Adaptive OFDM Systems With Imperfect Channel State Information

Adaptive orthogonal frequency division multiplexing (OFDM) has been shown to have significant improvement over basic OFDM in terms of spectral efficiency and bit error rate performance. However, the most important condition to achieve these benefits is the availability of accurate channel state information (CSI) at the transmitter. Imperfect CSI arises from noise at the receiver and due to a delay in providing the CSI from the receiver to the transmitter for the next data transmission. In this paper, we have studied the impact of imperfect CSI on the spectral efficiency of adaptive OFDM systems. We have proposed a robust loading algorithm to improve the performance of such systems. This algorithm applies the bit under loading phenomenon and makes efficient use of M-ary Phase Shift Keying (MPSK) modulation. Plots of spectral efficiency via simulations are provided.

The advantages envisioned from using large antenna arrays have made massive multiple- input multiple-output systems (also known as massive MIMO) a promising technology for future wireless standards. Despite the advantages that massive MIMO systems provide, increasing the number of antennas introduces new technical challenges that need to be resolved. In particular, symbol detection is one of the key challenges in massive MIMO. Obtaining accurate channel state information (CSI) for the extremely large number of chan- nels involved is a difficult task and consumes significant resources. Therefore for Massive MIMO systems coherent detectors must be able to cope with highly imperfect CSI. More importantly, non-coherent schemes which do not rely on CSI for symbol detection become very attractive. Expectation propagation (EP) has been recently proposed as a low complexity algo- rithm for symbol detection in massive MIMO systems , where its performance is evaluated on the premise that perfect channel state information (CSI) is available at the receiver. However, in practical systems, exact CSI is not available due to a variety of reasons in- cluding channel estimation errors, quantization errors and aging. In this work we study the performance of EP in the presence of imperfect CSI due to channel estimation er- rors and show that in this case the EP detector experiences significant performance loss. Moreover, the EP detector shows a higher sensitivity to channel estimation errors in the high signal-to-noise ratio (SNR) regions where the rate of its performance improvement decreases. We investigate this behavior of the EP detector and propose a Modified EP detector for colored noise which utilizes the correlation matrix of the channel estimation error. Simulation results verify that the modified algorithm is robust against imperfect CSI and its performance is significantly improved over the EP algorithm, particularly in the higher SNR regions, and that for the modified detector, the slope of the symbol error rate (SER) vs. SNR plots are similar to the case of perfect CSI. Next, an algorithm based on expectation propagation is proposed for noncoherent symbol detection in large-scale SIMO systems. It is verified through simulation that in terms of SER, the proposed detector outperforms the pilotbased coherent MMSE detector for blocks as small as two symbols. This makes the proposed detector suitable for fast fading channels with very short coherence times. In addition, the SER performance of this detec- tor converges to that of the optimum ML receiver when the size

In wideband multi-pair two-way relay networks, the performance of beamforming at a relay station (RS) is intimately related to the accuracy of the channel state information (CSI) available. The accuracy of CSI is determined by Doppler spread, delay between beamforming and channel estimation, and density of pilot symbols, including transmit power of pilot symbols. The coefficient of the Gaussian-Markov CSI error model is modeled as a function of CSI delay, Doppler spread, and signal-to-noise ratio, and can be estimated in real time. In accordance with the real-time estimated coefficients of the error model, an adaptive robust maximum signal-to-interferenceand- noise ratio (Max-SINR) plus maximum signal-to-leakage-and-noise ratio (Max-SLNR) beamformer at an RS is proposed to track the variation of the CSI error. From simulation results and analysis, it is shown that: compared to existing non-adaptive beamformers, the proposed adaptive beamformer is more robust and performs much better in the sense of bit error rate (BER); with increase in the density of transmit pilot symbols, its BER and sum-rate performances tend to those of the beamformer of Max-SINR plus Max-SLNR with ideal CSI.

In this letter, we analyze the ergodic capacity of bidirectional amplify-and-forward relay selection network. The imperfect channel state information (CSI) is taken into account, which includes outdated CSI and channel estimation error, caused by the time-variation of channel and the imperfect channel estimation, respectively. The lower bound of the ergodic capacity for this network is derived in a closed-form, and verified by the Monte-Carlo simulations. Furthermore, the effects of the imperfect CSI and the number of relays on the ergodic capacity are investigated. The results manifest that imperfect CSI will jeopardize the capacity, and increasing the number of relays contributes to enhance the capacity with imperfect CSI.

In this paper we introduce the concept of Adaptive Orthogonal Frequency Division Multiplexing (AOFDM) for two-way relay systems. In order to implement AOFDM at the nodes, the Channel State Information (CSI) is required. Usually CSI is estimated and hence the effect of estimation error should be considered while implementing AOFDM. In the case of two-way relay, channel estimation at the nodes usually result in the overall channel between the source and relay. But for implementing AOFDM, we require the individual channel between node and relay. We propose a simple method to obtain the individual channel assuming that the estimate of combined channel is available. The loading algorithm used is the Levin-Campello loading algorithm. But the general frame work provided by us can be used to implement other loading algorithms for two-way relay systems.

