Channel Estimation Error Variance Research Articles

Analysis of Variable Bit Rate Spread FBMC-Based Integrated Satellite–Terrestrial Broadcast System

For the joint impact of carrier frequency offset (CFO) and phase noise (PHN), the exact closed-form signal-to-interference-noise ratio (SINR) expressions are derived for novel Walsh Hadamard (WH)-spread filterbank multicarrier (SFBMC) transmission scheme in integrated satellite–terrestrial broadcast system (ISTBS). For this evaluation, variable bit rates (VBR)s for WH-SFBMC are considered for transmission in 3-state Fontan land mobile satellite suburban environment. Further, symbol error rate (SER) and spectral efficiency are analyzed based on the obtained SINR expressions. Such analyses are conducted to support VBR quality of service (QoS) in orthogonal frequency division multiplexing (OFDM)-based digital video broadcasting standards utilizing ISTBS. Furthermore, pilot-based channel estimation error variance is evaluated for VBR WH-SFBMC. Later, block-by-block system computational complexity of VBR WH-SFBMC, perfect reconstruction (PR)-filterbank multicarrier (FBMC), and OFDM schemes are evaluated. It is shown that, VBR WH-SFBMC is rate-dependent and relatively more complex system than single rate PR-FBMC and OFDM. However, the SER performance of WH-SFBMC is illustrated to outperform PR-FBMC and OFDM significantly even for higher bit rates in presence of CFO and PHN. Moreover, simulation and analytic results are in close approximation with each other. Thus, a trade-off exists between achieved error performance and system complexity.

Optimum Low-Complexity Decoder for Spatial Modulation

In this paper, a novel low-complexity detection algorithm for spatial modulation (SM), referred to as the minimum-distance of maximum-length (m-M) algorithm, is proposed and analyzed. The proposed m-M algorithm is a smart searching method that is applied for the SM tree-search decoders. The behavior of the m-M algorithm is studied for three different scenarios: i) perfect channel state information at the receiver side (CSIR), ii) imperfect CSIR of a fixed channel estimation error variance, and iii) imperfect CSIR of a variable channel estimation error variance. Moreover, the complexity of the m-M algorithm is considered as a random variable, which is carefully analyzed for all scenarios, using probabilistic tools. Based on a combination of the sphere decoder (SD) and ordering concepts, the m-M algorithm guarantees to find the maximum-likelihood (ML) solution with a significant reduction in the decoding complexity compared to SM-ML and existing SM-SD algorithms; it can reduce the complexity up to 94% and 85% in the perfect CSIR and the worst scenario of imperfect CSIR, respectively, compared to the SM-ML decoder. Monte Carlo simulation results are provided to support our findings as well as the derived analytical complexity reduction expressions.

Full/Half Duplex Cooperative NOMA Under Imperfect Successive Interference Cancellation and Channel State Estimation Errors

This paper investigates the application of non-orthogonal multiple access (NOMA) in a coordinated direct and relay transmission (CDRT) system, where the base station (BS) directly communicates with the near (i.e., cell-centric) user, while it requires the help of a dedicated full duplex (FD) relay to communicate with the far (i.e., cell-edge) user. For the considered NOMA-FD-CDRT system, we derive closed-form expressions for the outage probabilities and ergodic rates experienced by the downlink users, under the realistic assumptions of imperfect channel state information (I-CSI) and imperfect successive interference cancellation (I-SIC). Expressions for system outage probability and ergodic sum rate are also presented. The links are assumed to experience independent, non-identically distributed Nakagami-m fading. The analysis of outage probabilities are carried out for both integer and non-integer values of the fading severity index. Extensive simulation results are described to validate the accuracy of analytical results, and to illustrate the performance gain of the considered system, as compared to NOMA-HD-CDRT system and the orthogonal multiple access (OMA) based CDRT system. Our results show that, both channel estimation error variance and I-SIC factor have significant impact on the performance of the considered NOMA-FD/HD-CDRT system. Further, to ensure fairness in terms of outage, we numerically determine the power allocation coefficient at the BS that provides equal outage performance for both the near and the far users in the presence of I-CSI and I-SIC. Furthermore, we derive closed-form expression for the optimal power allocation (OPA) coefficient at the BS that minimizes the system outage probability of the NOMA-FD/HD-CDRT network under I-CSI. With the help of numerical and simulation investigations, we establish that the proposed OPA significantly reduces the system outage probability, as compared to random (i.e., non-optimal) power allocation at the BS.

Analysis of Nonorthogonal Training in Massive MIMO Under Channel Aging With SIC Receivers

We analyze the effect of channel aging on the achievable rate of time division duplexed massive multiple input multiple output systems serving a number of users under aging channels, using nonorthogonal multiple access (NOMA) and orthogonal multiple access (OMA). Using the recently proposed shared uplink pilot based channel estimation for NOMA, we derive bounds on the channel estimation error variance for the two schemes. We then derive the achievable spectral efficiencies of the two schemes. Using numerical results, we show that, in slowly varying channels, using NOMA with shared pilots is preferable over OMA, while the reverse is true under fast varying channels.

