Space-frequency linear dispersion codes for single carrier-frequency domain equalization

This paper proposes a new scheme of the rate compatible low-density parity-check (RC-LDPC) coded single carrier-frequency domain equalization (SC-FDE) system where RC-LDPC codes are combined with SC-FDE modulations. To construct a class of different RC-LDPC codes, we take advantage of a base matrix constructed by the progressive edge growth (PEG) algorithm. A special code matrix structure is used and modified to meet requirements of the different code rate. In addition, a pseudorandom sequence instead of traditional cyclic prefix (CP) is proposed to estimate the channel noise variance for LDPC decoding. The simulation results show that the modified RC-LDPC codes have better performance than that of current method and the RC-LDPC coded SC-FDE system obtains better performance compared with uncoded SC-FDE system.

This paper discusses a cyclic prefixed single carrier frequency-domain equalization (SC-FDE) scheme with two types of transmit diversity. Firstly, we propose a SC-FDE system with space-frequency block coding (SFBC). The transmit sequence of the proposed system is designed to have spatial and frequency diversities, which is equivalent to the SFBC. The corresponding combining receiver is derived under a minimum mean square error (MMSE) criterion. It is shown that the proposed system significantly outperforms the SC-FDE system with space-time block coding (STBC) over fast fading channels, while providing lower computational complexity than orthogonal frequency division multiplexing (OFDM) combined with SFBC. We verify the performance of two-branch transmit diversity systems including the proposed one through bit error rate (BER) analysis. Secondly, as a scheme that combines STBC and SFBC, a space-time-frequency block code (STFBC) SC-FDE system is presented. Computer simulation results show that the proposed STFBC SC-FDE system has better immunity to the distortion caused by both fast fading and severe frequency selective fading, compared to the SC-FDE system with the STBC or the SFBC scheme. Complexity analysis is also conducted to compare their computational loads of the transceiver. It is shown that the proposed STFBC SC-FDE system has lower computational complexity than the STFBC OFDM system.

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.

Multiuser multiple-input multiple-output (MU-MIMO) wireless systems that employ single-carrier frequency-domain equalization (SC-FDE) for uplink transmissions can provide high data rates with increased spectral efficiency under severe channel conditions. However, the availability of accurate channel estimates at the base station (BS) receiver is crucial for achieving peak performance. In this paper, we investigate the use of subspace decomposition and derive a novel algorithm for the blind estimation of MU-MIMO channels in SC-FDE systems, as specified by the 3GPP LTE. By exploiting the long data blocks available in LTE standards, our proposed blind algorithm can obtain accurate estimates of the MU-MIMO channels over every block of transmitted data. This provides for a bandwidth-efficient solution in SC-FDE systems by eliminating (reducing) the need to allocate an entire block of pilot sequences for each active transmitter. Furthermore, since the channel estimation is deployed at the BS, the computational complexity is not considered to be a significant burden for future systems in exchange for the increased spectral efficiency. The results of simulations over fading channels, using realistic system parameters representative of LTE-Advanced, demonstrate the advantages of our proposed blind subspace-based channel estimation algorithm and support the feasibility of the resulting MU-MIMO SC-FDE scheme with reduced training.

Reliable signal detection plays an essential role in enhancing the quality of signal transmission in wireless communication systems. In this paper, we combine signal detection theory with a deep learning model and propose a novel signal detection scheme based on adaptive ensemble long short term memory (AE-LSTM) neural network to handle wireless single carrier frequency domain equalization (SC-FDE) systems in an end-to-end manner. The feature information used for offline training of the deep learning model is extracted from the received signal containing channel state information (CSI) after the multi-path channel and fast Fourier transform (FFT), and the labels are assigned according to the constellation map adopted at the transmitter. To improve the adaptability of the system, we utilize the received power under different delays as the adaptive factor to integrate the output of each sub-network. Then the original data generated by the channel model is recovered by using the trained model instead of channel estimation and frequency domain equalization. Comparative experiments on SC-FDE symbol detection demonstrate that the proposed scheme achieves better performance in terms of reliability than the traditional scheme and the similar deep learning scheme.

Symbol timing synchronization is a key technology for SC-FDE (Single Carrier Frequency Domain Equalization) systems. The traditional Schmidl & Cox's and Minn's algorithms have some shortcoming on the existence of timing metric plateau and redundant peaks. To overcome these shortcomings, two symbol timing synchronization algorithms based on a novel structure of training symbol are proposed for SC-FDE systems in this paper. The proposed methods can take advantage of the correlations of the four parts of the training symbol to efficiently improve the accuracy of timing synchronization and the anti-multipath capability. The simulation results confirm that the performances of the proposed algorithms are superior to Minn's algorithm in AWGN channel and 3GPP Vehicular A channel.

The single-carrier frequency-domain equalization (SC-FDE) is now being considered as an important physical layer (PHY) option for the 60-GHz wireless personal area network (WPAN). We proposed using the complementary Golay sequences to improve the accuracy of the channel estimation in SC-FDE system. These sequences have the autocorrelation of unique main peak and zero sidelobe. We proved by simulations that it is very effective for SC-FDE system under fixed point low-density parity-check (LDPC) decoding.

Single-carrier frequency domain equalization (SC-FDE) has been shown to be an attractive transmission scheme for broadband wireless channels. However, its performance would degrade a lot if the channel is fast time-varying. In this paper, we analyzed the single-carrier fractional Fourier domain equalization (SC-FrFDE) system and applied it to the fast time-varying channel. It can solve the time-varying problem by selecting the optimal fractional Fourier transform order. To this SC-FrFDE system, its transmitter uses chirp-periodic circular prefix to eliminate ISI and this has an evident disadvantage that the receiver need to feedback the optimal fractional Fourier transform order to the transmitter through a feedback channel. To simplify the system, we propose to use zero padding (ZP) at the transmitter. There is already the overlap-add method as ZP in SC-FDE system. But the overlap-add method cannot be used in fast time-varying channels. Thus, we propose a new method as ZP. Simulation results show that our proposed method can significantly improve the system performance.