Many papers have studied the joint optimal transceiver design based on the assumption that channel state information (CSI) is perfect at both sides of transceiver, the same imperfect CSI is available at both ends or that transmitter has knowledge of channel distribution. To our knowledge, little effective work has been done on the practical situation that transmitter only knows the imperfect CSI different from the imperfect CSI at the receiver. So, we proposed a simple practical joint transceiver scheme for such CSI mismatch in this paper and applied it to three popular joint transceiver designs to analyze its performance. Simulation results show that the proposed scheme outperforms the conventional scheme at different channel estimation errors and vector quantization errors.

To achieve reasonable bit error rate (BER) perfor- mance, accurate channel state information (CSI) is required for linear minimum mean squared error turbo equalizer(LMMSE- TE), which is hard to be obtained under the circumstance that long training sequence is not available or channel is time-varying. Soft and hard iterative channel estimation (HICE) algorithms were proposed as fine channel estimation schemes after coarse estimation. In this paper, a new iterative channel correction (ICC) algorithm that belongs to the HICE based on the least mean square (LMS) algorithm is proposed. A cost function using hard decision variables on the output of TE is formed. We show that the gradient descent (GD) algorithm is effective to iteratively minimize the cost function. Furthermore, the iterative step-size to guarantee the convergence for the ICC is analyzed, the mean squared error (MSE) lower bound of the estimated channels for the ICC is derived and validated by the simulations. Our simulations show that, given an imperfect CSI with MSE below the upper bound, the LMMSE-TE incorporated with the ICC yields small performance degradation compared to that with perfect CSI, while the traditional LMMSE-TE suffers from severe error floor even with more iterations, thus showing the robustness of our proposed algorithm to the imperfect channel estimations.

One possible solution to improve the utilization of the capacity of time-varying radio channels is to make the transceivers adaptive. Application of adaptive modulation in orthogonal frequency division multiplexing (OFDM) systems is of particular interest. The objective of this paper is to investigate the receiver algorithms capable of blindly recognizing the modulation format of the received signal in adaptive OFDM systems of the HiperLAN/2 type. The performance of the studied algorithms is considered by computer simulations in OFDM system with adaptive modulation and channel estimation. The maximum likelihood (ML) and the generalized likelihood ratio test (GLRT) classifiers require only few symbols to provide acceptable performance when good channel estimation and relatively high SNR values are available. The novel classifier requires high SNR and more symbols to achieve acceptable performance, but its computational complexity is still lower than that of the ML and the GLRT classifiers.

In this paper, a simple decoded orthogonal frequency division multiplexing (OFDM) quasi orthogonal space time block coding (QOSTBC) wideband wireless system is proposed in the presence of Nakagami-m fading and imperfect channel state information (CSI). The proposed scheme preserves full diversity and full code rate with simple decoding complexity. The use of OFDM is to eliminate the problem of inter-symbol interference (ISI) caused by the frequency selectivity of the channel. Due to practical considerations, imperfect CSI is considered in this work to imitate real transmission scenarios. Simulation results show that in the case of Rayleigh fading and channel estimation error variance of 0, the proposed and the conventional schemes overlap. This shows the good capability of the OFDM technology on repealing the effect of ISI. In addition, it is noted that the performance improves as the Nakagami-m parameter increases. Moreover, it can be observed that as the imperfect estimation error variance increases the performance degrades.

Intelligent reflecting surface (IRS) is a promising new paradigm to achieve high spectral and energy efficiency for future wireless networks by reconfiguring the wireless signal propagation via passive reflection. To reap the potential gains of IRS, channel state information (CSI) is essential, whereas channel estimation errors are inevitable in practice due to limited channel training resources. In this paper, in order to optimize the performance of IRS-aided multiuser systems with imperfect CSI, we propose to jointly design the active transmit precoding at the access point (AP) and passive reflection coefficients of IRS, each consisting of not only the conventional phase shift and also the newly exploited amplitude variation. First, the achievable rate of each user is derived assuming a practical IRS channel estimation method, which shows that the interference due to CSI errors is intricately related to the AP transmit precoders, the channel training power and the IRS reflection coefficients during both channel training and data transmission. Then, for the single-user case, by combining the benefits of the penalty method, Dinkelbach method and block successive upper-bound minimization (BSUM) method, a new penalized Dinkelbach-BSUM algorithm is proposed to optimize the IRS reflection coefficients for maximizing the achievable data transmission rate subjected to CSI errors; while for the multiuser case, a new penalty dual decomposition (PDD)-based algorithm is proposed to maximize the users' weighted sum-rate. Simulation results are presented to validate the effectiveness of our proposed algorithms as compared to benchmark schemes. In particular, useful insights are drawn to characterize the effect of IRS reflection amplitude control (with/without the conventional phase shift) on the system performance under imperfect CSI.

