Effect Of Channel Estimation Error Research Articles

Massive MIMO Configurations for Multi-Cell Multi-User Relay Networks

The performance of massive multiple-input multiple-output (MIMO) configurations for multi-cell multi-user amplify-and-forward relay networks is investigated. Two massive MIMO signal processing techniques (SPT-1 and SPT-2) are proposed, and their computational complexity and performance gains are compared with multi-pair massive MIMO relaying (SPT-3) by deriving the partial and full achievable asymptotic sum rates for perfect and imperfect channel state information. Thereby, the cumulative effects of channel estimation errors, co-channel interference (CCI), and pilot contamination are investigated. The best relay selection for the multi-branch relaying is investigated. An optimal user power control algorithm based on max–min fairness is formulated, and thereby, the power allocation co-efficients and optimal common achievable user rate are derived in closed-form. Our analysis reveals that the effects of pilot contamination for the multi-cell massive MIMO relaying become more severe than that for the single-hop counterpart due to the multiple sources of CCI and propagation of residual interference in dual-hop transmissions.

A practical power allocation method for multi-user and multi-carrier networks

In the majority of studies on wireless networks, it is assumed that the receiver perfectly knows the channel. Since this is not the case for real life applications, the channel must be estimated in those systems. Thus, current cellular wireless communication systems are designed to perform coherent detection, and channel estimator is one of the most important part of a receiver. The channel estimation error must be minimized, because the error to be made during the channel estimation phase significantly affects the performance of the data detector. This can be made possible by allocating required amount of power to the pilot symbols to estimate channel with minimum error as possible as. Hence, this study examines how to allocate the power between pilot and data symbols to minimize the error of the data detector. The long term evolution provides an opportunity to change the radiation emitted in the pilot sub-carriers according to the data sub-carriers. Since this opportunity is expected to be the case for next generation cellular wireless networks, in this study, the effect of channel estimation error on data detection performance of a multi-user and multi-carrier cellular wireless communication system is investigated. The proposed solution is a practical one to approximate to the optimum solution of the resulting optimization problem without solving it. It is seen that the results obtained in computer simulations are very close to the optimum ones.

On the Total Energy Efficiency of Cell-Free Massive MIMO

We consider the cell-free massive multiple-input multiple-output (MIMO) downlink, where a very large number of distributed multiple-antenna access points (APs) serve many single-antenna users in the same time-frequency resource. A simple (distributed) conjugate beamforming scheme is applied at each AP via the use of local channel state information (CSI). This CSI is acquired through time-division duplex operation and the reception of uplink training signals transmitted by the users. We derive a closed-form expression for the spectral efficiency taking into account the effects of channel estimation errors and power control. This closed-form result enables us to analyze the effects of backhaul power consumption, the number of APs, and the number of antennas per AP on the total energy efficiency, as well as, to design an optimal power allocation algorithm. The optimal power allocation algorithm aims at maximizing the total energy efficiency, subject to a per-user spectral efficiency constraint and a per-AP power constraint. Compared with the equal power control, our proposed power allocation scheme can double the total energy efficiency. Furthermore, we propose AP selections schemes, in which each user chooses a subset of APs, to reduce the power consumption caused by the backhaul links. With our proposed AP selection schemes, the total energy efficiency increases significantly, especially for large numbers of APs. Moreover, under a requirement of good quality-of-service for all users, cell-free massive MIMO outperforms the colocated counterpart in terms of energy efficiency.

Bandwidth efficient optimal superimposed pilot design for channel estimation in OSTBC based MIMO–OFDM systems

This paper proposes optimal superimposed pilot (SIP) sequence design and pilot placement towards mean square error (MSE) minimization for channel estimation in spatially correlated/uncorrelated MIMO–OFDM channels. For uncorrelated channels, a closed form expression is derived for the optimal pilot sequence, number of pilot subcarriers and pilot locations. For correlated channels, the problem of designing the optimal SIP sequence is formulated as a semidefinite program. The proposed schemes lead to a substantial increase in the bandwidth efficiency since it employs pilot symbols on a significantly fewer number of subcarriers in comparison to existing schemes. It is shown that the proposed techniques achieve the Cramer–Rao bounds. In addition, a closed form analytical expression is derived for the bit-error rate of orthogonal space–time block codes (OSTBC) based MIMO–OFDM systems including the effect of channel estimation error arising from the proposed SIP based estimation techniques. Simulation results demonstrate the improved estimation performance and bandwidth efficiency of the proposed schemes.