Channel estimation in few mode fiber mode division multiplexing transmission system

Abstract It is abundantly clear that obtaining the channel state information (CSI) is of great importance for the equalization and detection in coherence receivers. However, to the best of the authors’ knowledge, in most of the existing literatures, CSI is assumed to be perfectly known at the receiver. So far, few literature discusses the effects of imperfect CSI on MDM system performance caused by channel estimation. Motivated by that, in this paper, the channel estimation in few mode fiber (FMF) mode division multiplexing (MDM) system is investigated, in which two classical channel estimation methods, i.e., least square (LS) method and minimum mean square error (MMSE) method, are discussed with the assumption of the spatially white noise lumped at the receiver side of MDM system. Both the capacity and BER performance of MDM system affected by mode-dependent gain or loss (MDL) with different channel estimation errors have been studied. Simulation results show that the capacity and BER performance can be further deteriorated in MDM system by the channel estimation, and an 1e-3 variance of channel estimation error is acceptable in MDM system with 0–6 dB MDL values.

PSO Based Sum Rate Optimization for MU-MIMO Linear Precoder with Imperfect CSI

It is well known that if the perfect CSI is available at the BS, achieving the maximum sum throughput is equivalent to minimizing the product of mean square error matrix determinants (PDetMSE). Due to the presence of background noise in the estimated signal, the channel estimation errors are unavoidable. Hence, in this paper, it is assumed that the imperfect CSI is available at the BS and the channel estimation error variance is known at the transmitter. It is shown that maximizing the achievable sum rate is not exactly equal to minimizing the PDetMSE if the channel estimation error variance is included in the system design. Particle Swarm Optimization algorithm is used here to solve the sum rate maximization problem under the imperfect CSI. The simulation results compare the proposed system, which considers the channel estimation error variance as an integral part of the system design, with an existing system which assumes the perfect CSI at the transmitter side.

Unitary Beamformer Designs for MIMO Interference Broadcast Channels

Interference broadcast channel (IBC) is a generalized scenario for interference channel (IC) where each base station (BS) transmits to multiple users in its own cell while sharing same time-frequency resources with other adjacent BSs. In this case, it has been shown that by using interference alignment (IA) and under the availability of perfect channel state information (CSI), the achievable degrees of freedom (DoFs) can be linearly scaled up with the number of users. However, in the presence of imperfect CSI, the sum rate becomes degraded, and the achievability of full DoF can not be guaranteed. In this paper, considering a multiple-input-multiple-output (MIMO) IBC with constant channel coefficients, we propose IA algorithms that result in unitary beamformers. First, we consider two improved beamformer designs based on minimizing the weighted-leakage interference (Min-WLI) and maximizing the signal-to-interference-plus-noise ratio (Max-SINR). Second, we propose a novel minimum-mean-square-error (MMSE)-based IA algorithm. Both the improved Max-SINR and the MMSE-based IA schemes are optimized upon the knowledge of the channel estimation error variance so as to achieve better performance under CSI mismatch. We then demonstrate that these two schemes outperform Min-WLI and the conventional Max-SINR IA under perfect and imperfect CSI. Furthermore, it is shown that the MMSE-based IA achieves the same performance trend as the improved Max-SINR IA does; however, the former needs less CSI to be available and has less computational complexity compared to the latter. Moreover, it is established that the MMSE-based IA can result in diagonalized, decoupled subchannels under perfect CSI. The superiority of the proposed algorithms over the conventional schemes is corroborated by numerical simulations.

Adaptive LS- and MMSE-Based Beamformer Design for Multiuser MIMO Interference Channels

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

Channel inversion and regularization revisited

In multiuser multiple-input-single-output (MISO) downlink, linear precoders like channel inversion (CI) and regularized CI (RCI) are more desirable than their nonlinear counterparts due to their reduced complexity. To achieve the full benefits of linear precoding, the availability of perfect channel state information (CSI) at base stations (BSs) is necessary. Since in practice, having access to perfect CSI is not pragmatic, in this paper, we evaluate the performance of CI and RCI under a generalized, imperfect CSI model where the variance of the channel estimation error depends on the signal-to-noise ratio (SNR) and thus covers digital and analog feedbacks as two special cases. Then, based on this imperfect CSI model, we quantify the asymptotic mean loss in sum rate and the achievable degrees of freedom (DoFs) by deriving the received signal-to-interference-plus-noise ratio (SINR) of each user. For example, it is shown that the achievable DoF is directly related to the SNR exponent of the channel estimation error variance. Also, two asymptotic gaps to capacity for the analog feedback are derived: mean loss in sum rate and power loss. In addition, we propose an adaptive RCI technique by deriving an appropriate regularization parameter as a function of the error variance and without imposing any restrictions on the number of users or antennas. It is shown that in the presence of CSI mismatch, while the comparative improvement of the standard RCI to CI becomes negligible, the adaptive RCI compensates this degraded performance of the standard RCI without introducing any extra computational complexity.

