MMSE subcarrier equalization for filter bank based multicarrier systems

Vector Orthogonal Frequency Division Multiplexing (OFDM) for single transmit antenna systems is a general transmission scheme, where OFDM and Single-Carrier Frequency Domain Equalization (SC-FDE) can be treated as two special/extreme cases. Due to its flexibility, it has drawn more and more attention recently. So far, all the studies about Vector OFDM assume the Maximum Likelihood (ML) receiver. In this paper, we investigate the performance of Vector OFDM with linear receivers, i.e., the Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers. We first show that the detection SNR gap between the MMSE and ZF receivers increases with both channel SNR and the vector blocks (VB) size defined in Vector OFDM. Then, it is proved that for both ZF and MMSE receivers, all the transmitted symbols have equal performance. This is different from the Vector OFDM with ML receiver, where different VBs may have different coding gain, and thus may have different performances. We analyze the diversity order for Vector OFDM with MMSE receiver, and show that, regardless of the Vector OFDM symbol length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> , the diversity order can be represented as min{[ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-R</sup> ], <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> }+1, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the VB size, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> is the spectrum efficiency in bits/symbol, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> is the maximum delay of the multipath channel. For Vector OFDM with ZF receiver, we show that the diversity order equals 1 and the performance is the same as the conventional OFDM at high SNR.

Conventional orthogonal frequency division multiplexing (OFDM) system utilizes cyclic prefix (CP) to remove the channel-induced inter-symbol interference (ISI) at the cost of lower spectral efficiency. In this paper, a generalized sidelobe canceller (GSC) based equalizer for ISI suppression is proposed for uplink multi-antenna OFDM systems without CP. Based on the block representation of the CP-free OFDM system, there is a natural formulation of the ISI suppression problem under the GSC framework. By further exploiting the signal and ISI signature matrix structures, a computationally efficient partially adaptive (PA) implementation of the GSC-based equalizer is proposed for complexity reduction. The proposed scheme can be extended for the design of a pre-equalizer, which pre-suppresses the ISI and realizes CP-free downlink transmission to ease the computational burden of the mobile unit (MU). Simulation results show that the proposed GSC-based solutions yield equalization performances almost identical to that obtained by the conventional CP-based OFDM systems and are highly resistant to the increase in channel delay spread.

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

An asymptotically minimum bit error rate (BER) linear block precoder is determined for block-by-block communication systems employing linear minimum mean square error (MMSE) equalisation and disjoint detection. The problem is solved by a two-stage optimisation procedure in which a lower bound on the BER is first minimised, and then it is shown how this minimised lower bound can be achieved. Simulation results show that the BER performance of the proposed scheme is superior to the standard MMSE precoder and several other conventional systems such as orthogonal frequency division multiplexing. At reasonable BERs, the signal-to-noise ratio (SNR) gain can be of the order of several decibels.

