Error performance of Uncoded Space Time Labelling Diversity in spatially correlated Nakagami‐q channels

Greater spectral efficiency has recently been achieved for Uncoded Space Time Labelling Diversity (USTLD) systems by increasing the number of antennas in the transmit antenna array. However, due to constrained physical space in hardware, the use of more antennas can lead to degradation in error performance due to correlation. Thus, this paper studies the effects of spatial correlation on the error performance of USTLD systems. The union bound approach, along with the Kronecker correlation model, is used to derive an analytical expression for the average bit error probability (ABEP) in the presence of Nakagami‐q fading. This expression is validated by the results of Monte Carlo simulations, which shows a tight fit in the high signal‐to‐noise ratio (SNR) region. The degradation in error performance due to transmit and receive antenna correlation is investigated independently. Results indicate that transmit antenna correlation in the USTLD systems investigated (3 × 3 8PSK, 2 × 4 16PSK, 2 × 4 16QAM, and 2 × 4 64QAM) causes a greater degradation in error performance than receive antenna correlation. It is also shown that 2 × 4 USTLD systems are more susceptible to correlation than comparable space‐time block coded systems for 8PSK, 16PSK, 16QAM, and 64QAM.     

Performance Analysis of Maximum-Likelihood Multiuser Detection in Space–Time-Coded CDMA With Imperfect Channel Estimation

In this paper, the performance of maximum-likelihood multiuser detection in space-time-coded code-division multiple-access (CDMA) systems with imperfect channel estimation is analyzed. A K-user synchronous CDMA system that employs orthogonal space-time block codes with M transmit antennas and N receive antennas is considered. A least-squares estimate of the channel matrix is obtained by sending a sequence of pilot bits from each user. The channel matrix is perturbed by an error matrix that depends on the thermal noise and the correlation between the signature waveforms of different users. Because of the linearity of the channel estimation technique, the characteristic function of the decision variable is used to obtain an exact expression for the pairwise error probability, and by using it, an upper bound on the bit error rate (BER) is obtained. The analytical BER bounds are compared with the BER obtained through simulations. The BER bounds are shown to be increasingly tight for large SNR values. It is shown that the degradation in BER performance due to imperfect channel estimation can be compensated by using a larger number of transmit/receive antennas     

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.     

Adaptive transmit antenna selection with pragmatic space-time trellis codes

We consider the problem of selecting a subset of transmit antennas in MIMO systems to minimize error probability when only partial channel information is available at the transmitter. An upper bound for error probability of space-time coded transmit antenna selection scheme conditioned on the channel state information is presented. Based on the performance analysis, a criterion of selecting a subset of available transmit antennas to minimize the upper bound on the PEP is proposed. In contrast to other transmit antenna selection schemes for uncoded transmission or with a fixed number of antennas within the selection subset in the literature, the proposed scheme can adaptively select both a variable number of transmit antennas and their corresponding space-time codes for transmission. Furthermore, we present pragmatic space-time trellis coding schemes for slow Rayleigh fading channels. The principal advantage of the schemes is that a single encoder and decoder can be used for systems with a variable number of transmit antennas. The performance of the pragmatic space-time codes with adaptive antenna selection and the effect of the imperfect channel estimation on performance are evaluated by simulations. It is shown that the adaptive selection offers considerable antenna selection gain relative to the antenna selection system with a fixed number of antennas within the selection subset     

可见光多天线空分键控技术研究

空分键控是一种新型的空间复用技术,每个时刻只有一个发送天线工作,携带信息的是天线的位置而非发送符号本身,因此该种方法频带利用率较低。为了提高频带利用率,基于广义空间调制的概念,提出了光多天线空分键控调制方法,这种调制方式中每个时刻有多个天线同时工作。首先建立了可见光通信中的多天线空分键控系统模型,并对其误码率性能进行了分析,然后由此为依据提出了一种基于最小距离最大化准则的天线选择算法以获得误码率性能的增益,最后通过蒙特卡罗仿真验证了该天线选择方法的有效性。      

