Single-carrier Multiple-input Multiple-output Research Articles

Beyond 300-Gbps/λ photonics-aided THz-over-fiber transmission employing MIMO single-carrier frequency-domain equalizer.

We experimentally realized a 320-GHz 320-Gbps/λ terahertz (THz) radio-over-fiber (RoF) system based on a photonics-aided scheme with the help of polarization-division multiplexing (PDM) technology and multiple-input, multiple-output (MIMO) transmission. In this system, the low-complexity MIMO single-carrier frequency-domain equalizer (SCFDE) is implemented to compensate for the polarization-related impairments of the PDM signal, and the demultiplexing performances between SCFDE and the commonly used constant modulus algorithm (CMA) are also compared in this proposed system. After 20-km standard single-mode fiber (SSMF) and 3-m 2 × 2 MIMO wireless link transmission, the bit error rate (BER) of the received 46-GBaud PDM 16-ary quadrature amplitude modulation (16QAM) signal satisfies the soft-decision forward error correction (SD-FEC) threshold with 15% overhead, which corresponds to a record-breaking net bit rate of 320 Gbit/s.

Carrier frequency offset estimation for MIMO single-carrier FDMA system in wireless communication

Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency-Division Multiplexing (OFDM) systems and Single-Carrier Frequency-Division Multiple Access (SC-FDMA) are so susceptible to carrier frequency offset (CFO) between transceivers. In this paper, a novel sequence called CAZBAR is proposed. The proposed CAZBAR sequence is based on constant amplitude zero autocorrelation (CAZAC) sequence and barker code. CAZBAR sequence shows better autocorrelation with higher peak at zero shift without ripples, which facilitates estimating carrier frequency offset in communication systems compared to other compensation methods in terms of mean square error (MSE). By applying CAZBAR sequence in MIMO SC-FDMA system 2 × 2 and 4×4, the bit error rate (BER) performance has improved significantly. At a BER=10-2, a SNR reduction of 11 dB is achieved for 2 × 2 system and 7 dB reduction for 4 × 4 system compared to other sequences. Which improves the performance of the whole system MIMO SC-FDMA. The CAZBAR sequence can be applied in 5G techniques, MIMO-OFDM, and MIMO SC-FDMA systems.

Frequency-Domain Turbo Equalization With Iterative Channel Estimation for MIMO Underwater Acoustic Communications

This paper proposes a new iterative receiver for single-carrier multiple-input–multiple-output (SC-MIMO) underwater acoustic (UWA) communications, which utilizes frequency-domain turbo equalization (FDTE) and iterative channel estimation. Soft-decision symbols are not only fed back to the equalizer to cancel the intersymbol interference (ISI) and cochannel interference (CCI), but also used as training signals in the channel estimator to update the estimated channel state information (CSI) after each turbo iteration. This iterative channel estimation scheme helps to combat the problem commonly suffered by block-processing receivers in fast time-varying channels. Compared with time-domain turbo equalization, FDTE achieves comparable performance with significantly reduced computational complexity. Using soft-decision symbols to reestimate the time-varying channels, iterative channel estimation further improves the accuracy of the estimated CSI. The proposed iterative receiver has been verified through undersea experimental data collected in the Surface Processes and Acoustic Communications Experiment 2008 (SPACE08).

LU-Based Beamforming Schemes for MIMO Systems

We present a time-domain broadband beamforming based on a unimodular-upper polynomial matrix decomposition. The unimodular factor is the product of elementary $J$ - orthogonal matrices and a lower-triangular matrix with 1's on the diagonal, as in the constant matrix lower upper (LU) decomposition. This leads to a $J$ - orthogonal LU polynomial matrix decomposition, as a combination of two classical matrix factorization methods: Smith canonical form and LU Gaussian elimination. The inversion of the unimodular factor, for use as a pre/postfilter in the beamforming scheme, is immediate and can be achieved with O(1) complexity. The resulting reduced multiple-input multiple-output (MIMO) channel is exactly diagonal, leading to separate single-input single-output (SISO) channels with no cochannel inteference. There is no need to model the MIMO channel as a Laurent polynomial as usual, thus introducing unnecessary delays just for technical reasons. In addition, it turns out that each of the resulting SISO channels, except to the last channel, reduces to a simple additive noise channel, with no intersymbol interference (ISI), except for unprobable original MIMO channels. However, these very interesting features are to be balanced with the possible noise enhancement in the postfiltering step. The performance in terms of bit error rate (BER) is studied and compared with the QR-based frequency-domain and time-domain broadband beamforming. In particular, the proposed beamforming scheme can be used both in orthogonal frequency-division multiplexing (OFDM) and in single-carrier MIMO systems, without a cyclic prefix (CP). Meanwhile, the QR-based scheme requires a CP extension.

