Determinant maximizing cost function impulse response shortening for discrete multitone transceivers

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.

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).

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.

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 introduction of multi-user multiple-input multiple-output (MU-MIMO) to distributed antenna-based small-cell networks is considered a promising approach toward 5G mobile networks to enhance the sum throughput. However, the inter-symbol interference (ISI) caused by the channel frequency-selectivity, the inter-antenna interference (IAI), and the inter-user interference (IUI) degrade the MU-MIMO downlink throughput. This paper proposes two joint transmit-and-receive (Tx/Rx) filtering schemes (called BD-SVD and MMSE-SVD) for MU-MIMO downlinks using single-carrier (SC) transmission and orthogonal frequency-division multiplexing (OFDM) transmission. In BD-SVD, IUI is removed by block diagonalization (BD) at the transmitter side, and then, the equivalent channel after BD is transformed into IAI-free eigenmodes using singular value decomposition (SVD). On the other hand, in MMSE-SVD, BD is not used and the channel is directly transformed into eigenmodes. IUI and IAI are suppressed by a minimum mean square error (MMSE)-based precoding at the transmitter assuming that each receiver does eigenmode reception. Furthermore, in the case of SC downlink, ISI is suppressed by applying MMSE-based Tx power allocation (PA) and Rx frequency-domain equalization (FDE) to each eigenmode. Numerical results show that BD-SVD and MMSE-SVD achieve a higher sum throughput than conventional MMSE precoding.

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.

In present days, there has been a race among the communication systems in different schemes and generations. Gradually the transmission rate of data is increasing tremendously and breaking the previous generation's record. Now people are thinking of transmitting data beyond imagination. Using multiple antennas both at transmitter and receiver side, MIMO wireless technology efficiently provides very high spectral efficiency, boost the data transmission rate, enhance link reliability and improve system coverage. While transmitting data over mobile radio channels at high bit rates, the impulse response of the channel can be extended over a lot of symbol periods, leading fading and Inter-symbol interference (lSI). Equalizers are used to minimize Fading and interference effects. The analysis of the paper is studying the performance of Minimum mean square error method in terms of BER for MIMO (2×2) and (3×3) wireless channels. Binary Phase Shift Keying (BPSK) modulation technique was used in Rayleigh flat fading channel. Simulating in MATLAB results show that Minimum mean square error (MMSE) receivers is good for noise free channel and is successful in removing ISI. Successive interference method with optimal ordering outperforms the MMSE however a few problems arise because of iterative nature of the algorithm.

In Discrete Multi-Tone (DMT) modulation systems, the well-known technique to overcome the Inter-Carrier Interference (ICI)/Inter-Symbol Interference (ISI) caused by the inadequate Cyclic Prefix (CP) length is to use a Time-Domain Equalizer (TDE) at the receiver front-end. An algorithm used to calculate the coefficients of the optimal shortening Time Domain Equalizer (TDE) was given by Melsa. However, this algorithm requires that the length of the TDE must be smaller than or equal to the memory length of the target impulse response. This paper modifies this algorithm and makes it not only fit for calculating the coefficients of the TDE with arbitrary length, but also have a much less computational time.

In this paper, a minimum mean squared error (MMSE) based turbo equalization scheme in delay-Doppler domain for a coded orthogonal time frequency space (OTFS) system is provided as a low complexity version requiring only a single matrix inversion. Also, we derived extrinsic log likelihood ratios (LLRs) for the turbo equalization, exploiting a priori information fed from a channel decoder, under the assumption that the equalized data symbol follows Gaussian distribution. We rigorously conducted link level evaluation to compare coded orthogonal frequency division multiplexing (OFDM) and OTFS over time-varying multipath channels (based on the channel model in 3GPP 5G New Radio) in 30 GHz band, which may cause severe inter-symbol interference (ISI) and/or inter-carrier interference (ICI) depending on numerology setup. The link level simulation verifies that OTFS is superior to OFDM in block error rate (BLER) performance, each being configured with the best numerology, over all the channel scenarios considered. OTFS shows better BLER performance with smaller subcarrier spacing (SCS) while OFDM has an intermediate SCS for the best BLER due to trade-off between ISI and ICI. Also, we measured normalized mean squared error (NMSE) to see how ISI and ICI affect the performance with respect to numerology, which is used to conjecture why the BLER performance has such peculiarity.