Transmit antenna selection of correlated MIMO multiuser cognitive radio networks in Nakagami‐m fading channels

In this paper, we examine the impact of antenna correlation on transmit antenna selection with receive maximal ratio combining (TAS/MRC) in multiple‐input multiple‐output multiuser underlay cognitive radio network (MIMO‐MCN) over a Nakagami‐m fading environment. The secondary network under consideration consists of a single source and M destinations equipped with multiple correlated antennas at each node. The primary network composed of L primary users, each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing paradigm, the transmission power of the proposed secondary system is limited by the peak interference limit on the primary network and the maximum transmission power at the secondary network. In particular, we derive exact closed‐form expressions for the outage probability and average symbol error rate of the proposed secondary system. To gain further insights, simple asymptotic closed‐form expressions for the outage probability and symbol error rate are provided to obtain the achievable diversity order and coding gain of the system. In addition, the impact of antenna correlation on the secondary user ergodic capacity has been investigated by deriving closed‐form expressions for the secondary user capacity. The derived analytical formulas herein are supported by numerical and simulation results to clarify the main contributions. Copyright © 2016 John Wiley & Sons, Ltd.     

衰落信道的空间相关性对空时编码性能的影响分析

研究空时编码的一个重要的基本假设就是各衰落信道互相独立,这一点在实际应用环境中不尽满足.本文首先详细推导了多发射天线、多接收天线间的瑞利衰落信道存在空间相关性的条件下,空时编码的成对错误概率的精确表达式,并基于此分析了其误码率性能,最后给出的空间相关条件下的空时分组编码的误码率性能仿真,验证了理论分析的有效性,同时可以得到已知信道状态信息的空时编码的相关检测方案对空间相关具有较强的鲁棒性的结论.     

Enhanced redesigned spatial modulation: Design and performance evaluation under correlated fading channels

Spatial modulation techniques (SMTs) have emerged as promising multiple‐input and multiple‐output (MIMO) technology for fifth generation (5G) networks, which can achieve an appealing trade‐off between conflicting design objectives such as reliability, hardware cost, complexity, spectral efficiency, and energy efficiency. Most of the SMTs suffer from significant performance deterioration under correlated fading channels. In this paper, a novel spectral efficient SMT referred as enhanced redesigned spatial modulation (EReSM) is proposed, which is robust against adverse channel correlation effects. At any time instant, EReSM activates either one or two transmit antennas and employs a robust bits to antenna index mapping that ensures the selection of antenna subsets with maximum spatial separation to mitigate the effect of spatial correlation. EReSM also exploits phase rotation of transmitted symbols as an additional dimension to convey an extra information bit. The rotation angles used for bit mapping are optimized for various modulation schemes to maximize the minimum euclidean distance between the symbols. To analyze the performance, analytical upper bound expression for average bit error probability (ABEP) is derived for both uncorrelated and spatially correlated channel conditions. Monte Carlo simulation results substantiate the accuracy of the analytical results and also demonstrate that the proposed EReSM outperform conventional redesigned spatial modulation (ReSM) by at least 4 dB.     

Efficient detection in uniform linear and planar arrays MIMO systems under spatial correlated channels

In this paper, the efficiency of various multiple‐input multiple‐output (MIMO) detectors was analyzed from the perspective of highly correlated channels, where MIMO systems have a lack of performance, besides in some cases, an increasing complexity. Considering this hard but a useful scenario, various MIMO detection schemes were accurately evaluated concerning complexity and bit error rate performance. Specifically, successive interference cancellation, lattice reduction, and the combination of them were associated with conventional linear MIMO detection techniques. To demonstrate effectiveness, a wide range of the number of antennas and modulation formats have been considered aiming to verify the potential of such MIMO detection techniques according to their performance‐complexity trade‐off. We have also studied the correlation effect when both transmit and receiver sides are equipped with uniform linear array and uniform planar array antenna configurations. The performance of different detectors is carefully compared when both antenna array configurations are deployed considering a different number of antennas and modulation order, especially under near‐massive MIMO condition. We have also discussed the relationship between the array factor and the bit error rate performance of both antenna array structures.     

