Near-Pilotless Single Carrier Communications Using Matrix Decomposition

TL;DR

This work tackles pilot overhead in SIMO single-carrier communications by introducing a near-pilotless blind decoding method based on matrix decomposition and alternating minimization to jointly estimate the transmitted data and the frequency-domain channel using only one pilot. By operating in the frequency domain and reconstructing the circulant data matrix, the method extracts data symbols while updating channel estimates, with an initial point derived from the top SVD component of the received signal. To address residual scaling and rotation, two correction schemes—Centroids Adjustment (CA) and QAM-to-QPSK (QQ)—are proposed, both leveraging a single pilot for alignment. Simulation results show the approach can outperform pilot-based MRC at low SNR, with CA/QQ providing notable BER improvements, and the method scales with longer sequences; future work aims to extend to multi-user/MIMO and more complex channel tap configurations.

Abstract

Single Input-Multiple Output (SIMO) systems are key enablers of high data rates in the next generation wireless communications. However in SIMO systems, channel estimation and equalization are challenging particularly in the presence of rapidly changing channels. The high pilot overhead required for channel estimation can reduce the system throughput for large antenna configuration. In this paper, we provide an iterative matrix decomposition algorithm for near-pilotless or blind decoding of SIMO signals, in a single carrier system with frequency domain equalization. This novel approach replaces the standard equalization and estimates both the transmitted data and the channel without the knowledge of any prior distributions, by making use of only one pilot. Our simulations demonstrate improved performance, in terms of error rates, compared to the more widely used pilot-based Maximal Ratio Combining (MRC) method.

Figures (7)

• Figure 1: The Proposed receiver architecture for an SC-FDE System takes the baseband received signal from $N_r$ receive antennas after CP removal, converts it to a matrix and processes it through an FFT block. In the frequency domain, matrix decomposition and alternating minimization techniques are used to jointly estimate the channel and decode the transmitted data. The estimated signal component is used to reconstruct the circulant matrix, bringing the signal back to time domain. Finally, the resulting time-domain samples are corrected for scaling and rotation and the bits are recovered.
• Figure 2: Centroids adjustment based scaling correction: The figure shows estimation of $m$ which tells us the right constellation among four output constellations by making use of the single pilot
• Figure 3: QAM to QPSK based RR correction: The example depicts a 64 QAM constellation with RR introduced. The $\alpha_{QQ}$ corresponds to the offset between the actual location of QPSK points (green points) and the residue point (red points)
• Figure 4: At 7 dB SNR, $P=1024$ , $N_r = 64$, $L=9$ for 64 QAM - Scatter-plots of : (A). Estimated ${X}$ from alternating minimization algorithm after IFFT block, (B). Output ${X_{de-rot}}$ after correcting ${X}$ with one pilot, (C). Signal ${X_{true}}$ obtained by correcting scaling using Centroids Adjustment (CA) method, (D). Signal ${X_{true}}$ obtained by correcting the rotational residue using QAM to QPSK (QQ) method.
• Figure 5: Comparison of uncoded BER of MRC using $10\%$ pilots and the proposed blind matrix decomposition algorithm.