Adaptively Regularized Phase Alignment Precoding for Multiuser Multiantenna Downlink

In multiantenna downlink, linear precoders like channel inversion (CI), regularized CI (RCI), and phase alignment (PA) are more desirable than their nonlinear counterparts due to their reduced complexity. However, to exploit the full benefits of multiuser downlink, the availability of perfect channel state information (CSI) at the base station (BS) is mandatory. Since such an assumption is not realistic in practice, subject to CSI mismatch, the downlink precoders may undergo a severe degradation in performance. Therefore, an adaptive linear precoder is required to achieve better performance under the availability of imperfect CSI at the BS. In this paper, we propose such a linear precoder by judiciously picking up an optimized regularization parameter based on the knowledge of the channel estimation error variance in advance. To do so, we first introduce a generalized CSI mismatch model where the variance of the channel estimation error is a function of the signal-to-noise ratio (SNR) and is thus able to accommodate a variety of distinct scenarios such as reciprocal channels and CSI feedback. It is shown that the proposed precoding scheme, dubbed adaptively regularized PA (RPA), is capable of achieving lower bit error rates (BERs) compared to standard linear precoders under both perfect and imperfect CSI.

Soft-Output MIMO Detectors with Channel Estimation Error

New expressions for the soft decision bit log-likelihood ratio (LLR) of a MIMO system using quadrature amplitude modulation (QAM) taking into account channel estimation error (CEE). The bit LLR for the maximum likelihood (ML) and the linear minimum mean-squared error (MMSE) receivers are derived, showing in both receivers explicit scaling of the LLR that is a function of the QAM symbol and the CEE variance. These new expressions for the LLRs are used to show that only modest improvements in the link performance are achieved relative to the LLRs that do not take into account the CEE. This indicates that separating the detector design from channel estimation does not significantly impact the system performance, which leads to simplifications in the overall receiver implementation.

Improved maximum a posteriori signal detection for amplify‐and‐forward relay networks with imperfect channel state information

In amplify-and-forward wireless relay networks, channel state information is required at the destination for signal detection when coherent distributed space-time coding is performed at the relays. The authors consider in this study signal detection in the case of imperfect partial channel knowledge at the destination. For the case of maximum a posteriori signal detection, they propose a modified detector formulation that takes the variance of channel estimation errors into account, and reduces the impact of channel uncertainty on the receiver performance. They show that the proposed modification permits a significant performance improvement, while increasing only slightly the receiver's complexity. It is of special interest for non-constant modulus signal constellations of relatively large size, as well as for relatively low pilot powers.

Impact of Uncertain Channel Estimation and Outdated Feedback on the Adaptive M-PSK Modulation

This paper investigates an adaptive M-ary phaseshiftkeying (M-PSK) modulation scheme over Rayleigh flatfading channels. The data rate is adapted according to thechannel state. At the receiver, the fading is estimated using pilot symbols. To cancel the channel impact, we correct the received signal by dividing it by the estimated value of the fading. So, we propose to adjust the modulation level by examining the statistics of the corrected signal. In contrast to the previous works on the adaptive M-PSK modulation techniques, our modulation switching protocol takes into account the channel estimation error variance. Moreover, we derive a new closed-form expression for the average bit error rate of the considered system.

Design of linear precoder for multiuser MIMO system with spatial correlation and imperfect CSI

AbstractMinimum mean square error (MMSE) based linear precoder in multiple antenna downlink wireless communication system with imperfect channel state information (CSI) at the base station (BS) is considered in this paper. The CSI available at the BS is modelled by incorporating antenna correlation at the BS, channel estimation error variance and temporal correlation coefficient. If the temporal correlation coefficient is known at the BS, the current CSI can be updated. To improve the performance of the system, the future channel is predicted using two‐dimensional MMSE prediction. In this paper, the proposed MMSE linear precoder is designed by considering the imperfect CSI and two‐dimensional predicted CSI. The computer simulation results validate the bit error rate performance of the proposed system when compared to the previously proposed precoders, which consider channel estimation error variance only. Copyright © 2013 John Wiley & Sons, Ltd.

