Computationally Efficient Lattice Reduction Aided Detection for MIMO‐OFDM Systems under Correlated Fading Channels

We analyze the relationship between channel coherence bandwidth and two complexity‐reduced lattice reduction aided detection (LRAD) algorithms for multiple‐input multiple‐output (MIMO) orthogonal frequency division multiplexing (OFDM) systems in correlated fading channels. In both the adaptive LR algorithm and the fixed interval LR algorithm, we exploit the inherent feature of unimodular transformation matrix P that remains the same for the adjacent highly correlated subcarriers. Complexity simulations demonstrate that the adaptive LR algorithm could eliminate up to approximately 90 percent of the multiplications and 95 percent of the divisions of the brute‐force LR algorithm with large coherence bandwidth. The results also show that the adaptive algorithm with both optimum and globally suboptimum initial interval settings could significantly reduce the LR complexity, compared with the brute‐force LR and fixed interval LR algorithms, while maintaining the system performance.     

Combined ML and QR Detection Algorithm for MIMO‐OFDM Systems with Perfect ChanneI State Information

An effective signal detection algorithm with low complexity is presented for multiple‐input multiple‐output orthogonal frequency division multiplexing systems. The proposed technique, QR‐MLD, combines the conventional maximum likelihood detection (MLD) algorithm and the QR algorithm, resulting in much lower complexity compared to MLD. The proposed technique is compared with a similar algorithm, showing that the complexity of the proposed technique with T=1 is a 95% improvement over that of MLD, at the expense of about a 2‐dB signal‐to‐noise‐ratio (SNR) degradation for a bit error rate (BER) of 10⁻³. Additionally, with T=2, the proposed technique reduces the complexity by 73% for multiplications and 80% for additions and enhances the SNR performance about 1 dB for a BER of 10⁻³.     

Design of reduced complexity feedback precoding for MIMO‐OFDM

Beamforming technique is applied to significantly increase the performance of a MIMO system, if the channel information (CI) of the communication system is available at the transmitter. For the transmitter to obtain the entire CI, however, a considerable reverse‐link bandwidth is required. To save the bandwidth, a limited‐rate closed‐loop system, therefore, uses a predetermined codebook which is derived from the CI. The codebook consists of a finite number of precoders out of which the index of the best one is transmitted from the receiver to the transmitter using only a few bits saving substantial bandwidth. However, the amount of bits that need to be fed back can still be significantly large for MIMO‐OFDM systems when the precoding matrix index (PMI) for each subcarrier should be transmitted. Such per‐subcarrier precoding scheme has high feedback overhead and also incurs huge computational cost to determine the best PMI for each subcarrier. We, therefore, propose a per‐band precoding scheme that precodes a band (group) of subcarriers by only one precoder. More importantly, we develop, for the proposed per‐band scheme, reduced‐complexity precoding selection methods that lead to the design of efficient receivers. The effectiveness of the proposed scheme is investigated through computer simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Bandwidth‐Efficient Selective Retransmission for MIMO‐OFDM Systems

In this work, we propose an efficient selective retransmission method for multiple‐input and multiple‐output (MIMO) wireless systems under orthogonal frequency‐division multiplexing (OFDM) signaling. A typical received OFDM frame may have some symbols in error, which results in a retransmission of the entire frame. Such a retransmission is often unnecessary, and to avoid this, we propose a method to selectively retransmit symbols that correspond to poor‐quality subcarriers. We use the condition numbers of the subcarrier channel matrices of the MIMO‐OFDM system as a quality measure. The proposed scheme is embedded in the modulation layer and is independent of conventional hybrid automatic repeat request (HARQ) methods. The receiver integrates the original OFDM and the punctured retransmitted OFDM signals for more reliable detection. The targeted retransmission results in fewer negative acknowledgements from conventional HARQ algorithms, which results in increasing bandwidth and power efficiency. We investigate the efficacy of the proposed method for optimal and suboptimal receivers. The simulation results demonstrate the efficacy of the proposed method on throughput for MIMO‐OFDM systems.     

Improved Wideband Precoding with Arbitrary Subcarrier Grouping in MIMO‐OFDM Systems

Precoding in the multiple‐input multiple‐output orthogonal frequency division multiplexing system is investigated. In conventional wideband precoding (WBP), only one precoder, obtained from the decomposition of the subcarrier independent channel matrix, is used for all subcarriers. With an investigation of the relationship between the subcarrier independent channel matrix and the temporal/frequency channels, an improved WBP scheme is proposed for practical scenarios in which a part of subcarriers are allocated to a user. The improved WBP scheme is a generalized scheme of which narrow‐band precoding and conventional WBP schemes are special modes. Simulation results demonstrate that the improved WBP scheme almost achieves the optimum performance of a single precoder and outperforms the conventional WBP scheme in terms of the bit error ratio and ergodic capacity with slight complexity increase. The largest advantage of the improved WBP scheme on signal‐to‐noise ratio in simulation results is over 2.1 dB.     

