Uplink Pilot Research Articles

Multi-Cell Multi-User Massive FD-MIMO: Downlink Precoding and Throughput Analysis

In this paper, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive Full-Dimension MIMO (FD-MIMO) network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically characterized and the characterized DoA estimation error is incorporated into the corresponding DL precoding and power allocation strategy. Simulation results verify the accuracy of our analytical characterization of the DoA estimation and demonstrate that the introduced multi-user MIMO precoding and power allocation strategy outperforms existing zero-forcing based massive MIMO strategies.

Multi-Cell Massive MIMO Uplink With Underlay Spectrum Sharing

The achievable rates are investigated for multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with underlay spectrum sharing. A general pilot sharing scheme and two pilot sequence designs (PSDs) are investigated via fully shared (PSD-1) and partially shared (PSD-2) uplink pilots. The number of simultaneously served primary users and secondary users (SUs) in the same time-frequency resource block by the PSD-1 is higher than that of PSD-2. The transmit power constraints for the SUs are derived to mitigate the secondary co-channel interference (CCI) inflicted at the primary base-station (PBS) subject to a predefined primary interference temperature (PIT). The optimal transmit power control coefficients for the SUs with max–min fairness and the common achievable rates are derived. The cumulative detrimental effects of channel estimation errors, CCI and intra-cell/inter-cell pilot contamination are investigated. The secondary transmit power constraint and the achievable rates for the perfect channel state information (CSI) case become independent of the PIT when the number of PBS antennas grows unbounded. Therefore, the primary and secondary systems can be operated independent of each other as both intra-cell and inter-cell interference can be asymptotically mitigated at the massive MIMO PBS and secondary base-station. Nevertheless, the achievable rates and secondary power constraints for the imperfect CSI case with PSD-1 are severely degraded due to the presence of intra-cell and inter-cell pilot contamination. These performance metrics depend on the PIT even in the asymptotic PBS antenna regime. Hence, the primary and secondary systems can no longer be operated independently for imperfect CSI with PSD-1. However, PSD-2 provides an achievable rate gain over PSD-1 despite the requirement of lengthier pilot sequences of the former than that of the latter.

Equal-Gain Transmission in Massive MIMO Systems Under Ricean Fading

This paper considers a multicell downlink (DL) massive MIMO system operating over Ricean fading channels in which each base station (BS) is equipped with a massive antenna array, while each user has a single antenna. We explore equal-gain transmission (EGT), line-of-sight (LOS) component-based EGT (LOS-EGT) and maximum-ratio transmission (MRT) under imperfect channel state information. Closed-form expressions for lower bounds of the achievable rates are derived for EGT over Ricean and Rayleigh fading channels, and for LOS-EGT and MRT over Ricean fading channels. With the obtained closed-form expressions, various power scaling laws concerning DL data transmit power and uplink (UL) pilot transmit power are established and discussed. In particular, it is found that, as the number of BS antennas $M$ grows unlimited, the lower bounds on the rates achieved with EGT, LOS-EGT and MRT schemes approach infinity and are not affected by pilot contamination, while the DL data transmit power and UL pilot transmit power can be scaled down proportionally to ${M^{ -a}}$ and ${M^{ - b}}$ (where $0 \leq a and $b > 0$ ), respectively. Numerical results corroborate the tightness and accuracy of these closed-form expressions and they also show that, when the number of antennas and intercell interference level are large, compared to the MRT, EGT and LOS-EGT are more resistant to intercell interference and pilot contamination.

Resource Allocation in SWIPT Networks Under a Nonlinear Energy Harvesting Model: Power Efficiency, User Fairness, and Channel Nonreciprocity

This paper considers a multiuser simultaneous wireless information and power transfer system with a nonlinear energy harvesting model, in which a multiantenna base station estimates the downlink channel state information (CSI) via uplink pilots. Each single-antenna user is equipped with a power splitter. Three crucial issues on resource management for this system include: 1) power-efficient improvement, 2) user-fairness guarantee, and 3) nonideal channel reciprocity effect mitigation. Potentially, a resource allocation scheme to address jointly such issues can be devised by using the framework of multiobjective optimization. However, the resulting problem might be complex to solve since the three issues hold different characteristics. Therefore, we propose a novel method to design the resource allocation scheme. In particular, the principle of our method relies on structuralizing mathematically the issues into a cross-layer multilevel optimization problem. On this basis, we then devise solving algorithms and closed-form solutions. Moreover, to instantly adapt the CSI changes in practice while reducing computational burdens, we propose a closed-form suboptimal solution to tackle the problem. Finally, we provide numerical results to show the achievable performance gains using the optimal and suboptimal solutions, and then validate the proposed resource allocation scheme.