Joint detection based on the total least squares

Joint detection can eliminate the inter-symbol interference which is caused by Multipath propagation, and multiple access interference which is caused by non-orthogonal multiplexing. In multipath fading channels, the error of channel estimation is inevitable. It will propagate to system matrix. In this dissertation, we utilize the joint detection to analyze the effect of channel estimation error Considering the error of system matrix and noise. We present the total least squares (TLS) way that can be used to overcome the defect of Zero Forcing Block Linear Equalizer (ZF-BLE). The emulated data have turned out that our proposed receiver is superior than the conventional ZF-BLE method.

Joint Power and Rate Control for Packet Coding Over Fading Channels

We consider random linear packet coding for fading channels with long propagation delays, such as underwater acoustic channels. We propose a scheme in which the number of coded packets to transmit is determined to achieve a prespecified outage/reliability criterion and investigate joint power and rate control with constrained resources. Using the channel state information that is obtained via feedback from the receiver, the transmitter adjusts its power and the number of coded packets so that the average energy per successfully transmitted bit of information is minimized. Two optimization constraints are imposed: 1) the transmit power should not exceed a maximum level; and 2) the number of coded packets should not exceed a maximum value dictated by the desired throughput and delay. We further extend the results to take into account the effect of inevitable channel estimation errors, and consider the case in which the transmitter has only an estimate of the channel gain. We design adaptation policies for such a case based on minimum mean square error (MMSE) channel estimation, taking into account the effect of channel estimation errors in an optimal manner to satisfy the required outage/reliability criterion. Finally, we compare the proposed technique to standard automatic repeat request (ARQ) protocols for underwater communications in terms of the throughput efficiency. Analytical results show that substantial energy savings and improvements in throughput efficiency are available from adaptive power/rate control. We also present experimental results obtained using channel gains measured during the Surface Process Acoustic Communication Experiment (SPACE-08), an at-sea underwater experiment conducted off the coast of Martha's Vineyard in fall 2008.

Robust Power Control for OFDM-Based Cognitive Radio Networks with QoS Guarantee

Traditional power control schemes in Orthogonal Frequency Division Multiplexing based Cognitive Radio Networks (CRNs) are achieved under perfect channel state information (e.g., exact parameter information). Due to the effect of channel estimation errors and feedback delays, however, channel uncertainties are inevitable in practical CRNs. In this paper, considering bounded uncertainties of channel gains, a robust power control algorithm is proposed to minimize the total transmit power of Secondary Users (SUs) subject to interference power constraint of primary user and quality of service constraint of SU where the non-convex optimization problem is converted into a convex optimization problem that is solved by using robust optimization theory. Computer experiments demonstrate the effectiveness of the proposed algorithm by comparing with the non-robust algorithm in the aspect of suppressing the effect of parameter perturbation.

Massive MIMO in Spectrum Sharing Networks: Achievable Rate and Power Efficiency

Massive multiple input multiple output (MIMO) is one of the key technologies for fifth generation and can substantially improve energy and spectrum efficiencies. This paper explores the potential benefits of massive MIMO in spectrum sharing networks. We consider a multiuser MIMO primary network, with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -antenna primary base station (PBS) and K single-antenna primary users (PUs), and a multiple-input-single-output secondary network, with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> -antenna secondary base station and a single-antenna secondary user. Using the proposed model, we derive a tight closed-form expression for the lower bound on the average achievable rate, which is applicable to arbitrary system parameters. By performing large-system analysis, we examine the impact of large number of PBS antennas and large number of PUs on the secondary network. It is shown that, when N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> and K grow large, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> must be proportional to ln K or larger, to enable successful secondary transmission. In addition, we examine the impact of imperfect channel state information on the secondary network. It is shown that the detrimental effect of channel estimation errors is significantly mitigated as N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> grows large.

