Capacity of Space Division Multiple Access
The adaptive antenna shown in Figure 7.16 provides a spot beam for each user, and it is this implementation which is the most powerful form of SDMA
Capacity of SDMA:
- An ideal adaptive antenna is able to form a beam for each user in the cell of interest, and the base station tracks each user in the cell as it moves
- Assume that a beam pattern, G(ɸ)is formed such that the pattern has maximum gain in the direction of the desired user
- Such a directive pattern can be formed at the base station using an N-element adaptive array antenna.
- Assume that a beam pattern, G (ɸ) with no variation in the elevation plane, such as shown in Figure 8.16can be formed by an array.
- The pattern (ɸ) can be steered through 360° in the horizontal (ɸ) plane such that the desired user is always in the main beam of the pattern.
- It is assumed that K users in the single cell CDMA system are uniformly distributed throughout a two-dimensional celland the base station antenna is capable of simultaneously providing such a pattern for all users in the cell
- On the reverselink, the power received from the desired mobile signals is Pr,0 .The powers of the signal incident at the base station antenna from K—1 interfering users are given by P r,i for i = 1…. k — 1.
- The average total interference power, I, seen by a single desired user, is given by
- Where ɸi is the direction of the i th user in the horizontal plane, measured in the x-axis, and E is the expectation operator.
- No interference from adjacent cells contributes to total received interference in equation (8.51).
- If perfect power control is applied such that the power incident at the base station antenna from each user is the same, then
- Pr,i =Pc for each of the K users, and the average interference power seen by user 0 is given by
- Assuming that users are independently and identically distributed throughout the cell, the average total interference seen by a user in the central cell is given by ― (3)
- where D is the directivity of the antenna,
- As the antenna beam pattern is made more narrow, D increases, and the received interference I decreases proportionally
- The average bit error rate for user 0 can thus be given by ―(4)
- Using the fact that the additional interference from adjacent cells simply adds to the interference level, the average probability of error for a particular user using directive antennas in a multiple-cell environment is given b ― (5)
- where f is the frequency reuse factor
- For an average probability of error of 0.001 in a propagation path loss environment of n = 4, the flat top beam system will support 350 users, whereas the omni-directional antenna will support only 100 users
- This increase in the number of users is roughly equal to the directivity offered by the flat top beam system, and illustrates the promise SDMA offers for improving capacity in wireless systems