Asymptotically Optimal Low-Complexity SC-FDE With Noise Prediction in Data-Like Improper-Complex Interference

In this paper, single-carrier (SC) block transmission of improper-complex data symbols is considered over a multiple-input multiple-output (MIMO) frequency-selective channel with data-like cochannel interference (CCI). To exploit the cyclostationarity and impropriety of the desired and the interfering signals, an equalizer is designed that oversamples the received signal and then processes the sampled block by using widely-linear (WL) feedforward (FF) and noise-predicting feedback (NP-FB) filters. For the given equalizer structure, the minimum mean-squared error (MMSE)-optimal WL FF and NP-FB filters have high computational complexity due to the augmented correlation matrix of the data-like CCI in the received signal. Motivated by the asymptotic property of the correlation matrix, we approximate in the frequency domain the matrix by a block matrix with diagonal blocks. This leads to the low-complexity WL design of a frequency-domain FF filter and a causally noise-predicting FB filter. It is shown that this MIMO SC frequency-domain equalizer with noise prediction is asymptotically optimal in the sense that the average mean-squared error converges to that of the MMSE-optimal equalizer as the block length tends to infinity. Numerical results show that the proposed equalizer performs well even with a moderate block length.

On the optimality of training signals for MMSE channel estimation in MIMO-OFDM systems

In this paper, we investigate the optimality of training signals for linear minimum mean square error (LMMSE) channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) with frequency-selective fading channels. This is a very challenging problem due to its mathematical intractability and has not been analytically solved in the literature. Using the Lagrange multiplier method, we derive the optimality conditions for training signal design. Important findings revealed on optimal training signals are twofold: (i) the energies of the training signals on each subcarrier are equal, and (ii) on each subcarrier, the training signals transmitted from the different antennas are orthogonal and of equal energy. We verify that our results are in line with the design principles that have been derived in single-carrier MIMO systems. Two types of optimal training signal examples that satisfy the optimality conditions are presented for practical implementations in MIMO-OFDM systems. Simulation results show that the training signals based on the optimality conditions outperform other non-optimal training signals in terms of channel estimation performance.

Iterative Overlap QRM-ML Block Detection for Single-Carrier MIMO Transmission Without CP Insertion

QR decomposition and M-algorithm based near maximum likelihood block detection (QRM-MLBD) significantly improves the single-carrier (SC) multiple-input multiple-output (SC-MIMO) transmission performance in a frequency-selective fading channel. In the conventional QRM-MLBD, the cyclic prefix (CP) is inserted in order to avoid the inter-block interference (IBI). However, CP insertion reduces the transmission efficiency. In this paper, an iterative overlap QRM-MLBD is proposed for SC-MIMO transmission with no CP insertion. It is confirmed by computer simulation that the iterative overlap QRM-MLBD with no CP insertion provides improved throughput performance while reducing the computational complexity over the conventional QRM-MLBD with CP insertion.

A General Framework for Optimum Iterative Blockwise Equalization of Single Carrier MIMO Systems and Asymptotic Performance Analysis

The paper proposes a general framework for both time-domain (TD) and frequency-domain (FD) iterative blockwise equalization in single carrier (SC) wideband multiple-input multiple-output (MIMO) channels. First, a novel turbo blockwise operating equalizer structure is proposed by jointly optimizing the feed-forward and feedback filters at each iteration based on the minimum mean squared error (MMSE) criterion. Optimization of the filter coefficients, utilized for feed-forward equalization and decision feedback, is performed in both time and frequency domains, and the equivalence between them is established by unifying the iterative block equalization with the feed-forward and feedback filters in various domains. The corresponding filters are obtained analytically in a closed form as a solution of the constrained Wiener-Hopf equation with the use of average reliability information. Second, asymptotic performance and diversity analysis of the proposed single carrier frequency domain equalizer (SC-FDE) is carried out that leads to insights on the structures of the filters in the high SNR regime. Furthermore, we elaborate on the rate and diversity tradeoff of the space-time coded SC-FDE based on the proposed equalizer structure and the space-frequency coded OFDM systems. Performance comparison between the proposed SC-FDE scheme and OFDM is made. The proposed SC-FDE scheme performs very close to the genie-aided performance bounds and better than OFDM based transmission.