Energy‐Efficiency Power Allocation for Cognitive Radio MIMO‐OFDM Systems

This paper studies energy‐efficiency (EE) power allocation for cognitive radio MIMO‐OFDM systems. Our aim is to minimize energy efficiency, measured by “Joule per bit” metric, while maintaining the minimal rate requirement of a secondary user under a total power constraint and mutual interference power constraints. However, since the formulated EE problem in this paper is non‐convex, it is difficult to solve directly in general. To make it solvable, firstly we transform the original problem into an equivalent convex optimization problem via fractional programming. Then, the equivalent convex optimization problem is solved by a sequential quadratic programming algorithm. Finally, a new iterative energy‐ efficiency power allocation algorithm is presented. Numerical results show that the proposed method can obtain better EE performance than the maximizing capacity algorithm.     

Superimposed Pilot Aided Multiuser Channel Estimation for MIMO‐OFDM Uplinks

This letter addresses the superimposed pilot aided multiuser channel estimation for the uplinks of multi‐input multi‐output orthogonal frequency‐division multiplexing systems. To mitigate the embedded‐data effects on the performance of channel estimation, a novel combining algorithm is proposed. Optimal pilot symbols are developed with respect to the least square channel estimate's mean square error. The averaged sum‐capacity lower bound is derived and simulated. Simulation results show that on a low signal‐to‐noise ratio regime, our proposed scheme achieves better performance and higher capacity than the conventional pilot aided approach.     

基于PIC的多载波系统联合检测译码算法

针对多入多出—正交频分复用（MIMO-OFDM）信号检测问题,基于并行干扰抵消技术提出了一种编码MIMO-OFDM系统联合检测与译码算法,通过在干扰抵消检测器和信道译码器之间传递判决信息提高系统的误比特率性能。计算机仿真表明,该算法获得的误码率性能较传统的迫零检测以及V-BLAST检测算法有了较大的提升。     

Improved Design Criterion for Space‐Frequency Trellis Codes over MIMO‐OFDM Systems

In this paper, we discuss the design problem and the robustness of space‐frequency trellis codes (SFTCs) for multiple input multiple output, orthogonal frequency division multiplexing (MIMO‐OFDM) systems. We find that the channel constructed by the consecutive subcarriers of an OFDM block is a correlated fading channel with the regular correlation function of the number and time delay of the multipaths. By introducing the first‐order auto‐regressive model, we decompose the correlated fading channel into two independent components: a slow fading channel and a fast fading channel. Therefore, the design problem of SFTCs is converted into the joint design in both slow fading and fast fading channels. We present an improved design criterion for SFTCs. We also show that the SFTCs designed according to our criterion are robust against the multipath time delays. Simulation results are provided to confirm our theoretic analysis.     

Zero‐forcing and codebook based beamforming scheme for practical usage of multiuser MIMO‐OFDM with uplink channel sounding

Since the concept of the multiuser multiple input multiple output (MU‐MIMO) system has been introduced for enhancement of capacity and flexibility, it has been accepted in various wireless standards. To enjoy the benefits of the MU‐MIMO system, full or partial channel information is necessary at the transmitter, but how to use the full or partial feedback information in the practical system perspective has not been investigated well. In this paper, we analyze the interference of full usage concurrent transmission codebook based on the MU‐MIMO systems and also investigate the usage of channel information for a codebook based scheme and a zero‐forcing beamforming (ZFBF) scheme. Based on the analytic results, we propose two adaptive schemes for the practical usage perspective in MU‐MIMO‐OFDM systems. Firstly, we propose an adjustable uplink channel sounding scheme, which depends on the number of users in a given cell/sector in frequency division duplexing system, with ZFBF MU‐MIMO‐OFDM systems. Secondly, we propose an adaptive switching scheme, which depends on signal‐to‐noise ratio, between the codebook based scheme and the ZFBF scheme. The performance of the proposed scheme is evaluated with computer simulations, and the simulation results show that the proposed scheme provides the enhanced throughput over entire signal‐to‐noise‐ratio regions. Copyright © 2014 John Wiley & Sons, Ltd.     

