Nonlinear Group-Blind Detection

Nonlinear Group-Blind Detection

In this section we extend the nonlinear multiuser detection methods discussed in Section 3.4 to asynchronous CDMA systems with multipath [456]. The idea is essentially the same as in the synchronous case. We first estimate the decorrelating detectors of the desired users, given by

Equation 3.210

Note that can be estimated only up to a phase ambiguity. Denote the output of the decorrelating detector as

Equation 3.211

Figure 3.20. Comparison of the performance of blind and group-blind linear detectors in correlated noise. K = 10, = 7.

where is the phase ambiguity induced by the channel estimator which can be estimated using (3.129).

Denote

Then (3.211) can be written as

Equation 3.212

Note that the covariance of v is given by

Equation 3.213

with

Equation 3.214

Based on (3.212), the slowest-descent-search method for estimating is given by the same procedure as (3.121)–(3.126), with the covariance matrix given by (3.214). The algorithm is summarized as follows.

Algorithm 3.9: [Nonlinear group-blind detector—multipath CDMA]

• Compute the signal subspace:

  Equation 3.215

  

  
  

  Equation 3.216

  

  
  

• Estimate the desired users' channels (cf. Section 2.7.3):

  Equation 3.217

  

  
  

  Equation 3.218

  

  
  

  Form using .

• Form the decorrelating detectors using (3.210).

• Estimate the complex amplitudes :

  Equation 3.219

  

  
  

  Equation 3.220

  

  
  

  Equation 3.221

  

  
  

  Equation 3.222

  

  
  

  Equation 3.223

  

  
  

  Equation 3.224

  

  
  

• Compute the Hessian:

  Equation 3.225

  

  
  

  and the Q smallest eigenvectors .

• Detect each symbol by solving the following discrete optimization problem using an exhaustive search [over ( Q + 1) points]:

  Equation 3.226

  

  
  

  Equation 3.227

  

  
  

  Equation 3.228

  

  
  

  Equation 3.229

  

  
  

• Perform differential decoding:

  Equation 3.230

  

  
  

Simulation Examples

The simulation set is the same as that in Section 3.5.2. Figure 3.21 shows that similar to the synchronous case, in multipath channels, the nonlinear group-blind multiuser detector outperforms the linear group-blind detector by a significant margin. Furthermore, most of the performance gain offered by the slowest-descent method is obtained by searching along only one direction.

Figure 3.21. Performance of a slowest-descent-based group-blind multiuser detector in a multipath channel. N = 15, K = 8, = 4. Each user's channel consists of three paths with randomly generated complex gains and delays. Only the spreading waveforms of the desired users are assumed known to the receiver. The BER curves of a linear group-blind detector and slowest-descent (nonlinear) group-blind detector with Q = 1 and Q = 2 are shown.