Error probability performance for W-CDMA systems with multiple transmit and receive antennas in correlated Nakagami fading channels

The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m (1960) fading channel framework. The impact of the array configuration (e.g., the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as the fading severity, angular spread and path delay profile) on the overall space-path diversity gain can be directly evaluated. In addition, the exact pairwise error probability of a convolutional coded system is obtained, and the coding gain of a space-path diversity receiver is quantified.     

A reliable relay selection scheme for SSK modulation in cooperative communication systems

Space shift keying (SSK) modulation is a scheme in which the indices of active transmit antennas play an essential role in carrying information bits. In SSK modulation, the communication channel acts as modulating unit. Therefore, using the conventional relay selection schemes based on channel coefficients are impossible in cooperative systems using SSK modulation. In this paper, we propose a novel relay selection scheme that is applicable in cooperative systems using SSK modulation. The proposed scheme is based on calculating and measuring the Euclidean distances between received signal and all active or inactive channel coefficients. The proposed relay selection scheme is applied for a cooperative communication system with multiple relay nodes and a direct link between source and destination. The analytical expressions are derived to calculate the average bit error rate over Rayleigh fading channels. The analytical and simulation results show that this relay selection scheme can provide a full cooperative diversity order, for SSK modulation. In addition, we show that this scheme can be used at destination as a signal selection method, to select the best received signal from different paths. The analytical results are validated using Monte Carlo simulation studies.     

Transmitter optimization and performance gain for multiple-input single-output systems with finite-rate direction feedback

Consider finite-rate channel-direction feedback in a system with multiple transmit but single receive antennas. We investigate how the transmitter should be optimized for symbol error rate with finite-rate feedback, and how the symbol error rate and outage probability improve as a function of the number of feedback bits. It is found that when the number of feedback directions is equal to or larger than the number of transmit antennas, transmit beamforming is optimal. Otherwise, the antennas should be divided into two groups, where antenna selection is used in the first group to choose the strongest channel, and equal power allocation is used in the second group. At high signal to noise ratio (SNR), the optimal power allocation between these two antenna groups is proportional to the number of antennas in each group. Based on high SNR analysis, we quantify the power gain of each feedback bit. It is shown that the incremental gain increases initially and diminishes when the number of feedback bits surpasses the logarithm (base 2) of the number of transmit antennas.     

On the robustness of space-time coding techniques based on a general space-time covariance model

The robustness of space-time coding techniques for wireless channels that exhibit both temporal and spatial correlation is investigated. A general space-time covariance model is developed and employed to evaluate the exact pairwise error probability for space-time block codes. The expressions developed for the pairwise error probability are used in conjunction with the union bound to determine an upper bound for the probability of a block error. The block error probability is evaluated for several space-time codes and for wireless channels that exhibit varying degrees of spatial and temporal correlation. Numerical results are presented for a two-dimensional Gaussian scatterer model which has been shown to be consistent with recent field measurements of wireless channels. The results demonstrate that the best-case wireless channel is uncorrelated in both space and time. Correlation between transmission paths, due to insufficient spacing of the transmit antennas or scatterers located in close proximity to the mobile, can result in a significant performance degradation. The conditions that result in uncorrelated transmission paths are quantified in terms of the effective scattering radius and the spacing of the transmit and receive antennas.     

