using orthogonal codes is lost when all users are not synchronized to a single time base.
• Orthogonality is also affected by channel properties like multi-path. In practical systems equalization is applied to recover the original signal.

An implementation is found written in m language (matlab), which has the following procedures:
1. kroneck Tensor Product
2. Sum the producted different
3. Convolution with the original code
4. get the even number of elements in the convolution result, and divide them by two, then get the original data array