Soft‐output MMSE MIMO detector under different channel estimation models

This study considers the effect of channel estimation error (CEE) on the soft-output bit log-likelihood ratio (LLR) in a multiple-input–multiple-output detection system which the source sends their quadrature amplitude modulation to the detector through Rayleigh fading channels. The new expressions of LLR with maximum-likelihood CE for deterministic channel model and minimum mean square error (MMSE) CE for random channel model are obtained separately for linear MMSE receiver using known pilot-symbol-aided CE. Meanwhile, the optimal power allocation between training and data transmissions for these two different LLR expressions, which attends to get the maximum ratio of signal and interference plus noise ratio, are obtained under the total transmitting power constraints. Numerical results show that the power allocation ratio sets to be ∼0.5 is optimal for two new different LLRs at the same total power and system noise. Moreover, the derived LLR expressions match the simulation result and outperform the conventional system without the consideration of CEE and optimal power allocation. Meanwhile, the system performance is better than the existing research with the consideration of CE.

Reducing codebook loss with reconfigurable receive antennas

In this study, a reconfigurable antenna codebook feedback (FB) scheme is investigated to reduce precoding codebook loss without increasing the number of FB bits. Analysis and simulations show that increasing the number of receive antenna states (S) has the same effect as codebook size expansion when the codeword and state selection is based on minimising the distance between channel and codeword. In addition, the authors propose an optimum selection approach. The signal to noise ratio (SNR) and rates achieved with perfect FB in a traditional non-reconfigurable antenna system, can be exceeded with only S = 2, using the proposed optimum selection. In fact doubling S gives an approximate SNR gain of 40% compared with S = 1. The authors also consider the effects of channel estimation errors and correlated antenna states. The authors show that the performance losses due to correlation can be quantified with a simple closed form result.

Impact of loop-back interference and channel estimation errors on full-duplex relay networks

This paper investigates the rate performance of full-duplex (FD) relay systems under the effect of channel estimation error and residual loop-back interference. The study considers both one-way and two-way amplify and forward (AF) relaying schemes. Power allocation techniques, applied at the sources and the relay, are proposed and shown to be effective that leads to near optimal solution. Comparison between the half-duplex (HD) and FD systems using optimum power allocation are made. Also, the impact of channel estimation error and loop-back interference on the rate of FD transmission are compared. It is shown that the destructive effect of loop-back interference dominates the effect of channel estimation error. Finally, assuming a bidirectional network, the performance of two-way analog network coding (ANC) scheme is compared to the plan of using two one-way AF relaying connections. The results show that it is better to use FD ANC for low transmission power and HD one for high power than using two one-way relaying schemes.

Multi-Pair Two-Way Massive MIMO AF Full-Duplex Relaying With Imperfect CSI Over Ricean Fading Channels

This paper investigates a multi-pair two-way massive MIMO amplify-and-forward full-duplex relay (FDR) system over Ricean fading channels, where multiple pairs of full-duplex users exchange information within pair through a full-duplex relay with a very large number of antennas (M for transmission and M for reception). First, the zero-forcing reception/zero-forcing transmission and maximum-ratio combining/maximum-ratio transmission processing matrices with imperfect channel state information at the relay are presented. Then, the corresponding asymptotic expressions (in M) of the end-to-end signal-to-interference-plus-noise ratio are derived. Finally, the asymptotic spectral efficiency (SE) and energy efficiency (EE) at the general power scaling schemes when the number of the relay antennas tends to infinity is analyzed. Theoretical analyses and simulation results show that, when M → ∞, the effects of channel estimation error, the self-loop of each user as well as the relay, inter-user interferences, the noise at users and the relay can be eliminated, respectively, if the power scaling scheme is properly selected. Besides, the considered multi-pair two-way FDR outperforms the multi-pair two-way half-duplex relaying on SE and EE performances when M is large. Moreover, a low complexity power control scheme is proposed to optimize the SE and we analyze the impact of the number of user pairs on the SE.

