Error Rate Analysis of Uplink MC-CDMA Systems under Imperfect Channel Estimation

Theoretical error rate performance of wireless communication systems are usually determined assuming that the perfect channel state information (CSI) is available at the receiver. However, in actual practice, the channel gains at the receiver are obtained via using some channel estimation (CE) techniques. Due to inherent presence of noise, the CE is not perfect resulting in the performance degradation. In this paper, we evaluate the error rate performance of an uplink multicarrier code-division multiple-access (MC-CDMA) system, considering different modulation techniques, where CE is performed using pilot symbol assisted (PSA) minimum mean-square error (MMSE) CE technique. The symbol error rate (SER) analysis of an uplink MC-CDMA system using multiuser detection techniques, such as MMSE and zero forcing (ZF), is presented under imperfect CE. Simulated results for SER are also shown to confirm the accuracy of the analytically derived results.     

Space-time trellis codes over rapid rayleigh fading channels with channel estimation?part ii: performance analysis and code design for non-identical channels

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.     

Blind estimation and detection of space-time trellis coded transmissions over the Rayleigh fading MIMO channel

We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).     

Adaptive Generator Sequence Selection in Multilevel Space–Time Trellis Codes

It has been shown that multilevel space–time trellis codes (MLSTTCs) designed by combining multilevel coding (MLC) with space–time trellis codes (STTCs) can provide improvement in diversity gain and coding gain of the STTCs. MLSTTCs assume perfect channel state information (CSI) at receiver and no knowledge of CSI at transmitter. Weighted multilevel space–time trellis codes (WMLSTTCs), designed by combining MLSTTCs and perfect CSI at transmitter are capable of providing improvement in coding gain of MLSTTCs. In this paper, we present improvement in performance of MLSTTCs by using channel feedback information from the receiver for adaptive selection of generator sequences. The selected generator sequences are used for encoding the component STTCs. The receiver compares current channel profile at receiver with a set of predetermined channel profiles, and sends an index of a predefined channel profile closest to the current channel profile to the transmitter. The transmitter selects a code set that matches best with the current channel profile at receiver using the index. The selected code set having different sets of generator sequences is used by STTC encoders to generate dynamic space–time trellis codes (DSTTCs). The DSTTCs act as component codes in multilevel coding for generating new codes henceforth referred to as multilevel dynamic space–time trellis codes (MLDSTTCs). Analysis and simulation results show that MLDSTTCs provide improvement in performance over MLSTTCs.     

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.     

Effects of channel estimation error on array processing based QO-STBC coded OFDM systems

This letter addresses the issues on performance degradation caused by channel estimation error of quasiorthogonal space-time block (QO-STBC) coded OFDM systems employing array processing decoder. The least square (LS) channel estimator is employed to obtain the required channel state information (CSI). Taking mean square error (MSE) as a performance metric, we evaluate the performance of the LS estimator in MIMO-OFDM systems over frequency selective channels, and its impact on symbol error rate (SER) using both analysis and simulations.     

Performance of Adaptive Modulation Scheme for Adaptive Minimum Symbol Error Rate Beamforming Receiver

This paper considers adaptive beamforming receiver that support multiple users, each having one transmit antenna. In certain circumstances, symbol error rate (SER) performance of the beamforming receiver degrades severely. In order to minimize the SER, minimum symbol error rate (MSER) beamforming receiver is utilized. Then, we propose an adaptive modulation scheme for the receiver to maintain the average SER below the target SER while maximizing the average throughput. The scheme uses the information on the direction of arrival and the average signal-to-noise ratio to decide the appropriate modulation mode. For comparison, the proposed scheme is also applied to minimum mean square error (MMSE) beamforming receiver system. Simulations were carried out in the presence of single and two interferers. Simulation results show that the performance of the proposed algorithm employing MSER beamforming is superior to its MMSE counterpart, with the largest advantage of 0.21 in the outage probability.     