The design of space-time codes for frequency flat, spatially correlated MIMO fading channels is considered. The focus of the paper is on the class of space-time block codes known as linear dispersion (LD) codes, introduced by Hassibi and Hochwald. The LD codes are optimized with respect to the mutual information between the inputs to the space-time encoder and the output of the channel. The use of the mutual information as both a design criterion and a performance measure is justified by allowing soft decisions at the output of the space-time decoder. A spatial Fourier (virtual) representation of the channel is exploited to allow for the analysis of MIMO channels with quite general fading statistics. Conditions, known as generalized orthogonality conditions (GOC), are derived for an LD code to achieve an upper bound on the mutual information, with the understanding that LD codes that achieve the upper bound, if they exist, are optimal. Explicit code constructions and properties of the optimal power allocation schemes are also derived. In particular, it is shown that optimal LD codes correspond to beamforming to a single virtual transmit angle at low SNR, and a necessary and sufficient condition for beamforming to be optimal is provided. Finally, numerical results are provided to illustrate the optimal code design for two examples of sparse scattering environments. The performance of the optimal LD codes for these scattering environments is compared with that of LD codes designed assuming the i.i.d. Rayleigh (rich scattering) model, and it is shown that the optimal LD codes perform significantly better. The optimal LD codes are also compared to beamforming LD codes and it is shown that beamforming is nearly optimal over a range of SNR's of interest.

This letter proposes a space-frequency block-coded (SFBC) single-carrier frequency-domain equalization (SC-FDE) system. The transmit sequence of the proposed system is designed to have spatial and frequency diversities, and the corresponding combining receiver is derived under a minimum mean square error criterion. It is shown that the proposed system significantly outperforms the space-time block-coded SC-FDE system over fast-fading channels while providing lower computational complexity than orthogonal frequency division multiplexing combined with the SFBC.

In this letter, an efficient cyclic prefix reconstruction (CPR) technique with turbo equalization is developed for a multi-input multi-output (MIMO) single-carrier frequency-domain equalization (SC-FDE) system. The proposed method consists of pre-processing estimation (PPE) and residual inter-carrier interference suppression (RICIS). The PPE is employed to compute initial values of MIMO turbo equalization, and the RICIS is used to mitigate residual intercarrier interference (ICI) after each iteration of the CPR. By applying the proposed method to MIMO SC-FDE system with insufficient cyclic prefix (CP), we can significantly improve its error performance, obtaining both the benefits of multiplexing gain and spectral efficiency gain

Recent research has shown that single carrier frequency domain equalization (SC-FDE) is an attractive technology for broadband wireless communications for its advantages such as lower peak-to-average power ratio and reduced sensitivity to carrier frequency offset, when compared to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, we propose a novel structure, FDE-NP, which consists of a linear frequency domain equalizer (FDE) and a time domain noise predictor (NP). It is shown that the proposed scheme has lower complexity and achieves better performance and complexity trade-off than the conventional FDE designs. In particular, by using a simple block interleaver/deinterleaver pair to rearrange the order of the received signals prior to decoding, delayed reliable decisions can be fed back to predict and cancel their post-cursor inter-symbol interference (ISI) effects to the following signals. Simulation results show that the proposed FDE-NP scheme achieves 1.5-2 dB performance improvement over the conventional FD-LE and FD-DFE schemes. Furthermore, we extend the design of unbiased and biased time domain equalizers (TDEs) into the frequency domain and propose the unbiased FDE. It is shown that although the unbiased FDE has a larger MSE than the biased one, it reduces the required SNR by about 0.3 dB in some cases

With partial channel state information (CSI) at the transmitter, the design of space-time codes for frequency flat, spatially correlated MIMO fading channels is considered. The focus of the paper is on the class of space-time block codes known as linear dispersion (LD) codes, introduced by Hassibi and Hochwald. For perfect CSI at the transmitter, the LD codes are optimized with respect to the instantaneous mutual information between the inputs to the space-time encoder and the output of the channel. An equivalent optimization problem is proposed and can that be solved by standard convex optimization algorithms. It is then conjectured that the LD codes obtained by maximizing the instantaneous mutual information converge to that obtained from maximizing the averaged mutual information in the large antenna asymptote. Based on the insights drawn from the conjecture, a limited feedback scheme for LD codes is proposed assuming a common codebook at the transmitter and receiver. The numerical result for a scattering environment suggests that the proposed feedback scheme achieves high performance at low complexity.

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.

Linear dispersion codes (LDCs) are an attractive tool for attaining spatial diversity in OFDM systems with multiple transmit antennas. To reach the potential gains, in each situation, the selection of a proper set of codes depends, in general, on the existence of a reliable feedback channel. We propose LDCs for multiple-input multiple-output (MIMO) channels with a fixed amount of feedback. The proposed scheme selects the LDC from a set of LDCs that minimizes the error probability based on the instantaneous channel conditions. The determination of the best set of LDCs is described as a constrained optimization problem. We present several good sets of LDCs, obtained from an optimization algorithm. Through simulation results we show that the proposed schemes outperform previously reported comparable results, yet at the price of increased complexity. We also show the performance gains that can be reached in practice with LDC, by critically evaluating the feedback channel impairments, such as errors and signalling delays, and also considering the effect of signalling overhead on the achievable throughput.