Effect of mutual interference and channel estimation error on outage performance of reactive relay selection in unlicensed systems

This study addresses the effects of channel estimation error and mutual interference between licensed and unlicensed systems on outage performance of reactive relay selection in unlicensed systems over independent non-identical (i.n.i) Rayleigh fading channels and under both the maximum transmit power constraint and primary outage constraint. Toward this end, power allocation for unlicensed users is first recommended to satisfy both constraints and account for channel estimation error and mutual interference. Then, we derive an exact closed-form outage probability representation for unlicensed systems to quickly evaluate this effect in key operation parameters. Various results corroborate the derived expressions and provide useful insights into system performance.

Experimental evaluation of theperformance of 2×2 MIMO-OFDM for vehicle-to-infrastructure communications

In this paper, a novel 2×2 multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) testbed based on an Analog Devices AD9361 highly integrated radio frequency (RF) agile transceiver was specifically implemented for the purpose of estimating and analyzing MIMO-OFDM channel capacity in vehicle-to-infrastructure (V2I) environments using the 920 MHz industrial, scientific, and medical (ISM) band. We implemented two-dimensional discrete cosine transform-based filtering to reduce the channel estimation errors and show its effectiveness on our measurement results. We have also analyzed the effects of channel estimation error on the MIMO channel capacity by simulation. Three different scenarios of subcarrier spacing were investigated which correspond to IEEE 802.11p, Long-Term Evolution (LTE), and Digital Video Broadcasting Terrestrial (DVB-T)(2k) standards. An extensive MIMO-OFDM V2I channel measurement campaign was performed in a suburban environment. Analysis of the measured MIMO channel capacity results as a function of the transmitter-to-receiver (TX-RX) separation distance up to 250 m shows that the variance of the MIMO channel capacity is larger for the near-range line-of-sight (LOS) scenarios than for the long-range non-LOS cases, using a fixed receiver signal-to-noise ratio (SNR) criterion. We observed that the largest capacity values were achieved at LOS propagation despite the common assumption of a degenerated MIMO channel in LOS. We consider that this is due to the large angular spacing between MIMO subchannels which occurs when the receiver vehicle rooftop antennas pass by the fixed transmitter antennas at close range, causing MIMO subchannels to be orthogonal. In addition, analysis on the effects of different subcarrier spacings on MIMO-OFDM channel capacity showed negligible differences in mean channel capacity for the subcarrier spacing range investigated. Measured channels described in this paper are available on request.

On the Analysis of MIMO-ZF Receiver Over Fully Correlated MIMO Rayleigh Fading with LMMSE Channel Estimation

For multiple-input multiple-output (MIMO) communication systems, the zero-forcing (ZF) receiver has attracted great research interest in recent years. The purpose of this work is to analyze the effect of channel estimation error on the performance of the MIMO-ZF receiver over spatially correlated Rayleigh fading channels. Unlike previous works, where the channel is assumed with transmit correlation but without receiver correlation, we treat the fully correlated channel cases. Furthermore, we assume that the channel estimation error is a Gaussian and correlated matrix. The distribution of the post-processing signal-to-noise ratios is approximated. An approximation of the average bit error rate (BER) is derived and compared to Monte Carlo simulation results. The proposed BER expression takes into consideration that the post-processing noise in not Gaussian. Numerical results show an excellent agreement between the analytical approximation and Monte Carlo simulation curves.