Frequency-Domain Turbo Equalization with Soft Successive Interference Cancellation for Single Carrier MIMO Underwater Acoustic Communications

This paper proposes a low-complexity frequency-domain turbo equalizer (FDTE) combined with phase rotation compensation and soft successive interference cancellation (SSIC) for single carrier multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. Different from existing time-domain turbo equalizers in MIMO UWA systems, the proposed receiver implements low-complexity turbo equalization in the frequency domain to combat severe inter-symbol interference (ISI) and employs a layered structure to cope with unbalanced MIMO channels. Soft, rather than hard, successive interference cancellation (SIC) is employed in the layered iterative turbo detection to alleviate co-channel interference (CCI), and phase compensation is utilized within the layered FDTE to mitigate phase rotation. The proposed scheme was evaluated by the SPACE08 experiment conducted in a shallow area of the Atlantic Ocean in October 2008. The 2-transducer 12-hydrophone MIMO system communicated with quaternary phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulation schemes over 200 m and 1000 m ranges, where the proposed FDTE-SSIC scheme achieved low bit error rates (BERs) with only a few iterations. Simulation results also demonstrated that the proposed FDTE-SSIC receiver provided lower BER than one-layer FDTE receivers with comparable complexity.

Cyclic-delay time-reversal space-time block codes for single-carrier transmission with frequency-domain decision-feedback equalization

Transmit diversity is an important multiple-input multiple-output (MIMO) approach to improve the transmission reliability; however, it is usually designed with maximum-likelihood detection. In this paper, we investigate a simple transceiver structure for single-carrier MIMO systems, in which the cyclic-delay time-reversal space-time block code (CDTR-STBC) is employed at the transmitter, and the frequency-domain decision-feedback equalization (FD-DFE) is used at the receiver. We separate the transmit antennas into two groups, and then, encode the groups by STBC and cyclically delay the data streams within each group. Such processing can mitigate the impact of error-propagation and reduce the signal-to-noise ratio (SNR) loss when FD-DFE is employed, in which SNR is defined as the ratio of the received signal power over the noise power at each receive antenna. To support our proposal, this paper also provides the performance analysis of FD-DFE. It is shown that the proposed scheme can achieve full diversity and full transmission rate for a MIMO system employing arbitrary antennas. Therefore, it has considerable performance improvement over the existing schemes.

Joint estimation and suppression of phase noise and carrier frequency offset in multiple-input multiple-output single carrier frequency division multiple access with single-carrier space frequency block coding

Carrier frequency offset (CFO) and phase noise are challenging problems in single carrier frequency division multiple access (SC-FDMA) system. In this study, the authors have studied single-carrier space frequency block coding (SC-SFBC) to reduce the peak to average power ratio (PAPR) of the multiple-input multiple-output (MIMO) SC-FDMA signal, in which Alamouti SFBC will change the signal spectrum structure, break the single-carrier property and increase PAPR. Also, the authors propose a joint algorithm to suppress the inter-carrier interference (ICI) caused by phase noise and CFO. Conventional methods are to estimate phase noise and CFO in other algorithms, which are pretty difficult and complicated to obtain accurate estimation results. Unlike the conventional works, the novelty of the authors proposed algorithm is that it directly calculates the interference components and then reconstructs the ICI matrix. Thus, it avoids the degrading interactions between phase noise and CFO estimations. The proposed algorithm exploits block-type pilot, which is a common pilot pattern in SC-FDMA communications and is used in other wireless communication standards. Simulation results show that the suppression performance keeps smooth while phase noise and CFO varies, and BER performance degradation can be significantly reduced in 3 dB.