Performance Analysis of Space-Time Coded CDMA System Over Nakagami Fading Channels with Perfect and Imperfect CSI

In this paper, the performance of multiuser CDMA systems with different space time code schemes is investigated over Nakagami fading channel. Low-complexity multiuser receiver schemes are developed for space-time coded CDMA systems with perfect and imperfect channel state information (CSI). The schemes can make full use of the complex orthogonality of space-time coding to obtain the linear decoding complexity, and thus simplify the exponential decoding complexity of the existing scheme greatly. Moreover, it can achieve almost the same performance as the existing scheme. Based on the bit error rate (BER) analysis of the systems, the theoretical calculation expressions of average BER are derived in detail for both perfect CSI and imperfect CSI, respectively. As a result, tight closed-form BER expressions are obtained for space-time coded CDMA with orthogonal spreading code, and approximate closed-form BER expressions are attained for space-time coded CDMA with quasi-orthogonal spreading code. Computer simulation for BER shows that the theoretical analysis and simulation are in good agreement. The results show that the space-time coded CDMA systems have BER performance degradation for imperfect CSI.     

A new optimized least-square sparse channel estimation scheme for underwater acoustic communication

In underwater acoustic (UWA) communication, orthogonal frequency division multiplexing (OFDM) is a promising technology that is highly essential to get channel state information meant for channel estimation (CE). Nevertheless, higher complexity, slower convergence, and poor performance, which degrade the performance estimation, are the limitations of the traditional CE methodologies. Thus, by amalgamating the least square (LS)-CE algorithm along with polynomial interpolated black widow optimization (PI-BWO) model, an optimized least square sparse (OLSS) CE algorithm has been proposed to intend for a UWA-OFDM communication system. Formerly, by utilizing the 2's complement shift left turbo encoding (2CSL-TE) methodology, the input signal is encoded. After that, the modulated encoded signal is provided for inverse fast Fourier transform (IFFT) operations; subsequently, they are transferred over the UWA channel toward the receiver OFDM. By employing the OLSS methodology, the received OFDM signal's interference-free region is utilized for sparse CE at the receiver. Regarding symbol error rate (SER), bit error rate (BER), mean square error (MSE), and peak signal-to-noise ratio (PSNR), the proposed model's experiential outcome is evaluated and analogized with the other prevailing methodologies. When analogized with the conventional models, the proposed estimation methodologies achieved better performance.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

Transceiver Design for MIMO Systems with Improper Modulations

This paper considers joint transceiver designs for single-user multiple-input, multiple-output systems employing improper constellations such as binary phase shift-keying and M-ary amplitude shift-keying (M-ASK). Proposed are novel joint linear transceivers that minimize the total mean squared error of the symbol estimation at the output of the decoder. The joint linear transceiver designs are carried out for both cases of perfect channel state information (CSI) and imperfect CSI at the transmitter and receiver. For the case of imperfect CSI, the channel model takes into account both transmit and receive correlations as well as the channel estimation error. The superiority of the proposed transceivers over the previously-proposed designs is verified by simulation results.     

Robust Non-linear Precoder for Multiuser MISO Systems Based on Delay and Channel Quantization

In multiuser multiple-input single-output (MISO) systems, non-linear precoder is able to achieve the theoretical sum capacity of downlink channel with perfect channel state information (CSI). However, the perfect CSI is not available at the transmitter in practical system, especially in frequency division duplex (FDD) system where the imperfect CSI is the delayed, quantized channel direction information relayed back from the receiver through a dedicated feedback channel. So the performance of conventional non-linear precoder degrades significantly. In this paper, a robust non-linear Tomlinson–Harashima precoding (THP) based on sum mean squared error (SMSE) minimization for the downlink of multiuser MISO FDD systems is proposed. The proposed precoder is robust to the channel uncertainties arising from channel delay and quantization error. Furthermore, an improved non-linear THP with channel magnitude information (CMI) consideration is introduced to compensate the instantaneous CMI shortage at the transmitter. Additionally, the computational complexity of both proposed precoders can be reduced remarkably by Cholesky factorization with symmetric permutation. Simulation results demonstrate the improvement in bit error ratio performance and illustrate the SMSE performance of the proposed algorithms compared with conventional THP with perfect CSI in the literature.     