Hybrid Time-Switching and Power Splitting SWIPT for Full-Duplex Massive MIMO Systems: A Beam-Domain Approach

In this paper, we consider the hybrid time switching (TS) and power splitting (PS) simultaneous wireless information and power transfer (SWIPT) protocol design in a full-duplex (FD) massive MIMO system. In this system, an FD base station (BS) serves a set of half-duplex (HD) users and a set of fixed HD sensors. The whole protocol can be divided into two phases based on the idea of TS. The first phase is Training Phase, which is designed for users uplink training and sensors energy harvesting as well as downlink training. Specifically, users transmit uplink pilots for beam-domain (BD) uplink channel estimation at the BS, and the BS transmits energy signals to sensors. Based on the idea of PS, sensors utilize the received energy signals for energy harvesting and BD downlink channel estimation. In the second phase, that is Information Transmission Phase, the BS intelligently schedules users and sensors based on the BD distributions of channels to mitigate self-interference and improve transmission spectral efficiency (SE). Then, the BS forms transmit beamformers for transmitting information to users and receive beamformers for receiving signals transmitted by sensors. By optimizing transmit powers at the BS during the two phases and the TS ratio, the system achievable sum-rate is maximized. Simulation results show the superiority of the proposed protocol on SE compared with conventional massive MIMO SWIPT protocol.

Pilot Contamination in Massive MIMO Induced by Timing and Frequency Errors

Pilot contamination in the uplink (UL) puts asymptotic limits on the downlink (DL) spectral efficiency in time-division duplex (TDD) massive multiple-input multiple-output (MIMO) systems relying on TDD channel reciprocity. Pilot contamination can be induced by the UL pilot reuse across different neighboring cells. In this paper, we show that receiver front-end impairments also contribute to pilot contamination. In particular, we consider a TDD multi-user (MU) massive MIMO orthogonal frequency-division multiplexing (OFDM) system, where either time-division multiplexed (TDM) pilots or frequency-division multiplexed (FDM) pilots are utilized for UL channel sounding. We endeavor to characterize the impacts of the residual timing offsets (TOs) and the carrier frequency offsets (CFOs) on the DL performance of the massive MIMO-OFDM system. Closed-form expressions of the asymptotic DL MU spectral efficiencies are derived in the presence of both TOs and CFOs under different scenarios. Our analytical results reveal how the residual TOs and CFOs destroy the orthogonality among the UL training sequences from different users and give rise to pilot contamination. Specifically, we show that the DL spectral efficiencies become bounded even when the number of antennas goes toward infinity. Furthermore, to alleviate the impacts of TOs and CFOs, we propose different pilot decontamination methods based on our analyses for both the TDM pilots and the FDM pilots. Numerical simulation results corroborate our analyses and designs.

Secure Communication in Spectrum-Sharing Massive MIMO Systems With Active Eavesdropping

Secure communication in underlay spectrum sharing multi-user massive multiple-input multiple-output systems with active eavesdropping is investigated. The primary base-station (PBS) shares its licensed spectrum with the secondary base-station (SBS), which constrains its transmit power subject to a primary interference temperature. The active eavesdropper contaminates the uplink pilots in an attempt to intercept the confidential downlink transmissions toward the legitimate primary/secondary user nodes (PUs/SUs). The achievable PU/SU rates, the rates leaked into the active eavesdropper, and the achievable secrecy rates are derived for the finite and infinite PBS/SBS antenna regimes. A power-ratio-based active pilot attack detection scheme is investigated, and thereby, the probability of detection is derived. Our analysis and simulation results reveal that the active pilot attacks severely degrades the achievable secrecy rates even in the asymptotic PBS/SBS antenna regime. Hence, in order to provide guaranteed physical layer security, the active pilot attacks must be detected, and dynamic pilot decontamination techniques need to be employed.

