Low Complexity Iterative Frequency Domain Decision Feedback Equalization

Abstract--The LS channel estimation was modified by implementing space and time code via introducing cyclic conjugate to both the information sequence and the pilot sequence in the time-domain. The bit error rate (BER) performance of orthogonal frequency division multiplexing (OFDM) and of single-carrier transmission with frequency-domain equalization (SC/FDE) with the new channel estimator in MIMO channels is compared. Computer simulations show that the BER performance of OFDM without sub-carrier adaptive modulation and encoding is similar to SC/FDE system while the MSE of the channel estimator of OFDM system is lower when the channel Doppler frequency shift is lower in MIMO channels. The performance of OFDM becomes better than SC/FDE when Doppler frequency shift is larger.

Single carrier transmission with frequency domain equalization (SC/FDE) provides a serious alternative to orthogonal frequency division multiplexing (OFDM) for broadband wireless access (BWA) systems as well as for W-LAN's. In this work we consider low complexity Turbo-like decision feedback equalization for conventional block wise SC/FDE. The proposed scheme accomplishes the efficiency of ideal decision feedback equalization. Simulation results show a remarkable performance increase for large signal constellations and highly frequency selective multipath channels.

In recent years, an Ultra Wideband (UWB) has attracted much attention in short range high speed wireless communications. Meanwhile, the single-carrier transmission with frequency domain equalization (SC-FDE) has also recently at- tracted much attention. It is reported that the SC-FDE sys- tem obtains an excellent performance as well as orthogonal frequency division multiplexing (OFDM), because the SC-FDE system has the advantage of frequency diversity gain even in strong frequency selective channels. However, in the SC-FDE system, the cyclic extension reduces the bandwidth efficiency. Thus, in the SC-FDE system, various methods to improve the bandwidth efficiency are reported. In this paper, we evaluate the improvement of bandwidth efficiency based on cyclic prefix (CP) reconstruction as a method of improving bandwidth efficiency of Ultra Wideband-Impulse Radio (UWB-IR) and Direct Sequence- Ultra Wideband (DS-UWB).

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.

In recent years, an Ultra Wideband (UWB) system has attracted much attention in short range high speed wireless communications. Meanwhile, the single-carrier transmission with frequency domain equalization (SC-FDE) is also attracting much attention. It is reported that the SC-FDE system obtains an excellent performance as well as orthogonal frequency division multiplexing (OFDM), because the SC-FDE system has the advantage of frequency diversity gain even in strong frequency selective channels. However, in the SC-FDE system, cyclic extension reduces the bandwidth efficiency. To improve the bandwidth efficiency, we proposed UWB-IR and DS-UWB with Frequency-Domain Equalization (FDE) and Cyclic Prefix (CP) reconstruction, and showed that when the channel estimation is ideal, the proposed system achieves the good performance. Both FDE and CP reconstruction use channel gains and thus the performance is expected to depend largely on the channel estimation accuracy. In this paper, we evaluate the effect of imperfect channel estimation on the performance of UWB-IR with MMSE-FDE and CP Reconstruction. We show that CP reconstruction is effective for UWB-IR with MMSE-FDE in the IEEE UWB multipath channels, CM3, CM4.

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 this paper, we derive the achievable rate of single-carrier frequency domain equalizer (SC-FDE) and orthogonal frequency division multiplexing (OFDM) systems, constrained on low resolution analog to digital converters (ADCs). We assume that there is a full knowledge of channels at both transmitter and receiver sides. We model low resolution ADCs with an additive uniform quantization noise. We consider an ultra-wide band millimeter wave (mm-Wave) system with a frequency selective channel. The channel is based on practical results at mm-Wave frequencies. Our numerical results show that SC-FDE systems with minimum mean square error (MMSE) equalizers outperform OFDM and SC-FDE systems with zero forcing (ZF) equalizers at high signal to noise ratio (SNR) regimes. Moreover, benefits of increasing the ADCs resolution are not significant due to exponentially increment in the power consumption of ADCs.