Channel Equalization for Single Carrier MIMO Underwater Acoustic Communications

Multiple-input multiple-output (MIMO) underwater acoustic (UWA) channels introduce both space-time interference (STI) and time-varying phase distortion for transmitted signals. In such cases, the equalized symbols produced by conventional equalizer aiming for STI cancelation suffer phase rotation and thus cannot be reliably detected. In this paper, we propose a new equalization scheme for high data rate single carrier MIMO UWA channels. Different from existing methods employing joint equalization and symbolwise phase tracking technology, the proposed scheme decouples the interference cancelation (IC) operation and the phase compensation operation, leading to a generalized equalizer structure combining an IC equalizer with a phase compensator. The decoupling of the two functionalities leads to robust signal detection, which is most desirable in practical UWA applications. MIMO linear equalizer (LE) is adopted to remove space-time interference, and a groupwise phase estimation and correction method is used to compensate the phase rotation. In addition, the layered space-time processing technology is adopted to enhance the equalization performance. The proposed equalization scheme is tested to be very robust with extensive experimental data collected at Kauai, Hawaii, in September 2005, and Saint Margaret's Bay, Nova Scotia, Canada, in May 2006.

A pilot-assisted non-Cyclic Prefixed MIMO-SCFDE system

A non-Cyclic Prefixed Multiple-Input Multiple-Output Single-Carrier Frequency-Domain Equalization (non-CP MIMO-SCFDE) system based on a recursive algorithm of Joint Channel Estimation and Data Detection (recursive-JCEDD) is proposed in this paper. Unlike the traditional CP MIMO-SCFDE system, the transmitted block of the proposed system is designed in the way that block-type pilot sequences and Single-Carrier (SC) information sequences have been arranged alternately without any cyclic prefix before each SC information sequence. Moreover, a recursive-JCEDD algorithm based on interference cancellation is proposed for the corresponding receivers. Simulation results show that the Bit Error Rate (BER) of the proposed system based on the recursive-JCEDD algorithm is lower than traditional CP MIMO-SCFDE or MIMO-OFDM with channel estimation for more than 0.5 dB.

Polynomial-Based Noise Variance Estimation for MIMO-SCBT Systems

In this paper, we present a polynomial-based noise variance estimator for multiple-input multiple-output single-carrier block transmission (MIMO-SCBT) systems. It is shown that the optimal pilots for noise variance estimation satisfy the same condition as that for channel estimation. Theoretical analysis indicates that the proposed estimator is statistically more efficient than the conventional sum of squared residuals (SSR) based estimator. Furthermore, we obtain an efficient implementation of the estimator by exploiting its special structure. Numerical results confirm our theoretical analysis.

Antenna Subset Selection for Cyclic Prefix Assisted MIMO Wireless Communications over Frequency Selective Channels

Antenna (subset) selection techniques are feasible to reduce the hardware complexity of multiple-input multiple-output (MIMO) systems, while keeping the benefits of higher-order MIMO systems. Many studies of antenna selection schemes are based on frequency-flat channel models, which are inconsistent to broadband MIMO systems employing spatial-multiplexing. In broadband MIMO systems aiming to provide high-data-rate links, the employed signal bandwidth is typically larger than the coherence bandwidth of the channel so that the channel will be of frequency selective nature. Within this contribution we provide an overview on joint transmitter-and receiver-side antenna subset selection methods for frequency selective channels and deploy them in MIMO orthogonal frequency division multiplexing (OFDM) systems and MIMO single-carrier (SC) systems employing frequency domain equalization (FDE).

Iterative FDIC Using 2D-MMSE FDE for Turbo-Coded HARQ in SC-MIMO Multiplexing

SUMMARY Multiple-input multiple-output (MIMO) multiplexing is an attractive technique to achieve very high-speed transmission with a limited bandwidth. Recently, we proposed an iterative frequency-domain interference cancellation (FDIC) for single-carrier MIMO (SC-MIMO) multiplexing. In our previous work, assuming that the interference from the other antennas can be perfectly cancelled in FDIC, one-dimensional minimum mean square error (1D-MMSE) frequency-domain equalization (FDE) was used. However, the residual interference remains after performing FDIC. In this paper, to improve the transmission performance with iterative FDIC, we replace 1D-MMSE FDE by 2D-MMSE FDE, which takes the residual interference from the other antennas after FDIC into account. We investigate, by computer simulation, the throughput performance of rate compatible punctured turbo coded hybrid ARQ (RCPT-HARQ) with MIMO multiplexing in a frequency-selective Rayleigh fading channel.