In this thesis, we cope with the fundamental mathematical and physical problems of the space-time-Doppler UWB system design for fading channels: multi-input multi-output (MIMO) wireless communication with adaptive filtering. The estimation algorithm from equalizer providing an accurate parameters estimate is investigated. UWB radio is a fast emerging technology with uniquely attractively features inviting major advances in wireless communications, networking, radar, imaging, and positioning systems. By its rule-making proposal in 2002, the Federal Communications Commission (FCC) in the United States essentially unleashed huge new bandwidth (3.6-10.6 GHz) at the noise floor, where UWB radios overlaying coexistence RF systems cerate using low-power ultra-short information bearing pulses. Right now, there are three basic types of UWB: multiband OFDM UWB (MB-OFDM UWB), impulse-UWB (I-UWB), and direct sequence UWB (DS-UWB). We focus on I-UWB and MB-OFDM-UWB, and compare their performance. A simple means for spreading the spectrum of low duty cycle pulse trains is time hopping (TH), with pulse position modulation (PPM) for data modulation at the rate of many pulses per data bit. The main contribution of this thesis for I-UWB is the design of leading edge detectors, coherent correlation detector (CCD), and pilot performance enhancement compared with different Rayleigh and Ricean fading conditions. For MB-OFDM UWB, we have considered the performance analysis and design criteria of MIMO OFDM UWB systems for high data-rate wireless transmission. The signal processing of frame detection, time synchronization, frequency synchronization, channel estimation, synchronization tracking using pilot subcarriers and 2-D MIMO detection algorithms is discussed. The main contributions of this thesis are 1) Compared with receiver employing the Maximum Likelihood (ML) detector, the receiver employing a low-complexity linear Minimum Mean Square Error (MMSE) demodulator can perform a limited performance loss in spatially uncorrelated channels. 2) Due to the operations of spreading and dispreading combined with MMSE-based frequency domain equalization, the adverse effects of the low-SNR subcarriers on the average BER performance are potentially improved. This is a direct consequence of spreading, because even if the signal corresponding to a specific chip is obliterated by a deep frequency domain channel fade, after dispreading these effects are spread over the Walsh-Hadamard Transform (WHT) length. Hence there is a high chance of still recovering all the partially affected subcarrier symbols without errors. 3) As a test case, the OFDM-based 200 Mb/s MB-UWB network (IEEE 802.15.3a) are considered, but the simulation results are shown above section. 4) The simulation channel can be easily applied to NOS and NLOS situation with WHT transformation from Simulink model. The fading channels of UWB with low/high signal to noise ratio (SNR), multipath effects, and multiuser interference may introduce large errors in location. The location engine performs the following tasks: █ Data fusion techniques: Different data fusion techniques are implemented using Time Of Arrival (TOA), Angle Of Arrival (AOA), or a combination of both. █ Channel modeling: A multipath, multiuser channel environment is created that models path loss, shadowing, Rayleigh fading, and Doppler frequency effects. █ Parameter estimation: TOA and AOA estimation algorithms are implemented as part of the location finding engine. Different variations of algorithms are implemented for performance and comparison purposes. █ Configuring the physical layer for different wireless networks. Among the programmable parameters are spreading factor, packet size, training length, constellation type, modulation technique, carrier frequency, level of transmitted signal power, and the number of antennas at the transmitter for both sides. █ Configuring the mobile user conditions. The wireless channel models depend on the Doppler frequencies present in the environment. The Doppler frequency depends on the mobile speed and carrier frequencies as input and generates a Rayleigh fading channel with the U-shape Doppler spectrum. █ Configuring the environmental parameters and network geographical structure. One of the factors affecting the performance of the wireless location system is the environment type (e.g., bad urban, urban, suburban, or rural area). For example, in a bad urban area with many blocking objects and buildings, non-line of sight (NLOS) effects plays an important role in the estimation accuracy.

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.

In this work, we proposed Offset-Quadrature Amplitude Modulation (OQAM) for Discrete Wavelet Transform (DWT) as alternative of Multi-Carrier Modulation (MCM) systems. Instead of the upsampler in the conventional DWT-MCM, OQAM is used in each level. In OQAM, each symbol will be separate into two components, in-phase and quadrature. With OQAM, maximum phase variation will decrease to its half value, which means that the performance of the RF power amplifier will improved. In addition, half symbols period will offset (stagger) the quadrature and in-phase components of the modulated signal to achieve low bit error rate. By contrast, in conventional orthogonal frequency division multiplexing (OFDM), without using the guard interval (Cyclic Prefix (CP)), inherent interferences cause degeneration in received symbols. In this paper, the proposed system model enhanced the spectrum efficiency and becomes more robust to the frequency selective environments. The simulation results illustrate that our proposed system model improves the system performance in terms of probability of errors compared with the OFDM system.

In comparison to Orthogonal Frequency Division Multiplexing (OFDM), Wavelet Packet Modulation (WPM) offers much lower side lobes in transmitted signal, which reduces inter-carrier interference (ICI) and narrowband interference (NBI). It is also spectrally efficient since it does not utilize cyclic prefix (CP), nevertheless, it requires an efficient equalization technique to counter the inter symbol interference (ISI) and ICI created by the channel. In this paper, performance comparison of OFDM and WPM for several multipath wireless channels is presented. We propose a novel application of zero-forcing (ZF) and minimum mean square error (MMSE) algorithms as time-domain channel equalization techniques for WPM systems. It is shown that, for a multipath wireless channel, WPM using MMSE-equalizer has a better bit error rate (BER) performance as compared to ZF-equalizer in WPM, as well as OFDM system.

An orthogonal frequency division multiplexing (OFDM) is one of the effective techniques used in wireless communications. In OFDM systems, channel impairments due to multipath dispersive wireless channels can cause deep fades in wireless channels. The OFDM receiver also requires an accurate and computationally efficient channel state information when coherent detection is involved. Therefore, it needs a good robust estimation method of the channel in wireless communication for OFDM systems. And one of these channel estimation methods is minimum mean square error (MMSE) channel estimation. MMSE channel estimation one most used method in OFDM systems. In this work we enhanced robustness of MMSE channel estimation by using it in base of quasi-cyclic low density parity check (QC-LDPC) coded OFDM system.

Filter bank multi-carrier with offset QAM(FBMC/OQAM) is a multi-carrier modulation technique that can be an alternative to conventional orthogonal frequency division multiplexing(OFDM) with cyclic prefix (CP) in wireless network. FBMC has a higher spectrum efficiency and effective emission power without CP. Because the orthogonality only exists in real domain, the channel estimation in FBMC/OQAM system is more challenging. In this paper, the IAM preamble-based method and the DFT-based channel estimation are combined to do the estimation. And two improved DFT-based channel estimation methods are proposed to remove the noise in the channel impulse response(CIR) of conventional DFT-based method. The proposed are proved to have a better performance than the conventional DFT-based.

