Massive multiple-input multiple-output - orthogonal frequency division multiplexing (MIMO-OFDM) systems face the challenge of high channel acquisition overhead while providing significant spectral efficiency (SE). Adjustable phase shift pilots (APSPs) are an effective technique to acquire channels with low overhead by exploiting channel sparsity. In this paper, we extend it to multiple groups and propose multi-group adjustable phase shift pilots (MAPSPs) to improve SE further. We first introduce a massive MIMO-OFDM system model and transform the conventional channel model in the space-frequency domain to the angle-delay domain, obtaining a sparse channel matrix. Then, we propose a method of generating MAPSPs through multiple basic sequences and investigate channel estimation processes. By analyzing the components of pilot interference, we elucidate the underlying mechanism by which interference affects MMSE estimation. Building upon this foundation, we demonstrate the benefit of phase scheduling in MAPSP channel estimation and establish the optimal design condition tailored for scheduling. Furthermore, we propose an implementation scheme based on Zadoff-Chu sequences that includes received signal pre-processing and pilot scheduling methods to mitigate pilot interference. Simulation results indicate that the MAPSP method achieves a lower mean square error (MSE) of estimation than APSP and significantly enhances SE in mobility scenarios.

Estimating massive multiple-input multiple-output - orthogonal frequency division multiplexing (MIMO-OFDM) channels with low pilot overhead presents a significant challenge. Leveraging channel sparsity and pilot argument information (PAI), we propose a multi-group adjustable phase shift pilot (MAPSP) channel estimation method aimed at reducing pilot overhead. We first introduce a sparse channel model in angle-delay domain. Then, we propose the approach of generating phase shift pilots by dividing user terminals (UT) into groups and explore channel estimation based on the sparse channel model. We demonstrate that pilot interference can be mitigated by phase scheduling and received signal pre-processing. Capitalizing on this property, we propose a MAPSP implementation scheme. Simulation results indicate that the proposed MAPSP technique achieves a lower mean square error (MSE) of estimation than APSP and significantly enhances spectral efficiency.

In this paper, we derive the Bayes-Optimal estimator based on approximate message passing (AMP) algorithm in massive multiple-input multiple-output (MIMO) systems, which requires statistical channel state information (CSI). According to the analysis of channel model in beam domain, the covariance matrix is derived for CSI acquisition. With the aid of statistical CSI, the convergence of the proposed algorithm has significant improvement in comparison with which use the expectation-maximization (EM) algorithm to fit the statistical CSI. Simulations show great mean squared error (MSE) performance that approximates the Minimum Mean Square Error (MMSE) estimator, and better convergence performance than other AMP algorithm can be achieved. Besides, the results prove that performance of the random pilot in this algorithm is close to that of the orthogonal pilot based on Zadoff-Chu sequences.

The large-scale multiple-input multiple-output (MIMO) system achieves high spectral efficiency, and its performance is ultimately limited by pilot contamination. Since the channel energy usually concentrates in a significant angle region, some mean-square-error (MSE)-based schedule methods have been proposed to mitigate the contamination, but these methods cannot guarantee the quality of service (QoS) for each served terminal. In order to overcome this deficiency, we derive an asymptotic achievable rate for each served terminal under the spatially correlated channel. Further, we analyze how the achievable rate is affected by the degree of channel overlap in the angle region. Based on the analysis result, we design a low-complexity schedule algorithm to guarantee the QoS and find the optimal number of served terminals. Numerical results show that the proposed schedule algorithm outperforms the MSE-based one in terms of QoS and fairness, and can maximize the number of served terminals.

In this paper, the turbo minimum mean square error- parallel interference cancelation (Turbo MMSE-PIC) receiver is incorporated with link adaptation schemes to achieve promising performance gains for uplink MIMO transmission, in parallel, adapt the link in the actual channel conditions with assist from performance prediction technology. We first predict the turbo receiver's performance as a basic metric for link adaptation scheme. Then, a new strategy of selecting the precoding matrices, the number of spatially multiplexed layers as well as modulation coding schemes are proposed, resulting in the proposed three-steps selection. In this method, the number of layers and modulation coding schemes to be feedback is initialized and used to set a shortened range of them. Then the number of layers is updated to take full advantage of iterative processing, instead of the initial value in the conventional strategy. In so doing, the benefit of turbo receivers is efficiently claimed while low computational complexity can be achieved.

In this paper, we investigate the optimal pilot for multiple-input multiple-output and orthogonal frequency-division multiplexing (MIMO-OFDM) systems. The optimal pilot is obtained by minimizing the mean-square-error (MSE) of the linear minimum MSE (LMMSE) channel estimation, which is related to the channel correlation matrices in space, time, and frequency domains. We obtain that the optimal pilot is the statistical precoded sequence in the transmit eigenmode with proper power allocation. In general, the power allocation has no closed-form solution, so we present some suboptimal schemes to approximate the optimal one. Simulations show that the proposed statistical precoded pilot outperforms the conventional one, and the suboptimal schemes can well approximate the optimal one.

