Adaptive Group-Blind Linear Multiuser Detection

Adaptive Group-Blind Linear Multiuser Detection

As for the blind linear multiuser detector discussed in Chapter 2, the group-blind linear multiuser detectors can also be implemented adaptively. Specifically, for example, since the form II linear hybrid detector can be written in closed form as a function of the signal subspace components, we can use a suitable subspace tracking algorithm in conjunction with this detector and a channel estimator to form an adaptive detector that is able to track changes in the number of users and their composite signature waveforms [412]. Figure 3.16 contains a block diagram of such a receiver. The received signal r [i] is fed into a subspace tracker which sequentially estimates the signal subspace components (U_s, L_s). The received signal r [i] is then projected onto the noise subspace to obtain z [i], which is in turn passed through a bank of parallel linear filters, each determined by the signature waveform of a desired user. The output of each filter is fed into a channel tracker which estimates the channel state of that particular user. Finally, the linear hybrid group-blind detector is constructed in closed form based on the estimated signal subspace components and the channel states of the desired users. This adaptive algorithm is summarized as follows. Suppose that at time i – 1, the estimated signal subspace rank is r [i – 1] and the signal subspace components are U_s[i – 1], L_s[i –1], and s²[i – 1]. The estimated channel states for the desired users are f_k[i – 1], 1 k . Then at time i, the adaptive detector performs the following steps to update the detector and detect the data.

• Update the signal subspace: Using a particular signal subspace tracking algorithm, update the signal subspace rank r[i] and the signal subspace components U_s [i], L_s [i], and s² [i].

• Estimate the desired users' channels (cf. Section 2.7.4):

  Equation 3.180

  

  
  

  Equation 3.181

  

  
  

  Equation 3.182

  

  
  

  Equation 3.183

  

  
  

  Form using .

• Form the detectors:

  Equation 3.184

  

  
  

• Perform differential detection:

  Equation 3.185

  

  
  

  Equation 3.186

  

  
  

Figure 3.17 is a comparison of the adaptive performance of the MMSE and hybrid group-blind detectors using the NAHJ subspace tracking algorithm discussed in Section 2.6.3. During the first 1000 iterations there are eight total users, six of which are known by the group-blind detector. At iteration 1000, four new users are added to the system. At iteration 2000, one additional known user is added and three unknown users vanish. We see that there is a substantial performance gain using the group-blind detector at each stage and that convergence occurs in less than 500 iterations.

Figure 3.18 is created with parameters identical to Fig. 3.17 except that the tracking algorithm used is an exact rank-one SVD update. Again we see a significant improvement in performance using the group-blind detector. More important, when we compare Figs. 3.17 and 3.18 we see very little difference between the performance we obtain using the NAHJ subspace tracking and that we obtain using an exact SVD update.

Figure 3.19 shows the steady-state BER performance of our receiver using NAHJ subspace tracking and the exact SVD update for both blind and group-blind multiuser detection. The number of users is eight and the number of known users is six. At SNR above about 11 dB we see that the group-blind detectors provide a substantial improvement in BER. At lower SNR, the group-blind detectors seem to suffer from the noise enhancement problems that often accompany zero-forcing detectors. Recall that the hybrid group-blind detector zero-forces interference from known users and suppresses interference from unknown users via the MMSE criterion. Once again, note the relatively small difference between the performance of NAHJ and that of exact SVD, especially at high SNR.