Multi carrier modulation is Orthogonal Frequency Division Multiplexing (OFDM), dividing the large band spectrum into small (narrow) band spectrum.OFDM offers flexibility in adaptation to time varying channel condition by adopting the parameters at each subcarrier accurately.Due to the multipath effect the OFDM system suffers Inter Symbol Interference (ISI).ISI can be reduced by introducing the guard band (cyclic prefix).Time-varying channel estimation is an important activity in next generation wireless communication.Channel estimation is required mainly for the significant signal processing operation in multiple input multiple output MIMO-OFDM systems.In this project DFT -based channel estimation based on block type arrangement is implemented in MAT Lab.The bit error rate (BER) of DFT (Discrete Fourier Transform)based channel estimation is less than the BER of LS (Least Square) and MMSE (Minimum Mean Square Error) based channel estimation with same signal to noise ratio (SNR).

Linear precoding plays an important role in the spatial multiplexing multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems which are considered one of the primary candidates for the physical-layer techniques in the next-generation wireless communication systems. It requires the channel state information (CSI) at the transmitter to adapt the transmitted signal to the channel conditions. In most communication systems, the CSI is estimated at the receiver and fed back to the transmitter. However, the error performance in a precoded MIMO-OFDM system is significantly degraded due to the long feedback delay that causes the outdated CSI at the transmitter. In this paper, a novel approach using multi-block linear channel prediction is proposed to combat the feedback delay in a limited feedback precoded spatial multiplexing MIMO-OFDM system. The time-varying channel is modeled by autoregressive (AR) process, whose coefficients are obtained by linear minimum mean square error (MMSE) method. To increase prediction range, block-based channel samples are used to establish the AR model, and multiple blocks are employed to iteratively predict the CSI. Simulation results show that the performance degradation caused by large feedback delay can well be mitigated.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Orthogonal frequency-division multiplexing (OFDM) is a promising scheme for multicarrier (MC) transmission. The combination of OFDM and code-division multiple access (CDMA) which is referred to as OFDM–CDMA, has recently attracted much research interest in wireless communications. In this paper, we evaluate the downlink performance for two forms of adaptive OFDM–CDMA receivers in multipath fading channels: 1) MC–CDMA and 2) MC–direct sequence (DS)–CDMA. We propose theoretical minimum mean square errors (MMSEs) for MC–CDMA and MC–DS–CDMA to compare the performances in different situations. Moreover, one drawback of OFDM schemes is the rate reduction due to the cyclic prefix (CP) overhead, which significantly affects the channel utilization in MC–DS–CDMA systems. We propose adaptive receiver structures with both subcarrier- and code-interval equalizations to improve the performance of MC–DS–CDMA systems with shorter or no CP. Simulation results demonstrate the effectiveness of the proposed receivers and the correctness of the theoretical derivations. </para>

SummaryIn this work, a deep learning (DL)‐based massive multiple‐input multiple‐output (mMIMO) orthogonal frequency division multiplexing (OFDM) system is investigated over the tapped delay line type C (TDL‐C) model with a Rayleigh fading distribution at frequencies ranging from 0.5 to 100 GHz. The proposed bi‐directional long short‐term memory (Bi‐LSTM) channel state information (CSI) estimator uses online learning during training and offline learning during the practical implementation phase. The design of the estimator takes into account situations in which prior knowledge of channel statistics is limited and targets excellent performance, even with limited pilot symbols (PS). Three separate loss functions (mean square logarithmic error [MSLE], Huber, and Kullback–Leibler Distance [KLD]) are assessed in three classification layers. The symbol error rate (SER) and outage probability performance of the proposed estimator are evaluated using a number of optimization techniques, such as stochastic gradient descent (SGD), momentum, and the adaptive gradient (AdaGrad) algorithm. The Bi‐LSTM‐based CSI estimator is trained considering a specific number of PS. It can be readily seen that by incorporating a cyclic prefix (CP), the system becomes more resilient to channel impairments, resulting in a lower SER. Simulations show that the SGD optimization approach and Huber loss function‐trained Bi‐LSTM‐based CSI estimator have the lowest SER and very high estimation accuracy. By using deep neural networks (DNNs), the Bi‐LSTM method for CSI estimation achieves a superior channel capacity (in bps/Hz) at 10 dB than long short‐term memory (LSTM) and other conventional CSI estimators, such as minimum mean square error (MMSE) and least squares (LS). The simulation results validate the analytical results in the study.