Robust Time Reversal-based Transmit Optimization for Green Heterogeneous Networks

Time reversal (TR) beamforming, considered as one of most prominent linear precoders, has showed the feasibility in conventional communications. In this paper, we propose the TR-based transmit optimization for heterogeneous networks (HetNets) where multiple femtocells apply TR precoders over frequency selective channels, with the signal-to-inference-plus-noise ratio (SINR) and interference constraints at single-antenna femtocell user devices. In multi-femtocell network environments, we exhibit that TR outperforms the well-known zero-forcing beamforming. Particularly, we focus on the practical case of imperfect channel estimation at femtocell base stations. The robust optimization methodology is hence devised by taking into account the average effect of channel estimation error (CEE) on system performance. Under the assumption of estimation error in time-varying channels, we derive the exact closed-form expressions of the desired signal, inter-symbol interference (ISI), inter-user interference (IUI), co- and cross-layer interference terms, respectively. These derivations allow us to tackle the proposed robust algorithm by convex optimization techniques. In final, numerical results are shown to confirm the validation of our proposal. DOI: http://dx.doi.org/10.5755/j01.eee.21.3.10431

Game theoretic power allocation for fading MIMO multiple access channels with imperfect CSIR

In this paper, we formulate the power allocation (PA) problem for uplink of MIMO fading multiple access channels using a game theoretic framework with channel estimation error at receiver side. We investigate the effect of the error on derived PA policy and on performance of the system. Furthermore, it is assumed that the CSI at transmitter side is imperfect i.e., each transmitter is informed with the statistics of the channels instead of the instantaneous channel states. We use lower bound of mutual information between each user and the base station to derive a utility function for the concave game, regarding the channel estimation error. Following the formulation of problem, existence and uniqueness of the game's equilibrium are investigated and it is proved that the proposed game has a unique Nash equilibrium (NE). Also a primal-dual subgradient based best-response algorithm is designed to find the NE. The algorithm updates the policy of each player regarding the given policy of other players, at each iteration. Finally, simulation results of the achieved PA policy are illustrated to investigate the effect of channel estimation error. In particular, simulations show that the overall system performance will be improved when channel estimation error in modeling the PA game is considered.

On the Capacity of Iteratively Estimated Channels Using LMMSE Estimators

This paper investigates the capacity of radio channels when iterative channel estimation, data detection, and decoding are employed. Knowing the capacity gain from iterative detection versus purely pilot-based channel estimation helps a designer compare the performance of an iterative receiver against a noniterative receiver and select the best balance between performance and cost. A bound is put on the linear minimum mean square error (LMMSE) channel estimation error, based on which a bound on the capacity is obtained. The attainable capacity is related to the channel estimation error of the receiver. The bounds take into account the uncertainty in symbol detection on channel estimation and incorporate the effect of channel estimation error on channel capacity. The interaction between the symbol detector and the decoder is analytically characterized and depicted in an extrinsic information transfer (EXIT) chart, where a bound on the detector curve is found. With optimal LMMSE pilot-based channel estimation, the results of this paper demonstrate that iterative channel estimation provides insignificant capacity advantage at fading rates below 1% of the symbol rate, although a computational-cost gain is still available. Iterative channel estimation provides a capacity benefit if suboptimal pilot signaling is used to provide initial channel estimates.

Throughput Scaling of MIMO Channels With Imperfect CSIT in the Low-SNR Regime

We study the effect of channel estimation error on the performance of water-filling in point-to-point multiple-input- multiple-output (MIMO) channels at low signal-to-noise ratios (SNRs). In this regard, we derive the water-filling throughput of a MIMO channel in the presence of imperfect channel state information at the transmitter (CSIT). The asymptotic growth rate for the throughput, i.e., R, is then found and is compared with the asymptotic growth rate for the capacity with perfect CSIT, i.e., CP, as a function of the signal-to-estimation-error ratio (SER). We show that, at low SNR, for moderate values of the SER, water filling based on erroneous channel estimates can still achieve significant throughputs asymptotically.

Performance Evaluation of the Joint Detection with Channel Estimation Error

In previous B. Steiner channel estimation algorithm adopted in Time DivisionSynchronous Code Division Multiple Access (TD-SCDMA) system, but there are some errors in estimated channel due to noise. However, due to using the short training sequences available, the resulting estimation of the channel and detected data suffer from unavoidable errors. In this paper, we analyze the effect of channel estimation error on joint detection and evaluate the performance of TD-SCDMA systems with channel estimation error. The simulation results are consistent with the theory analysis.