Secure performance analysis and detection of pilot attack in massive multiple-input multiple-output system

This article studies the physical layer security of massive multiple-input multiple-output system in time-division-duplex mode. Specifically, a single-cell downlink massive multiple-input multiple-output communication system is considered. The resulting achievable secrecy rate is investigated in the presence of passive or active eavesdroppers. The analytical results reveal that the massive multiple-input multiple-output system is naturally immune to passive eavesdroppers, but will be dramatically degraded by active attack. On account of the risk caused by active attack, a simple and effective detection algorithm is proposed. Uplink pilots with random phases are transmitted during the detection operation. By comparing the phase deviation change of the received pilot signals’ cross product, the active eavesdroppers can be detected exactly. The closed-form expressions for probabilities of detection, false alarm, and false rejection are obtained respectively, which can demonstrate the robust performance of the proposed detection scheme. To maximize the secrecy energy efficiency of the system, the optimal power allocation strategy is studied under total power constraints. This optimization problem is efficiently solved by fractional programming. Numerical simulation results are derived to validate the secrecy performance of the massive multiple-input multiple-output system, the active pilot attacker detection performance, and the energy efficiency optimization effect.

Covariance Matrix Estimation for Massive MIMO

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

Beam-domain hybrid time-switching and power-splitting SWIPT in full-duplex massive MIMO system

In this paper, we consider the beam-domain hybrid time-switching (TS) and power-splitting (PS) simultaneous wireless information and power transfer (SWIPT) protocol design in full-duplex (FD) massive multiple-input multiple-output (MIMO) system, where the FD base station (BS) simultaneously serves a set of downlink half-duplex (HD) users (cellular users) and a set of fixed uplink HD users (fixed sensor nodes) which are uniformly distributed in its coverage area. In order to reduce the computational complexity, we investigate the beam-domain representation of massive MIMO channels based on the basis expansion model, and then the beam-domain SWIPT protocol which lies in intelligently scheduling the users and sensors based on the beam-domain distributions of their associated channels to mitigate SI and enhance transmission efficiency is designed for full-duplex massive MIMO system. The whole beam-domain hybrid TS and PS SWIPT protocol is divided into two phases based on the ideal of TS. The first phase is used for cellular users uplink training and sensor nodes energy harvesting as well as downlink training, wherein the cellular users transmit uplink pilots for uplink channel estimation at the BS, while the BS simultaneously transmits energy signals to the sensor nodes. Based on the idea of PS, the sensor nodes utilize the received energy signals for energy harvesting and downlink channel estimation. In the second phase, the BS forms the transmit beamformers for information transmission to the users as well as the receive beamformers for the sensors transmit their data to the BS simultaneously. By optimizing the TS ratio and transmit powers at the BS in two phases, the system achievable sum rate performance is maximized. Simulation results show the superiority of the proposed protocol on spectral efficiency compared with the existing massive MIMO SWIPT protocol.

Massive MIMO Performance—TDD Versus FDD: What Do Measurements Say?

Downlink beamforming in Massive multiple-input and multiple-output (MIMO) either relies on uplink pilot measurements-exploiting reciprocity and time-division duplexing operation, or on the use of a predetermined grid of beams with user equipments reporting their preferred beams, mostly in frequency-division duplexing operation. Massive MIMO in its originally conceived form uses the first strategy, with uplink pilots, whereas there is currently significant commercial interest in the second, grid-of-beams. It has been analytically shown that with isotropic scattering (independent Rayleigh fading) the first approach outperforms the second. Nevertheless, there remains controversy regarding their relative performance in practical channels. In this contribution, the performances of these two strategies are compared using measured channel data at 2.6 GHz.

A Game Theoretic Approach to Setting the Pilot Power Ratio in Multi-User MIMO Systems

We consider the uplink of a single cell multi-user multiple input multiple output (MU-MIMO) system, in which the base station acquires channel state information at the receiver by means of uplink pilot signals. Since each mobile station has a sum power budget that is used to transmit pilot and data symbols, the pilot power ratio (PPR) has a large impact on the system performance in terms of spectral and energy efficiency. We formulate the problem of PPR setting as a non-cooperative game, in which each mobile station aims at minimizing the mean squared error of the uplink received data symbols at the base station. We show that in this game a unique Nash equilibrium exists, and propose an iterative decentralized algorithm—termed best PPR algorithm (BPA)—that is guaranteed to converge to that Nash equilibrium. Since BPA dynamically responds to the measured interference, it outperforms widely used schemes that use a predetermined PPR. BPA also performs close to the global optimum, especially when mobile stations with similar path loss values are co-scheduled in the MU-MIMO system. Based on these insights, we propose a practical signaling mechanism for implementing BPA in MU-MIMO systems.

