Optimal Pilot Design Research Articles

Optimal Pilot Design for Channel Estimation in OFDM-based Cognitive Radios

Optimal Pilot Design for Channel Estimation in OFDM-based Cognitive Radios

Noniterative Joint Frequency Offset and Channel Estimation for MIMO OFDM Systems Using Cascaded Orthogonal Pilots

In this paper, we reconsider the issues of frequency offset and channel estimation in multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. We first design “cascaded orthogonal” pilot symbols and adopt the properties of Fourier transform and Hadamard product to deliver a closed-form estimate of frequency offset; meanwhile, another closed-form estimate of channel under minimum mean square error (MSE) criterion is presented. A tight lower bound for the MSE of the channel is also derived. The proposed channel estimator is robust to the residual frequency offset, whereas the frequency offset estimator is nearly independent of the unknown channel vector and is also robust to channel variations. Simulation results show that the proposed method greatly reduces the MSE of the channel in the moderate-to-high value of signal-to-noise ratio (SNR), even at a large normalized (by subcarrier spacing) frequency offset |ν| = 0.5. Compared with the optimal pilot design without frequency offset, our solution performs only slightly worse for low values of frequency offset (|ν| ≤ 0.01), but the difference is insignificant. The computational complexity of the proposed scheme is also much lower than that of the conventional iterative means.

MIMO-OFDM Channel Estimation in the Presence of Frequency Offsets

Optimal pilot design and placement for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with frequency offsets are considered. Both the single-frequency- offset case and the multiple-frequency-offset case are treated. We show that the constant-envelope (CE) condition is sufficient but not necessary for pilot design, and that pilots with multiple envelopes can also achieve the optimal performance in terms of the mean square error (MSE) minimization, provided that an additional constraint on the pilot placement is satisfied simultaneously. New pilot designs, which take into account the multiple-frequency-offset case, are proposed to eliminate inter- pilot-interference (IPI) and to optimize the MSE performance. The least-squares (LS) and linear minimum mean square error (LMMSE) channel estimators for the multiple-frequency- offset case are designed for uncorrelated and correlated MIMO-OFDM channels, respectively. The LMMSE estimator requires the channel covariance matrix. Both optimal adaptive pilot power allocation and suboptimal uniform pilot power allocation are developed for the proposed LMMSE estimator. The adaptive allocation performs 4 dB better than the uniform allocation in the high noise region, but they both perform identically in the low noise region. Performance comparisons are made against several previous pilot designs due to [1], [2]. The proposed LMMSE estimator significantly outperforms the LS estimator.

Joint pilot tone and channel estimator design for OFDM systems

Optimal pilot design is an important issue for OFDM systems since the pilot tones significantly affect channel estimation performance. Unlike the conventional approaches which derive the optimal pilot tones along with a certain channel estimation method, this paper proposes a novel approach that optimizes the pilot tones and the channel estimator jointly based on the MMSE criterion. It can be shown that the proposed approach not only outperforms the conventional ones at low SNRs, but also reduces the complexity of the channel estimator at the receiver.

Capacity Bound of MIMO Systems with MPSK Modulation and Time-Multiplexed Pilots

In this letter, we elucidate the ergodic capacity of multiple-input multiple-output (MIMO) systems with M-ary phase-shift keying (MPSK) modulation and time-multiplexed pilots in frequency-flat Rayleigh fading environment. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For mathematical tractability, we derive an easy-computing closed-form lower bound of the channel capacity. Based on the lower bound, the optimal power allocation between the data and pilots is also presented in closed-form, and the optimal training length is investigated by numerical optimization. It is shown that the transmit scheme with equal training and data power and optimized training length provides suboptimal performance, and the transmit scheme with optimized training length and training power is optimal. With the latter scheme, in most situations, the optimal training length equals the number of the transmit antennas and the corresponding optimal power allocation can be easily computed with the proposed formula.

Capacity Bound of MIMO Systems with MPSK Modulation and Superimposed Pilots

The enormous capacity potential of multiple-input multiple-output (MIMO) is based on some unrealistic assumptions, such as the complete channel state information (CCSI) at the receiver and Gaussian distributed data. In this paper, in frequency-flat Rayleigh fading environment, we investigate the ergodic capacity of MIMO systems with M-ary phase-shift keying (MPSK) modulation and superimposed pilots for channel estimation. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For the mathematical tractability, we also derive an easy-computing closed-form lower bound of the channel capacity. Furthermore, the optimal power allocation between the data and pilots is investigated by numerical optimization. It is shown that more power should be devoted to the data in low SNR environments and to the pilots in high SNR environments.