We present a novel iterative (turbo) receiver with tunable complexity for reliable detection of (uncoded) payload data transmitted over long intersymbol interference (ISI) channels affected by crosstalk, as those typically encountered in emerging HDSL2 services standardized by ANSI T1.418 recommendation. The proposed receiver combines in an original way "minimum mean square error (MMSE) estimation principle," "turbo-processing principle" and "crosstalk-prediction principle" for achieving both suboptimal maximum a posteriori probability channel equalization and reliable soft-mitigation of ISI tail plus crosstalk. More in detail, according to the turbo-processing principle, at each iteration suitable extrinsic information is extracted from the equalizing and interference-canceling modules and used as "a priori information" for the next iteration. Several simulation results on typical HDSL-like test-loops confirm the superiority of the proposed turbo-detector (TD) over current solutions based on conventional MMSE decision-feedback equalizers and precoders (such as the Tomlinson-Harashima precoder). The numerical tests also point out that performance of the presented TD on typical high bit-rate digital subscriber lines (HDSL) is not limited by error-floor phenomena, even at error-probabilities below 10/sup -7/.

Discrete multitone modulation allows for a simple receiver structure if the impulse response of the communication channel is shorter than the cyclic prefix. In ADSL, a time-domain equalizer (TEQ) is used to fulfil this requirement. Without a TEQ, unwanted intercarrier interference (ICI) and intersymbol interference (ISI) occur. In this paper, quadratic forms are developed to calculate the contributions of ICI and ISI to the desired signal. Based on these expressions, a new method for calculating the TEQ coefficients, which minimizes the effects of ICI, ISI, and additive noise, is derived. Simulations in the context of ADSL compare the performance of this new algorithm with one that is state of the art.

<abstract><p>Advanced wireless communication technologies, such as 5G, are faced with significant challenges in accurately estimating the transmitted signal and characterizing the channel. One of the major obstacles is the interference caused by the delay spread, which results from receiving multiple signal copies through different paths. To mitigate this issue, the orthogonal frequency division modulation (OFDM) technique is often employed. Efficient signal detection and optimal channel estimation are crucial for enhancing the performance of multi-carrier wireless communication systems. To this end, this paper proposes a Long Short Term Memory-Projected Layer (LSTM-PL) deep neural network(DNN) based channel estimator to detect received OFDM signal. The results show that the LSTM-PL algorithm outperforms traditional methods such as Least Squares(LS), Minimum Mean Square Error (MMSE) and other LSTM deep learning channel estimation methods like Long Short Term Memory(LSTM)-DNN and Bidirectional-LSTM(Bi-LSTM)-DNN, as evidenced by Symbol-Error Rate (SER) outcomes.</p></abstract>

In a multicarrier modulation system, a time domain equalizer (TEQ) traditionally shortens the transmission channel impulse response (CIR) to mitigate intersymbol interference (ISI). In this paper, we propose a data-rate optimal TEQ filter bank whose data rates at the equalizer output of this filter bank are significantly better than those of the Maximum Bit Rate and Minimum ISI methods and similar to those of the least-squares per-tone equalizer method for ADSL CIRs, transmit filters, and receive filters. The contributions of this study are: (1) a new model for multicarrier demodulator output SNR that includes ISI, near-end crosstalk, white Gaussian noise, and the digital noise floor, (2) data rate optimal time domain per-tone TEQ filter bank, and (3) a new achievable upper bound on achievable bit rate.

In highly time-varying fading channel, the Discrete Fourier Transform Spreading Orthogonal Frequency Division Multiplexing (DFTS-OFDM) signal would be damaged significantly by the inter-channel interference (ICI) due to the loss of orthogonality among subcarriers which leads a fatal degradation of bit error rate (BER) performance. To solve this problem, this paper proposes a time domain equalization (TDE) technique in conjunction with a time domain channel impulse response (CIR) estimation method for the DFTS-OFDM signal without using a guard interval (GI). The features of proposed method is to employ a time domain training sequence (TS) both for the estimation of time domain CIR at every sampling time and for removing the inter-symbol interference (ISI) incurred in the multipath fading channel. The proposed method also employs the TDE with a maximum likelihood (ML) estimation method in the demodulation of received time domain signal at every symbol instead of using the conventional Minimum Mean Square Error-Frequency Domain Equalization (MMSE-FDE) method. This paper presents various simulation results to demonstrate the effectiveness of proposed demodulation method for the DFTSOFDM signal without GI as comparing with the conventional MMSE-FDE and TDE methods both of usingGI under highly mobile environments.

In code division multiple access (CDMA) systems transmitting over time-varying multipath channels, both intersymbol interference (ISI) and multiple access interference (MAI) arise. The conventional suboptimum receiver consisting of a bank of matched filters is often inefficient because interference is treated as noise. The optimum multi-user detector is too complex to be implemented at present. Four suboptimum detection techniques based on zero forcing (ZF) and minimum mean square error (MMSE) equalization with and without decision feedback (DF) are presented and compared. They combat both ISI and MAI. The computational complexity of all four equalizers is essentially the same and they are independent of the size of the data symbol alphabet. It is shown that all four equalizers considerably outperform the conventional receiver. The MMSE equalizers are superior to the corresponding ZF equalizers. Furthermore, the equalizers with DF perform better than the corresponding equalizers without DF. An algorithm termed channel sorting is introduced to reduce the impairing effect of error propagation on the equalizers with DF. >