Suppressing Pilot Contamination in Massive MIMO Downlink via Cross-Frame Scheduling

A novel downlink scheduling strategy for time-division duplexing massive multiple-input multiple-output networks is proposed to relieve the pilot contamination. Specifically, users of slow-channel variation and simultaneous uplink pilot transmission are scheduled in different downlink subframes for adjacent cells, and hence the pilot contamination is significantly suppressed at the price of outdated channel state information. We investigate this trade-off by deriving the distribution of downlink signal-to-interference ratio in terms of Doppler effect, which can be approximated tightly and simply by Gaussian distribution. Based on it, a learning-based algorithm is developed for robust downlink rate allocation without priori knowledge on the users’ distribution. It is shown that the proposed cross-frame strategy can effectively improve the overall downlink performance of cell-edge users.

Max–Min Fair Transmit Precoding for Multi-Group Multicasting in Massive MIMO

This paper considers the downlink precoding for physical layer multicasting in massive multiple-input multiple-output (MIMO) systems. We study the max–min fairness (MMF) problem, where channel state information at the transmitter is used to design precoding vectors that maximize the minimum spectral efficiency (SE) of the system, given fixed power budgets for uplink training and downlink transmission. Our system model accounts for channel estimation, pilot contamination, arbitrary path-losses, and multi-group multicasting. We consider six scenarios with different transmission technologies (unicast and multicast), different pilot assignment strategies (dedicated or shared pilot assignments), and different precoding schemes (maximum ratio transmission and zero forcing), and derive achievable spectral efficiencies for all possible combinations. Then, we solve the MMF problem for each of these scenarios, and for any given pilot length, we find the SE maximizing uplink pilot and downlink data transmission policies, all in closed forms. We use these results to draw a general guideline for massive MIMO multicasting design, where for a given number of base station antennas, number of users, and coherence interval length, we determine the multicasting scheme that shall be used.

On the Performance of Multiuser MIMO Systems Relying on Full-Duplex CSI Acquisition

In this paper, we propose a combined full duplex (FD)- and half duplex (HD)-based transmission and channel acquisition model for an open-loop multiuser multiple-input multiple-output (MIMO) systems. Assuming residual self-interference at the base station (BS), the idea is to utilize the FD mode during the uplink (UL) training phase in order to achieve simultaneous downlink (DL) data transmission and UL CSI acquisition. More specifically, the BS begins serving a user when its CSI becomes available, while at the same time, it also receives UL pilots from the next scheduled user. We investigate both zero-forcing (ZF) and maximum ratio transmission MIMO beamforming techniques for the DL data transmission in the FD mode. The BS switches to the HD mode once it receives the CSI of all users and it employs ZF beamforming for the DL data transmission until the end of the transmission frame. Furthermore, we derive closed-form approximations for the lower bounded ergodic achievable rate relying on the proposed model. Our numerical results show that the proposed FD–HD transmission and channel acquisition approach outperforms its conventional HD counterpart and achieves higher data rates.

Aligning Power in Multiple Domains for Pilot Decontamination in Massive MIMO

Pilot contamination in the uplink (UL) can severely hurt the channel acquisition performance at the base station (BS) in a massive multiple-input multiple-output (MIMO) system. To mitigate the interference, it is critical to explore all the allowed avenues to provide more orthogonal resources for the users to transmit non-interfering UL pilots. In this paper, with a realistic massive MIMO orthogonal frequency-division multiplexing (OFDM) system model, allowing the channels to be both frequency-selective and time-selective, we propose to mitigate the UL pilot contamination through aligning the channel power in multiple domains, i.e., the time, angular, and Doppler domains. First, we show how to align the power-delay profiles of different users so that the pilots sent within one common reference OFDM symbol are orthogonal. Second, we demonstrate our proposed time-varying pilots can asymptotically mitigate the pilot contamination by aligning the Doppler power spectra (DPSs) judiciously even when the UL channels vary with time. Furthermore, in the case of massive MIMO, as the angles of arrival of the UL paths are acquired by the BS, we show the pilot contamination can be reduced or eliminated by jointly aligning the DPSs and the angular power spectra. Extensive computer simulations convince us the proposed Power Aligning principle can serve as the baseline design philosophy for the UL pilots in massive MIMO.