Subcarrier grouping with environmental sensing for MIMO‐OFDM systems over correlated double‐selective fading channels

Multiple‐Input, Multiple‐Output (MIMO)‐orthogonal frequency division multiplexing (OFDM) is a promising technique in 5G wireless communications. In high‐mobility scenarios, the transmission environments are time‐varying and/or the relative moving velocity between the transmitter and receiver is also time‐varying. In the literature, most of previous works mainly focused on fixed subcarrier group size and precoded the MIMO signals with unitary channel state information. In this way, the subcarrier grouping may naturally lead to big loss of channel capacity in high‐mobility scenarios because of the channel state information difference on the subcarriers in each group. To employ the MIMO‐OFDM technique, adaptive subcarrier grouping scheme may be an efficient way. In this paper, we first consider MIMO‐OFDM systems over double‐selective i.i.d. Rayleigh channels and investigate the quantitative relation between subcarrier group size and capacity loss theoretically. With developed theoretical results, we also propose an adaptive subcarrier grouping scheme to satisfy the preset capacity loss threshold by adjusting grouping size with the sensed environmental information and mobile velocity. Theoretical analysis and simulation results show that to achieve a better system capacity, a sparse scattering, lower signal‐to‐noise ratio, and lower velocity as well as properly large antenna number are matched with larger subcarrier group size. One important observation is that if the antenna number is too large and higher than a threshold, which will not bring any additional gain to the subcarrier grouping. That is, the system capacity loss will converge to a lower bound expeditiously with respect to antenna number, which is given in theory also. Copyright © 2016 John Wiley & Sons, Ltd.     

Computationally efficient variational Bayesian method for PAPR reduction in multiuser MIMO‐OFDM systems

This paper investigates the use of the inverse‐free sparse Bayesian learning (SBL) approach for peak‐to‐average power ratio (PAPR) reduction in orthogonal frequency‐division multiplexing (OFDM)‐based multiuser massive multiple‐input multiple‐output (MIMO) systems. The Bayesian inference method employs a truncated Gaussian mixture prior for the sought‐after low‐PAPR signal. To learn the prior signal, associated hyperparameters and underlying statistical parameters, we use the variational expectation‐maximization (EM) iterative algorithm. The matrix inversion involved in the expectation step (E‐step) is averted by invoking a relaxed evidence lower bound (relaxed‐ELBO). The resulting inverse‐free SBL algorithm has a much lower complexity than the standard SBL algorithm. Numerical experiments confirm the substantial improvement over existing methods in terms of PAPR reduction for different MIMO configurations.     

Iterative Soft-Kalman Filter-based Data Detection and Channel Estimation for Turbo Coded MIMO–OFDM Systems

MIMO channels are often assumed to be constant over a block or packet. This assumption of block stationarity is valid for many fixed wireless scenarios. However, for communications in a mobile environment, the stationarity assumption will result in considerable performance degradation. In this paper, we focus on a new channel estimation technique for Turbo coded MIMO systems using OFDM. In the proposed MIMO–OFDM system, pilots are placed on selected subcarriers and used by a pair of Kalman filter (KF) channel estimators at the receiver. The KF channel estimates are then utilized by a MIMO–OFDM soft data detector based on the computationally efficient QRD-M algorithm. The soft detector output is fed back to the Kalman filters to iteratively improve the channel estimates. The extrinsic information generated by the Turbo decoder is also used as a priori information for the soft data detector. The overall receiver thus combines MIMO data detection, KF-based channel estimation, and Turbo decoding in a joint iterative structure yielding computational efficiency and improved bit-error rate (BER) performance. Parts of this paper were presented at ICC’2005, Seoul, Korea. This work was supported in part by NSF Grant No. CCF-0429596. This work was done when he was with the Nokia Research Center in Dallas, USA.     

OFDM系统中低复杂度联合译码和信道估计方法研究

本文针对OFDM(Orthogonal Frequency Division Multiplexing)系统提出了一种低复杂度联合译码和信道估计算法的接收机。接收机首先通过导频对信道进行估计，然后使用Turbo码译码输出判决信息对信道参数进行稳健的估计。仿真结果表明，即使系统误码率大于10^-2，经过3次迭代估计，系统性能提高仍有0．5-1dB；在高信噪比下，可显著地降低系统的误码底限。本文同时还给出了译码迭代次数对系统性能的影响。     

Peak‐to‐average power ratio reduction of a hidden training sequence‐aided precoding scheme for MIMO‐OFDM