An orthogonal frequency division multiplexing (OFDM) transmission system is known to exhibit superior performance compared to a single carrier system in a multipath environment. However, the communication quality degrades severely because of delayed waves exceeding the guard interval and the Doppler shift. To solve this problem, various systems have been proposed that use an adaptive array to suppress undesired signals. In this paper, we propose a system that uses the same signal in the guard interval inserted at the head and the guard interval at the tail of the OFDM effective symbol in an OFDM transmission system and operates a minimum mean square error (MMSE) adaptive array. To clearly show the effectiveness of the proposed system, we analyzed the basic performance by a computer simulation. These results demonstrated excellent operation as an MMSE adaptive array and superior undesired signal suppression. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(10): 1–9, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10121

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique. It supports high data rates over wireless radio channels. Due to high peak-to-average power ratio, OFDM is sensitive to the non-linear effects of the power amplifier. So, many methods of PAPR reduction techniques have been proposed. Of these, the distortionless method of PAPR reduction is Partial Transmit Sequence (PTS) technique. But this method suffers from high computational complexity. Modified PTS technique has been proposed to address the issue of high computational complexity. Modified PTS technique adopts a neighbourhood search algorithm to find the optimum set of phase factors. In this paper, the performance the OFDM system by using modified PTS technique combined with interleaving and pulse shaping is evaluated by employing Least Square (LS) and Minimum Mean Square Error (MMSE) channel estimation methods. Mean Square Error (MSE) and Bit error rate (BER) are the performance measures that are employed to analyse the performance of the OFDM system. The simulation result shows that the performance of OFDM system improves with PAPR reduction.

The performance of linear filters degrade drastically when applied to mitigate intersymbol interference caused by channels with frequent nulls in their spectral characteristics like, e.g., time-dispersive radio channels. In such cases, the well-known decision feedback equalizer (DFE) is one possible nonlinear approach to improve the quality of the receiver. However, adapting the DFE filter coefficients to equalize time-varying channels is computationally intense, especially if the dimension of the observation vector is very high. In this paper, we apply the conjugate gradient (CG) algorithm to a conventional minimum mean square error (MMSE) DFE in order to reduce its computational complexity. Moreover, we compare its performance to the one of MMSE DFE versions which are based on the computationally efficient least-mean-square (LMS) or recursive least-squares (RLS) algorithm, respectively. The analysis additionally includes a detailed investigation of computational complexity with respect to the required number of floating point operations (FLOPs). Simulation results when applied to a digital communications system show the ability of the CG based MMSE DFE to outperform either the LMS and the RLS based MMSE DFE although its computational complexity is even smaller in most of the cases.

Faster-than-Nyquist (FTN) signaling was originally proposed by Mazo, which provides the opportunity of increasing data transmission rate effectively. However, this induces unavoidable ISI effects at the receiver and leads to higher receiver complexity. So far, a number of time domain equalization receiver algorithms have been proposed, which have higher demodulation complexity in FTN system with infinite ISI. Against this background, people put forward low complexity iterative frequency domain decision feedback equalization and simulate to show that frequency domain equalization can reduce computational complexity of FTN. In order to promote the practical application of FTN, this paper expands low complexity IBDFE to frequency-selective fading channels. At the same time, simulation results verify its feasibility.

Single-Carrier Frequency Division Multiple Access (SC-FDMA) has been selected as the uplink transmission scheme in the 3GPP Long Term Evolution standard. SC-FDMA has reduced sensitivity to phase noise and a lower Peak-to-Average Power Ratio (PAPR) compared to Orthogonal Frequency Division Multiple Access. In this paper we propose joint Tomlinson-Harashima Precoding and transmit power allocation for SC-FDMA. We derive the optimum power allocation for SC-FDMA transmission for both Zero-Forcing (ZF) and Minimum Mean-Square Error (MMSE) LE receivers in order to maximize the achievable data rate subject to constant transmit power. Although this improves the system's performance and offers a 1-2 dB improvement over Frequency-Domain Decision Feedback Equalization (FD-DFE), when the proposed transmit power allocation scheme is combined with decision feedback equalization the system incurs a performance degradation due to error propagation. In this paper we propose a joint implementation of the derived power allocation scheme with THP. Here we show that the system's performance is further improved over both FD-LE and FD-DFE when transmit power allocation is applied.

In this paper, we investigate and compare the performance of single- and multi-carrier modulation schemes for indoor visible light communication (VLC). Particularly, the performances of single carrier frequency domain equalization (SCFDE), orthogonal frequency division multiplexing (OFDM) and on-off keying (OOK) with minimum mean square error equalization (MMSE) are analyzed in order to mitigate the effect of multipath distortion of the indoor optical channel where nonlinearity distortion of light emitting diode (LED) transfer function is taken into account. Our results indicate that SCFDE system, in contrast to OFDM system, does not suffer from high peak to average power ratio (PAPR) and can outperform OFDM and OOK systems. We further investigate the impact of LED bias point on the performance of OFDM systems and show that biasing LED with the optimum value can significantly enhance the performance of the system. Bit-interleaved coded modulation (BICM) is also considered for OFDM and SCFDE systems to further compensate signal degradation due to inter-symbol interference (ISI) and LED nonlinearity.

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).