An MMSE-Nulling Partial-PIC Receiver for Multiuser Downlink MIMO MC-CDMA Systems

SUMMARY A minimum mean square error (MMSE) nulling partialparallel interference cancellation (PPIC) receiver for downlink multiple-input multiple-output (MIMO) multicarrier (MC)-CDMA systems is pro-posed. Our analysis shows that, for multiuser MIMO MC-CDMA systems,interference due to frequency selectivity in multipath fading channel causesdetrimental effects on cancelling, thus V-BLASTreceiver shows severe per-formance degradation. The proposed receiver with multistage processing does not produce an error floor in frequency selective fading channel en-vironments and achieves substantial performance gains. The system per-formance of the proposed receiver was evaluated through computer sim-ulations. The simulation results show that, with two stage PPIC process-ing, the proposed receiver achieves performance gains of 2.5–4dB at targetBER of 10 −3 over the linear MMSE receiver. key words: MIMO, MC-CDMA, V-BLAST, PIC 1. Introduction The development of wireless communication systems forhigh data rate transmission and high system flexibility isone of the main targets in next generation wireless com-munications research. MIMO MC-CDMA systems haveattracted significant research interest due to its high spec-tral efficiency, large system capacity and high flexibility fordata rate, and it has been proposed as one of the promissingcandidates for 4th generation wireless communication sys-tems [1]. MIMO MC-CDMA systems are combinations ofMIMO transmission, orthogonal frequency division multi-plexing (OFDM) signaling and CDMA schemes. MC mod-ulation, realized via OFDM, is well suited to high data rateapplications such as multimedia packet transmission andmobile internet in frequency selective fading channels.MIMO systems can achieve very high spectral effi-ciency without additional power or bandwidth in a rich mul-tipath environment by exploiting the extra space dimension.Vertical Bell Labs lAyered Space Time (V-BLAST) is a pop-ular single-carrier single-user MIMO detection algorithm,which is based on the ordered successive interference can-cellation (OSIC) [2]. The principle behind OSIC is that atthe beginning of each stage, the substream with the high-

A Channel Estimation Algorithm for MIMO-SCFDE

This letter proposes a novel method for channel estimation in a single-carrier multiple input-multiple output (MIMO) system with frequency-domain equalization/detection. To this end, we construct novel short MIMO training sequences that have constant envelope in the time domain to preclude the peak-to-average power ratio problem encountered in many systems that utilize the frequency domain for data recovery. Simultaneously, the spectrum in the frequency domain is flat except for a grid of nulls for predefined frequency tones. Armed with these sequences, we provide an algorithm that is optimal in the least squares (LS) sense at a potentially low computational cost. Results show that the algorithm performs identically to other proposed LS techniques. Furthermore, the algorithm is extremely bandwidth efficient in that the total training overhead required to obtain full CSI is just one block.

Layered Space-Frequency Equalization in a Single-Carrier MIMO System for Frequency-Selective Channels

Frequency-domain equalization (FDE) has been shown to be an effective approach to combat frequency-selective wireless channels. In this letter, we propose a layered space-frequency equalization (LSFE) architecture for a single-carrier (SC) multiple-input multiple-output (MIMO) system, where MIMO FDE is employed at each stage or (layer) of detection. At a particular stage, a group of the best data streams in the minimum mean square error sense are detected and are canceled from the received signals. Simulation results show that our proposed LSFE structures can outperform layered space-time equalization (LSTE) structures and uncoded orthogonal frequency division multiplex (OFDM), especially at a higher delay spread. Performance is enhanced further, by incorporating the FDE with time-domain decision feedback at each stage of LSFE. We also provide performance analysis for LSFE, in comparison with OFDM.

Per-tone equalization for mimo ofdm systems

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with channel order larger than the cyclic prefix (CP) length. Writing the demodulating fast Fourier transform (FFT) as a sliding FFT followed by a downsampling operation, we show in this paper that by swapping the filtering operations of the MIMO channel and the sliding FFT, the data model for the temporally smoothened received signal of each individual tone of the MIMO OFDM system is very similar to the data model for the temporally smoothened received signal of a MIMO single-carrier (SC) system. As a result, to recover the data symbol vectors, the conventional equalization approach for MIMO SC systems can be applied to each individual tone of the MIMO OFDM system. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative to the recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. In the second part of this paper, we focus on direct per-tone equalizer design and adapt an existing semi-blind equalizer design method for space-time block coding (STBC) SC systems to the corresponding semi-blind per-tone equalizer design method for STBC OFDM systems.