LTE PUCCH CDM (Walsh Codes as example)

In LTE PUCCH, CDM (Orthogonal Sequence) is used to increase capacity for each TTI (1ms). The principal concept of CDM can be elaborated using following example:

Simple Walsh Matrix:

1. (1 -1 1 1)          
2. (1 1 -1 1)        
3. (-1 1 1 1)
4. (1 1 1 -1)

User A, data = 1 0 1   => (1-1 1)
User B, data = 0 0 1   => (-1 -1 1)

For transmitter side:
Select sequence number 1 as code for User A, after multiplication, User A's data to be transmitted become (1 -1 1 1) | (-1 1 -1 -1) | (1 -1 1 1)

Select sequence number 4 as code for User B, after multiplication, User B's data to be transmitted become (-1 -1 -1 1) | (-1 -1 -1 1) | (1 1 1 -1)

Add User A and User B's matrix together for transmission, the total data become
(0 -2 0 2) | (-2 0 -2 0) | (2 0 2 0)


For receiver side:
To extract User A's data, multiple received codes matrix with assigned code.
[(0 -2 0 2) | (-2 0 -2 0) | (2 0 2 0)] * (1 -1 1 1) = (0+2+0+2) | (-2+0-2+0) | (2+0+2+0)
                                                                         = (4 -4 4)

Interpret 4 as 1 and -4 as 0, User A's data become 1 0 1.

The same procedure used to recover User B's data.