We analyze a peak‐to‐average power ratio (PAPR) reduction property based on a hidden training sequence‐aided precoding scheme for MIMO‐OFDM systems. In addition to the benefits of a hidden training sequence‐aided precoding scheme such as improvement in bandwidth efficiency and frequency diversity gain, we address that power amplifier efficiency can be improved without any additional complexity burden. By mathematically analyzing PAPR of the precoded MIMO‐OFDM signal with a hidden training sequence, we demonstrate that PAPR reduction can be obtained by varying the allocated power to the hidden training sequence. Because of the low PAPR property of this scheme, it is possible to utilize a low‐cost power amplifier, resulting in the reduction in the total cost for hardware implementation. Copyright © 2014 John Wiley & Sons, Ltd.     

Peak‐to‐average power ratio reduction in space–time coded MIMO‐OFDM via preprocessing

In this paper, we propose a trellis exploration algorithm based preprocessing strategy to lower the peak‐to‐average power ratio (PAPR) of precoded MIMO‐OFDM. We first illustrate the degradation in PAPR due to optimal linear precoding in MIMO‐OFDM systems. Then we propose two forms of multi‐layer precoding (MLP) schemes to reduce PAPR. In both schemes, the inner‐layer precoder is designed to optimize system capacity/BER performance. In the first MLP scheme (MLP‐I), a common outer‐layer polyphase precoding matrix is employed. In the second MLP scheme (MLP‐II), data stream corresponding to every transmit antenna is precoded with a different outer‐layer polyphase precoding matrix. Both outer‐layer precoders are custom designed using the trellis exploration algorithm by applying the aperiodic autocorrelation of OFDM data symbols as the metric to minimize. Simulation results indicate that both MLP schemes show superior PAPR performance over conventional MIMO‐OFDM with and without precoding. In addition, MLP better exploits frequency diversity resulting in BER performance gains in multi‐path environments. Copyright © 2010 John Wiley & Sons, Ltd.     

MIMO OFDM系统中同步和信道的联合估计

提出了一种MIMO OFDM系统的定时恢复、频率同步和信道估计的联合算法。为了减少算法的复杂度，算法分两步完成：首先利用接收信号的自相关函数进行粗同步和信道估计，得到时延和频偏的粗估计，然后在粗估计基础上采用最大似然准则进行精确的同步和信道估计。仿真结果表明，该算法能够达到很好的效果，系统误码率接近已知信道响应时的情况。     

MIMO OFDM系统中的Turbo子载波均衡

在MIMO OFDM系统中,为了对抗同天线干扰及由于保护间隔不足而引起的码间干扰和载波间干扰,该文给出了一种基于MMSE的Turbo子载波均衡器。在该算法中,软输入软输出(SISO)的子载波均衡器与软输入软输出(SISO)解码器通过迭代进行软信息交换。仿真结果表明,与非迭代的子载波均衡器相比,该文给出的Turbo子载波均衡器能够有效利用时间和空间分集,使系统性能得到了改善。     

多载波CDMA系统中联合检测译码方法研究

为了提高多载波CDMA(MC-CDMA)系统的抗干扰能力与系统容量,提出了一种将信道参数检测与纠错码译码联合运算进行的方法,得到了一种反馈级联结构.在分析MC-CDMA系统接收性能时,通常假设信道参数能精确估计,但对于时变信道在实现上是困难的;根据本文提出的级联结构,先用导频符号进行信道参数估计,再用导频符号的译码信息作为导频符号进行信道参数的进一步优化,构成一种联合检测译码结构,能有效地降低导频符号数量,并提高了信道参数估计精度.通过仿真,与传统的方法进行了性能比较,联合检测译码方案能获得较大系统增益,是一种优化方案.     

An Efficient Scheme to Achieve Differential Unitary Space‐Time Modulation on MIMO‐OFDM Systems

Differential unitary space‐time modulation (DUSTM) has emerged as a promising technique to obtain spatial diversity without intractable channel estimation. This paper presents a study of the application of DUSTM on multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) systems with frequency‐selective fading channels. From the view of a correlation analysis between subcarriers of OFDM, we obtain the maximum achievable diversity of DUSTM on MIMO‐OFDM systems. Moreover, an efficient implementation strategy based on subcarrier reconstruction is proposed, which transmits all the signals of one signal matrix in one OFDM transmission and performs differential processing between two adjacent OFDM blocks. The proposed method is capable of obtaining both spatial and multipath diversity while reducing the effect of time variation of channels to a minimum. The performance improvement is confirmed by simulation results.