In this paper, we consider channel estimation for amplify-and-forward (AF) relay network with orthogonal frequency division multiplexing (OFDM) modulation. We propose a superimposed training strategy at relay that allows the destination node to obtain the separate channel information of the source-->;relay link and the relay-->;destination link. The proposed training strategy only requires two transmission phases and is thus compatible with the two-phase data transmission scheme, i.e., the training can be embedded into data transmission. Since the optimal minimum mean square error (MMSE) estimator and the maximum a posteriori (MAP) estimator cannot be expressed in close-forms, we propose to obtain the initial channel estimates from the low complexity suboptimal linear estimators, e.g., linear minimum mean-square error (LMMSE) or least square (LS), and then resort to iterative approaches to improve the estimation accuracy.

In this paper, we consider the channel estimation for the classical three-node relay networks that employ the amplify-and-forward (AF) transmission scheme and the orthogonal frequency division multiplexing (OFDM) modulation. We propose a superimposed training strategy that allows the destination node to separately obtain the channel information of the source→relay link and the relay→destination link. Specifically, the relay superimposes its own training signal over the received one before forwarding it to the destination. The proposed training strategy can be implemented within two transmission phases and is thus compatible with the two-phase data transmission scheme, i.e., the training can be embedded into data transmission. We also derive the Cramér-Rao bound for the random channel parameters, from which we compute the optimal training sequence as well as the optimal power allocation. Since the optimal minimum mean square error (MMSE) estimator and the maximum a posteriori (MAP) estimator cannot be expressed in closed-form, we propose to first obtain the initial channel estimates from the low complexity linear estimators, e.g., linear minimum mean-square error (LMMSE) and least square (LS) estimators, and then resort to the iterative method to improve the estimation accuracy. Simulation results are provided to corroborate the proposed studies.

This paper compares several feedback schemes of a limited feedback system in a coordinated cellular networks. In a coordinated system one user can be served by different base stations (BSs) simultaneously. Conventional codebook is intended for single BS, its aim is to maximize the amplitude of the receive signal. When multiple BSs are equipped, phase discrimination among different BSs at the receive side may lead to performance degradation. Brute-force search through the entire BSs is a heavy burden especially when the BS number is large. In order to mitigate the negative effects, we present one solution dedicated to the coordinated system in this paper. When the BS number is small, we put forward a codebook design scheme based on the Lloyd codebook. When the BS number is large, we propose phase criterion instead of amplitude criterion in choosing the beamforming vector. Both schemes work well under their operating region. With our solution we can effectively reduce performance degradation in a coordinated cellular networks while still maintain a low complexity burden. Simulation results verify the effectiveness of our proposed schemes.

In this paper, we propose a new channel estimation prototype for the amplify-and-forward (AF) two-way relay network (TWRN). By allowing the relay to first estimate the channel parameters and then allocate the powers for these parameters, the final data detection at the source terminals could be optimized. Specifically, we consider the classical three-node TWRN where two source terminals exchange their information via a single relay node in between and adopt the maximum likelihood (ML) channel estimation at the relay node. Two different power allocation schemes to the training signals are then proposed to maximize the average effective signal-to-noise ratio (AESNR) of the data detection and minimize the mean-square-error (MSE) of the channel estimation, respectively. The optimal/sub-optimal training designs for both schemes are found as well. Simulation results corroborate the advantages of the proposed technique over the existing ones.

In this paper, we address the preamble-based channel estimation problem for orthogonal frequency-division multiplexing (OFDM) systems using multiple amplify-and-forward (AF) relays. We first establish a linear minimum mean-square-error (LMMSE) channel estimator which directly estimates the overall channels from the source to the destination. Then, based on the assumption that the channel correlations between the relays are unknown at the source terminal, a suboptimal training sequence and precoding matrices in closed form are designed to approach the optimal estimation performance at low-complexity.

In this work, we consider channel estimation for an amplify-and-forward (AF) two way relay network (TWRN), where two terminal nodes exchange information via a single relay node in between. A new concept of channel estimation by performing the power allocation at the relay node is introduced. As an example, we consider the maximum likelihood (ML) channel estimation at relay node and derive the power allocation factor such that the average effective signal-to-noise ratio (AESNR) at the terminal nodes is maximized. Nonetheless, the idea of using power allocation at relay node can be straightforwardly extended to more general scenarios. The simulation results show the advantages of the proposed method over the existing techniques.