An Upper Bound on the Capacity Loss Due to Imprecise Channel State Information for General Memoryless Fading Channels

A remarkably simple upper bound on the capacity loss due to imprecise channel state information (CSI) is presented for single-input single-output (SISO) general memoryless fading channels, (Capacity Loss) ≤ log(1+var(h - ĥ)SNR) where var(h - ĥ) represents the variance of channel estimation error, i.e. CSI inaccuracy. The bound extends earlier work on Rayleigh channels to general memoryless channels and confirms that the effect of CSI inaccuracies on the communication capacity is secondary to the receiver noise when the signal-to-noise ratio (SNR) is smaller than the reciprocal of the channel estimation error variance, SNR <; 1/var(h - ĥ). An extension to the single-input multiple-output (SIMO) case is also provided.

Improved Lattice Reduction-Aided MIMO Successive Interference Cancellation Under Imperfect Channel Estimation

Lattice reduction (LR) and successive interference cancellation (SIC) are two well-known techniques that can be used to improve detection performance over linear detectors for multiple-input multiple-output (MIMO) systems. However, the LR technique and the SIC technique usually need perfect knowledge on the channel at the receiver, and the use of these techniques with an erroneous channel matrix even worsens the detection performance compared to linear detectors. In this correspondence, we shall show how to modify these techniques to make them robust under imperfect channel estimation. Information needed for the proposed algorithm is moderate; the variance of channel estimation error is the only requirement. Furthermore, our algorithm is not sensitive to the error in the variance of channel estimation error.

Iterative Sphere Detectors for Imperfect Channel State Information

This manuscript presents an iterative detector based on a generalized Schnorr-Euchner enumeration for the case of imperfect channel state information. The detector determines the most contributive N∈{1,2} terms in each of the two log-sum-exponents. The objective function of the tree search is modified to account for (a) the channel estimation error variance and (b) the input a priories. Due to (a), the decomposition of the objective into the form used in conventional tree search is not possible. Moreover, both (a) and (b) invalidate the use of the progressive zigzag order. Because of this, a generalized Schnorr-Euchner enumeration is proposed where explicit sorting is done. Unlike the conventional tree search, the node weights are not computed in an additive way where the weight of a child node is the sum of the weights of the parent and the branch connecting them. The advantage of the proposed detectors compared to iterative channel estimation and decoding is that the repetition of the channel estimation and the QR decomposition is not needed. Also since they are based on the Schnorr-Euchner enumeration, they do not require an initial radius estimation and if channel estimation errors are small enough to be ignored, the search step becomes division- and square-root-free.

On Lower Bounding the Information Capacity of Amplify and Forward Wireless Relay Channels with Channel Estimation Errors

We formulate a capacity lower bound for the dual-hop wireless relay channel which employs an amplify-and-forward (AF) protocol at the relay node. In AF relaying, even when the fading channel in both hops is complex Gaussian distributed, the overall dual-hop channel is non-Gaussian. WPe highlight that there is a fundamental difference between Gaussian and non-Gaussian channels in terms of deriving their capacity lower bound. Specifically for non-Gaussian channels, the channel estimation error variance depends on the received pilot signal and is, in general, different from the average error variance. Whereas for Gaussian distributed channels, which have been predominantly studied in the literature, the channel estimation error variance conditioned on the observed pilot signal coincides with the average error variance. We provide an example using the AF dual-hop channel to exhibit the numerical difference between the true capacity lower bound and that obtained by using the average instead of the conditional error variance.

Concatenated coded modulation techniques and orthogonal space-time block codes in the presence of fading channel estimation errors

Performance of coding and modulation systems in fading channels is usually analysed under the assumption that the receiver has perfect knowledge of channel condition. However, various shortcomings in practical channel estimation techniques lead to imperfections, resulting in channel estimation errors. The authors analyse a practical coding and modulation scheme for multiple-antenna systems considering channel estimation errors. The novelty of this study resides in providing error probability bounds for concatenated trellis coded modulation (TCM) or bit-interleaved coded modulation (BICM) schemes with orthogonal space-time block codes (OSTBC) under imperfect channel estimation assumption. Moreover, our analytical results quantify the performance degradation associated with various levels of channel estimation error variance. The authors also show that if channel estimation quality does not improve sufficiently with SNR, there would be error floor in performance, such that the coded system could get outperformed by a system with differential signalling that requires no channel estimation. Simulation results are presented, which confirm the validity of the analytical results.

CDMA-SFBC Downlink Performance

In this paper a generic code division multiple access (CDMA)-space frequency block coded (SFBC) system for downlink transmission is proposed. Closed form expressions for the bit error rate (BER) performance of the proposed CDMA-SFBC downlink system are derived and numerically evaluated considering different scenarios. The closed form BER expressions are derived for both the M-ary phase shift keying (MPSK) and the M-ary quadrature amplitude modulation (MQAM) techniques considering different CDMA-SFBC configurations. The BER expressions are evaluated for a wide range of system parameters assuming Rayleigh fading. These parameters include M-ary size and channel estimation error variance. Such evaluations are crucial not only for system performance prediction, but also for network management, monitoring and future cross-layer design.