This paper studies the over-the-air computation (AirComp) in an orthogonal frequency division multiplexing (OFDM) system with imperfect channel state information (CSI), in which multiple single-antenna wireless devices (WDs) simultaneously send uncoded signals to a multi-antenna access point (AP) for distributed functional computation over multiple subcarriers. In particular, we consider two scenarios with best-effort and error-constrained computation tasks, with the objectives of minimizing the average computation mean squared error (MSE) and the computation outage probability over the multiple subcarriers, respectively. Towards this end, we jointly optimize the transmit coefficients at the WDs and the receive beamforming vectors at the AP over subcarriers, subject to the maximum transmit power constraints at individual WDs. First, for the special case with a single receive antenna at the AP, we propose the semi-closed-form globally optimal solutions to the two problems using the Lagrange-duality method. It is shown that at each subcarrier, the WDs’ optimized power control policy for average MSE minimization follows a regularized channel inversion structure, while that for computation outage probability minimization follows an on-off regularized channel inversion, with the regularization dependent on the transmit power budget and channel estimation error. Next, for the general case with multiple receive antennas at the AP, we present efficient algorithms based on alternating optimization and convex optimization to find converged solutions to both problems. It is shown that with finite receive antennas at the AP, a non-zero computation MSE for AirComp is inevitable due to the channel estimation errors even when the transmit powers at WDs tend to infinity, while with massive receive antennas, the average MSE and outage probability vanish when the channel vectors are independent and identically distributed. Finally, numerical results are provided to demonstrate the effectiveness of the proposed designs.

Automatic modulation classification (AMC) is an important task in open-loop adaptive orthogonal frequency division multiplexing (OFDM) systems. This paper proposes a channel prediction method to improve the performance of the AMC employed in the adaptive OFDM system. Efficient techniques of noise reduction and interpolation are exploited to achieve an appropriate prediction quality. Simulation results show that the proposed method enhances the performance significantly.

In this study, the authors address antenna selection (AS)‐aided massive multi‐user multiple‐input‐multiple‐output (MU‐MIMO) system based on maximum signal‐to‐noise ratio, where imperfect channel state information (CSI), time‐varying channel and antenna spatial correlation are considered. More explicitly, a computationally simple training‐based channel estimator is firstly employed for obtaining the imperfect down‐link CSI. Channel quantisation (CQ) is subsequently introduced by the feedback link which is used for feeding back so‐obtained CSI to base station. Time varying coefficient is utilised to characterise channel time variety and antenna spatial correlation is modelled by Kronecker model. Furthermore, the authors derive closed‐form ergodic channel capacity of the AS‐aided MU‐MIMO system with channel estimation error, CQ error and delay feedback, which has not yet been addressed in the state‐of‐the‐art approaches. Simulation results are provided to demonstrate the tightness of their theoretical computations of the ergodic channel capacity.

Pilot-assisted channel training for acquiring the channel state information (CSI) is a very critical functionality in URLLC to ensure reliable data transmission. In this paper, we consider the joint uplink and downlink URLLC transmission in which the source uploads a packet to the BS, and then BS forwards this packet to the destination. CSI in the uplink can be estimated at BS by sending a training pilot from source while for the downlink, an extra codebook-based channel quantization is required at destination to measure the estimated channel and feedback the limited-precision results to BS for beamforming before data transmission. This could bring about channel estimation errors, quantization errors and decoding errors, respectively caused by limited training symbols, limited feedback overheads and finite blocklength. In view of this, we for the first time investigate the transmission performance of URLLC under this circumstance and design a performance optimization framework to maximize the transmission reliability. Particularly, the impact of channel estimation accuracy on the transmission reliability of URLLC is studied based on the finite blocklength information theory. An analytical closed-form expression of transmission error probability under imperfect CSI is also derived with respect to key parameters, like the training pilot length, feedback bits and data transmission durations. By jointly optimizing those parameters, we could derive the maximum transmission reliability. Simulation results are provided to validate the effectiveness of our proposed performance optimization framework.

In this paper, we study the performance of block diagonalization (BD) scheme for a downlink multiuser multi-input multi-output (MIMO) system with imperfect channel state information (CSI). At each mobile user, information about the channel is obtained by applying the minimum mean-square-error (MMSE) channel estimation method. The channel state information is fed back to the base station through error-free uplink channels. A theoretical analysis is performed showing that channel estimation errors contribute to co-channel interferences thus deteriorating sum rate capacity. Computer simulations are performed to evaluate the impact of channel estimation errors on the sum rate capacity. The results show that if the MSE of the channel estimation is not less than 10-2, the impact of channel estimation errors is significant and cannot be neglected. To combat this adverse effect, a proper transmit power level is required for the training signals.