We investigate channel estimation for long term evolution (LTE) uplink over frequency-selective fading multiple-input multiple-output (MIMO) channels. As the conventional DFT-based channel estimation algorithm used for obtaining the channel impulse response (CIR) in wide band may not be applicable in narrow band of LTE uplink, which results an irreducible error floor, we propose an novel channel estimation based on discrete cosine transform (DCT), assuming only two users transmit simultaneously in the same frequency band (or SDMA). By exploiting the properties of reference signals of each user, type I DCT can separate channel response of each user in DCT-domain completely. Then, optimal channel estimation in the linear minimal mean square error (MMSE) sense in DCT-domain is derived. Finally, the performance of the proposed channel estimation is verified via simulation.

In this paper, we present a polynomial-based noise variance estimator for multiple-input multiple-output single-carrier block transmission (MIMO-SCBT) systems. It is shown that the optimal pilots for noise variance estimation satisfy the same condition as that for channel estimation. Theoretical analysis indicates that the proposed estimator is statistically more efficient than the conventional sum of squared residuals (SSR) based estimator. Furthermore, we obtain an efficient implementation of the estimator by exploiting its special structure. Numerical results confirm our theoretical analysis.

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.

In practical orthogonal frequency division multiplexing (OFDM) systems, some virtual subcarriers are reserved for easing the requirements on the filter. In this case, the conventional discrete Fourier transform (DFT)-based filtering in frequency-domain suffers from a spectral leakage, which results in an irreducible error floor. On the other hand, the DFT-based filtering or interpolation in time-domain also has performance degradation for system with high Doppler frequency. In order to solve these two problems, we propose a two dimensional discrete cosine transform (2D DCT)-based channel estimator for OFDM systems with virtual subcarriers and high Doppler frequency. Simulation results show that the performance of the proposed method can well approach the 2D minimum mean square error (MMSE) channel estimation.

The performance of linear receivers for detection of the single carrier frequency division multiple access transmission over frequency-selective fading channels is investigated in this work. Firstly, the cumulative distribution functions (CDF) of output signal to interference plus noise ratios (SINR) with zero forcing frequency domain equalization (ZF-FDE) and minimum mean squared error frequency domain equalization (MMSE-FDE) are derived by employing the numerical inversion of Laplace transforms. Next, based on the CDFs of the output SINRs, the approximate average bit error rate expressions as functions of the average receive signal to noise ratio for Gray-coded quaternary phase shift keying constellations are obtained. Finally, analytical and Monte Carlo simulated results are compared, and they perfectly agree for both ZF-FDE and MMSE-FDE.

This paper investigates low-complexity soft-input soft-output (SISO) detectors for multiple-input multiple-output (MIMO) transmission over frequency-selective channels. The detectors are developed with a unified detection procedure, that is space-time pre-filtering followed by a reduced dimension MAP detection. The condition of perfect pre-filtering is discussed and several suboptimal pre-filtering methods are proposed. Simulation results show that the proposed SISO detectors can make a good trade-off between performance and computational complexity in frequency-selective fading MIMO channels with various spatial correlating factor and Ricean components.

Low complexity channel estimation for single-carrier block transmission systems over multiple-input multiple-output time varying frequency-selective channels is investigated. A time slot structure that uses Golay complementary sequences with perfect periodic autocorrelations as two-sided pilot blocks is presented. Employing this strucutre, optimal least square estimate in the minimum mean square error (MMSE) sense is achieved. Furthermore, a computationally efficient algorithm which is named as fast periodic Golay correlation is proposed based on the specific generator and the properties related to circulant matrices. Finally, the simulation results show the MMSE performance of the proposed scheme and algorithm.

We investigate channel estimation for timeslot-structured single-carrier block transmission (SCBT) over space-, time-, and frequency-selective fading multiple-input multiple-output (MIMO) channels. A MIMO-SCBT with a dual cyclic timeslot structure is presented first. Then, an optimal channel estimation in the minimal mean square error (MMSE) sense on the timeslot basis is investigated. It is shown that the optimal pilots for the timeslot-based MMSE channel estimation are related to the statistical channel state information in eigenmode. Under the assumption that the transmit correlation is unknown at the transmitter, the optimal pilots satisfy the same condition as reported for the block-based least-square (LS) channel estimation in literature, and the channel estimation can be simplified to initial block-based LS channel estimation followed by space-time postprocessing. Particularly, for spatially uncorrelated channels, the space-time postprocessing can be reduced to pathwise processing. A new design of the pilot sequences is given, which leads to an efficient implementation of the channel estimation. Later on, a more efficient implementation for the initial channel estimation is obtained by using the structure of the pilot sequences, and discrete cosine transform (DCT)-based implementation is developed for the space-time postprocessing to approximate the optimal solution with low implementation complexity. Finally, the performance of the proposed channel estimation is verified via simulations.

In this paper, we present a generalized multi-carrier (GMC) transmission technique in multi-input and multi-output (MIMO) channel environments for beyond 3G mobile communications. Several key techniques including the design and implementation of the GMC synthesis/analysis system, adaptive double cyclic timeslot structure, pilot design and channel estimation, and iterative detection/decoding are briefly discussed. Link-level simulation results in Rayleigh fading MIMO channels are provided