On the CRLB for Blind Receiver I/Q Imbalance Estimation in OFDM Systems: Efficient Computation and Closed-Form Bounds

Abstract

Modern mobile communication receivers are often implemented with a direct-conversion architecture, which features a number of advantages over competing designs. A notable limitation of direct-conversion architectures, however, is their sensitivity to amplitude and phase mismatches between the in-phase and quadrature signal paths. Such in-phase and quadrature-phase (I/Q) imbalances introduce undesired image components in the baseband signal, degrading link performance -- most notably by increasing the bit-error ratio. Considerable research effort has therefore been devoted to digital techniques for estimating and mitigating these impairments. Existing approaches generally fall into two categories: data-aided methods that exploit known pilots, preambles, or training sequences, and blind techniques that operate without such prior information. For data-aided estimation, Cramér-Rao lower bounds (CRLBs) have been established in the literature. In contrast, the derivation of a CRLB for the blind I/Q-imbalance estimation case is considerably more challenging, since the received data is random and typically non-Gaussian in the frequency domain. This work extends our earlier conference contribution, which introduced a CRLB derivation for the blind estimation of frequency-independent (FID) receiver I/Q imbalance using central limit theorem (CLT) arguments. The extensions include a computationally efficient method for calculating the bound, reducing complexity from cubic in the number of samples to linear in the fast-Fourier transform (FFT) size, along with a simplified closed-form approximation. This approximation provides new insights into the allocation dependent performances of existing estimation methods, motivating a pre-estimation filtering modification that drastically improves their estimation performance in certain scenarios.

Figures (5)

• Figure 1: Basic block diagram of the equivalent baseband signal processing chain with I/Q imbalance.
• Figure 2: Normalized kurtosis versus number of allocated subcarriers $L_s$ with ${N_{\text{DFT}}} = 4096$ for different QAM modulation orders.
• Figure 3: I/Q imbalance estimation CRLB ($10 \log_{10} [\mathbf{C}_{\hat{\boldsymbol{\uptheta}}_{\alpha}}]_{2,2}$) for frequency-selective and frequency-flat channels, and MSE performance of various estimators versus the number of allocated subcarriers. (a) Contiguously allocated subcarriers starting from the lowest subcarrier indices. (b) Symmetrically allocated subcarriers centered around DC. The x-axis of (b) is reversed so that full allocation appears where both plots meet.
• Figure 4: I/Q imbalance estimation CRLB for frequency-selective and frequency-flat channels, and performance of various estimators versus $\xi_s$ in dB for the maximum $L_s$ with an asymmetric allocation (top) and for a full allocation (bottom).
• Figure 5: I/Q imbalance estimation CRLB for frequency-selective and frequency-flat channels, and performance of various estimators versus the $\text{ILR}_{\unit{dB}}$ for a half bandwidth allocation (top) and for a full allocation (bottom).