Symbol Error Rate of MIMO MRC Systems over Time-Varying Fading Channels

The outdated channel state information (CSI) at the transmitter and receiver, which is resulted from time variation of channels, is considered in multiple-input multiple-output systems employing maximal ratio combining. Closed-form expressions for the cumulative distribution function of output signal-to-noise ratio and symbol error rate under time-varying channels are presented to evaluate the effect of outdated CSI. The analytical results are compared with Monte Carlo simulations and a good agreement is obtained.     

Achievable diversity order by space-time trellis coding combined with MLED and OFDM over frequency selective fading channels

Space-time trellis code (STTC) in frequency selective fading channel using maximum likelihood equalization and detection (MLED), and orthogonal frequency division multiplexing (OFDM) are compared in this paper for channels with arbitrary delay profile. The performance bound for both schemes are first derived and their performances are compared both analytically and through simulations. Code design, receiver complexity, interleaver design and the robustness issues are addressed in these comparisons.     

Performance Analysis of Alamouti Space-Time Block Code Over Time-Selective Fading Channels

Alamouti orthogonal space-time block code (Alamouti in IEEE J Sel Areas Commun 16(8):1451–1458, 1998) has been applied widely in wireless communication, e.g., IEEE 802.16e-2005 standard. In this paper, theoretical analysis of symbol error rate performance for Alamouti orthogonal space-time block code (AOSTBC) over time-selective fading channels with a zero-forcing linear receiver is derived. Firstly, a closed-form expression (i.e., not in integral form) is derived for the average symbol pair-wise error probability (SPEP) in time-selective frequency-nonselective independent identically distributed Rayleigh fading channels. Then, the SPEP is used to derive a tight upper bound (UB) for the symbol-error rate (SER) of AOSTBC via establishing algorithmic Bonferroni-type upper bound. Extensive simulation results show that the curves for the UB coincide with the simulated SER curves for various antenna configurations even at very low signal-to-noise ratio regimes. The UB thus can be used to accurately predict the performance of AOSTBC code over time-selective fading channels when a zero-forcing receiver is used.     

Timing error detector design and analysis for orthogonal space-time block code receivers

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.     

Space–Time Constellation Design for Partial CSI at the Receiver

The design of signal constellations for a communication system using multiple transmitter antennas over a Rayleigh-fading channel is considered under the assumption that no channel state information (CSI) is available at the transmitter and the receiver has acquired a CSI estimate with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge at the receiver and allows a smooth transition between these two cases. The data detection performance as a function of the CSI error covariance is analyzed and used to investigate the design of training blocks if such blocks are transmitted to provide CSI to the receiver. Moreover, two approaches to design constellations adapted to the error covariance of the receiver CSI are presented. Whereas the first approach is based on a generic gradient search method, the second approach uses an appropriate combination of constellations designed for perfect and no CSI at the receiver. Simulations confirm the benefits of the presented designs.     

Performance of S + N Selection Diversity Receivers in Correlated Rician and Rayleigh Fading

The performances of two signal-/?/wi-noise (S + N) selection diversity receivers employing noncoherent M-ary frequency shift keying (MFSK) in slow, flat, correlated Rayleigh and Rician fading channels are examined. The branches are assumed to be equally correlated for Rician fading. The correlation model for Rayleigh fading is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Digital multi-carrier spread spectrum versus direct sequence spreadspectrum for resistance to jamming and multipath

We compare single user digital multi-carrier spread spectrum (MC-SS) modulation with direct sequence (DS) SS (with a modified implementation) in the presence of narrowband interference (NBI) and multipath fading. We derive closed-form expressions for the symbol error probability for both the linear MMSE receiver as well as the conventional matched-filter receiver under different scenarios: additive white Gaussian noise (AWGN) channel with NBI, multipath channel with or without NBI. We show that DS-SS can achieve the same performance as MC-SS if the spreading code is carefully designed to have perfect periodic autocorrelation function (PACF). On the other hand, MC-SS is more robust to narrowband interference and multipath fading than is DS-SS with the widely used spreading codes that do not possess perfect PACE. Our analysis reveals that the performance improvement of MC-SS is precisely due to the implicit construction of an equivalent spreading code having nonconstant amplitude but possessing perfect periodic autocorrelation