Optimal Design of Semi-Orthogonal Multiple-Access Massive MIMO Systems

We study an uplink scenario of single-cell multi-user massive multiple-input multiple-output (mMIMO) communication systems with a semi-orthogonal multiple-access (SOMA), where the channel state information is acquired by transmitting uplink pilot signals superimposed on uplink data signals. We analytically find the optimal resource allocation parameters; e.g., pilot and data transmit power and training duration, which maximize achievable sum-rates by minimum mean-square error (MMSE) channel estimation and maximum ratio combining (MRC) for data detection. Our results indicate that the optimized SOMA encouragingly outperforms the optimized conventional time-division duplex protocol in terms of both energy- and spectral efficiency.

Eradication of pilot contamination and zero forcing precoding in the multi‐cell TDD massive MIMO systems

In massive multiple-input multiple-output (M-MIMO) systems, the base station (BS) estimates the downlink and uplink channels using the uplink pilot training in conjunction with channel reciprocity property of time division duplex (TDD) operation. However, this channel estimation is contaminated due to the use of non-orthogonal pilot sequences for the uplink training in neighbouring cells that results in inter-cell interference. This study proposes an effective pilot contamination elimination scheme along with zero forcing precoding for multi-cell TDD M-MIMO systems. In the proposed scheme, each BS is assigned with a specific orthogonal variable spreading factor (OVSF) code row and a set of Zadoff–Chu (ZC) sequences are used for uplink pilot training. Then, the set of ZC sequences is multiplied element-wise at each BS with its OVSF code row to generate the orthogonality among the pilot sequences across the neighbouring cells. The proposed method can promise uncontaminated channel estimation and interference free downlink transmission without requiring the knowledge of the channels’ second-order statistics and without increasing the training overhead by a factor equal to the number of interfering cells. The simulation results authenticate the effectiveness and superiority of the proposed scheme over other schemes.

Novel Multi-cell Precoding Schemes for TDD Massive MIMO Systems

Two novel multi-cell precoding schemes, maximum ratio combining precoding with base station cooperation (MRC-BSC) and zero forcing precoding with BS cooperation (ZF-BSC), are proposed for time division duplex massive multiple-input multiple-output system. By making full use of other cells (not target cell) channel estimate information and changing the matrix structure of classical single-cell maximum ratio combining (MRC) precoding and zero forcing (ZF) precoding, proposed precoding schemes are obtained to reduce inter-cell interference with low complexity. The expressions of lower bound per-user achievable rate of proposed precoding schemes for different uplink pilot reuse factors situations are derived through theoretic analysis. Simulation results demonstrate that the proposed MRC-BSC and ZF-BSC can always achieve higher rates than single-cell MRC precoding and ZF precoding. For each precoding scheme, the downlink achievable rate can be improved greatly when enlarging the uplink pilot reuse factor. In addition, the proposed precoding schemes does not affect (or even improve) other cells' performance while improving the target cell's performance.

Channel estimation and channel tracking for correlated block-fading channels in massive MIMO systems

This paper presents a channel estimation and tracking method for correlated block-fading channels in massive MIMO wireless cellular systems. In order to conserve resources, the proposed algorithm requires the uplink pilot signal only once, at the start of communication. By utilizing the temporal correlation between consecutive Resource Blocks (RBs) and the error correction capability of turbo codes, the channel matrix in subsequent RBs is estimated at the Base Station (BS) itself using the uplink data of current the RB and the estimated channel matrix of previous the RB. Compared to existing blind estimation methods, the proposed method places fewer limitations on the system settings such as the number of BS antennas, the number of users, and the number of coherent channel usage compared to existing blind estimation methods. Simulation results show that the proposed algorithm provides better performance for a moderate RB size, a high-order of QAM scheme, and a smaller ratio of the number of BS antennas and mobile terminals (N/K). For a reasonably small N/K (order of 10), the proposed scheme achieves a lower symbol error probability than the conventional pilot-based estimation approach.