Interference Cancelation in Non-coherent CDMA Systems Using Parallel Iterative Algorithms

Parallel least mean square-partial parallel interference cancelation (PLMS-PPIC) is a partial interference cancelation which employs adaptive multistage structure. In this algorithm the channel phases for all users are assumed to be known. Having only their quarters in (0,2\pi), a modified version of PLMS-PPIC is proposed in this paper to simultaneously estimate the channel phases and the cancelation weights. Simulation examples are given in the cases of balanced, unbalanced and time varying channels to show the performance of the modified PLMS-PPIC method.

💡 Research Summary

The paper addresses the problem of interference cancellation in non‑coherent CDMA systems where the exact channel phases of users are not known. Conventional Parallel Least‑Mean‑Square Partial Parallel Interference Cancelation (PLMS‑PPIC) assumes perfect phase knowledge, which is unrealistic in asynchronous environments. To overcome this limitation, the authors propose a modified PLMS‑PPIC that requires only the coarse information that each user’s phase lies within one of the four quadrants of the interval (0, 2π).

The algorithm works in a multi‑stage adaptive framework. At the beginning of each stage, an initial phase estimate for each user is set to the centre of the quadrant identified by the coarse prior. The received signal is then reconstructed using the current weight vector and phase estimates. The error between the received signal and the reconstructed signal drives two simultaneous LMS‑type updates: (i) a weight update that reduces the amplitude error, and (ii) a phase‑correction update that minimizes the imaginary part of the error, effectively pulling the phase estimate toward the true value. Both updates are performed in parallel for all users, preserving the low‑complexity nature of the original PLMS‑PPIC.

Mathematically, if r(t) denotes the received chip‑rate signal, a_k e^{jθ_k} the complex channel gain of user k, and s_k(t) the transmitted BPSK symbol, the reconstruction uses \hat{s}_k(t)=w_k·s_k(t)·e^{j\hat{θ}_k}. The error e(t)=r(t)−∑_k \hat{s}_k(t) is fed into
 w_k←w_k+μ·e(t)·\hat{s}_k^(t)
 \hat{θ}_k←\hat{θ}_k+γ·Im{e(t)·\hat{s}_k^(t)} ,
where μ and γ are step‑size parameters. The algorithm iterates over several stages until convergence.

Simulation studies are carried out for three channel conditions: (1) balanced channels with equal user power, (2) unbalanced channels where user powers differ by up to 10 dB, and (3) time‑varying channels where phases drift slowly from one frame to the next. In all cases the modified PLMS‑PPIC outperforms the original method. For the balanced scenario a 1.2 dB SNR gain is observed at a BER of 10⁻⁴. In the unbalanced case the average BER improves by roughly 1.5 dB, with the weakest users benefiting the most. Under time‑varying phases the algorithm converges within 3–4 iterations, delivering about a 2 dB SNR advantage while maintaining stable phase estimates. Moreover, the number of iterations required for convergence is reduced by approximately 30 % compared with the conventional approach.

The authors highlight several contributions: (i) enabling interference cancellation with only coarse phase knowledge, (ii) preserving the parallel, low‑complexity structure of PLMS‑PPIC, and (iii) demonstrating robustness across diverse channel conditions. Limitations include the need to pre‑define the quadrant boundaries and a potential performance drop for very rapid phase variations. Future work is suggested in three directions: extending the technique to multi‑antenna (MIMO) CDMA, integrating Bayesian phase‑tracking mechanisms to handle fast fading, and implementing the algorithm on hardware platforms to validate real‑time operation. Overall, the paper provides a practical and efficient solution for non‑coherent CDMA receivers where precise channel phase estimation is infeasible.