Exact SEP and performance bounds for orthogonal space‐time block codes in cooperative multiantenna AF relaying networks

In this paper, we derive a moment generating function (MGF) for dual‐hop (DH) amplify‐and‐forward (AF) relaying networks, in which all nodes have an arbitrary number of antennas, with orthogonal space‐time block code (OSTBC) transmissions over Rayleigh fading channels. We present an exact error rate expression based on the derived MGF and another analytical approach to derive achievable performance bounds as closed‐forms of symbol error rate, outage probability, and normalized channel capacity. Furthermore, we derive the asymptotic behavior of symbol error rate and outage probability. From this asymptotic behavior, it is shown that the diversity order and its dependence on antenna configurations can be explicitly determined. Simulation results are also presented to verify their accuracy by comparing with numerical results and to provide an insight to the relationship between relaying networks' antenna configuration and diversity order. It is confirmed that the transmit antenna gain of the source node and the receive antenna gain of the relay node can be obtained only when the relay is close to the destination, and then, the transmit antenna gain of the relay node and the receive antenna gain of the destination node can be obtained only when the relay is close to the source.     

Space-time bit-interleaved coded modulation for OFDM systems

Space-time coding techniques significantly improve transmission efficiency in radio channels by using multiple transmit and/or receive antennas and coordination of the signaling over these antennas. Bit-interleaved coded modulation gives good diversity gains with higher order modulation schemes using well-known binary convolutional codes on a single transmit and receive antenna link. By using orthogonal frequency division multiplexing (OFDM), wideband transmission can be achieved over frequency-selective fading radio channels without adaptive equalizers. In this correspondence, we combine these three ideas into a family of flexible space-time coding methods. The pairwise error probability is analyzed based on the correlated fading assumption. Near-optimum iterative decoders are evaluated by means of simulations for slowly varying wireless channels. Theoretical evaluation of the achievable degree of diversity is also presented. Significant performance gains over the wireless local area network (LAN) 802.11a standard system are reported.     

Approximate performance analysis of coded OSTBC-OFDM systems over arbitrary correlated generalized ricean fading channels

A framework for analyzing the performance of coded OSTBC-OFDM systems over arbitrary correlated generalized Ricean fading channels is established. The moment generating function of the signal-to-noise ratio at the input to the channel decoder is derived assuming correlated transmitter and receiver antennas and correlated paths in frequency selective channels. The probability of outage, the pairwise error probability, and the bit error rate are then evaluated. Bit-interleaved and iteratively decoded turbo product codes, Gray encoded M-ary quadrature amplitude modulation, and other parameters of the IEEE 802.16 Standard are used to illustrate numerical results.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Diversity Analysis of Peaky FSK Signaling in Fading Channels

Error performance of noncoherent detection of on-off frequency shift keying (OOFSK) modulation over fading channels is analyzed when the receiver is equipped with multiple antennas. The analysis is conducted for two cases: 1) the case in which the receiver has the channel distribution knowledge only; and 2) the case in which the receiver perfectly knows the fading magnitudes. For both cases, the maximum a posteriori probability (MAP) detection rule is derived and analytical probability of error expressions are obtained. Numerical and simulation results indicate that for sufficiently low duty cycle values, lower error probabilities with respect to FSK signaling are achieved. Equivalently, when compared to FSK modulation, OOFSK with low duty cycle requires less energy to achieve the same probability of error, which renders this modulation a more energy efficient transmission technique. Also, through numerical results, the impact of number of antennas, antenna correlation, duty cycle values, and unknown channel fading on the performance are investigated.     

Trellis code‐aided high‐rate M‐QAM space‐time labeling diversity using a unitary expansion

In this paper, we present a high‐rate M‐ary quadrature amplitude modulation (M‐QAM) space‐time labeling diversity (STLD) system that retains the robust error performance of the conventional STLD system. The high‐rate STLD is realised by expanding the conventional STLD via a unitary matrix transformation. Robust error performance of the high‐rate STLD is achieved by incorporating trellis coding into the mapping of additional bits to high‐rate codes. The comparison of spectral efficiency between the proposed trellis code‐aided high‐rate STLD (TC‐STLD) and the conventional STLD shows that TC‐STLD with 16‐QAM and 64‐QAM respectively achieves a 12.5% and 8.3% increase in spectral efficiency for each additional bit sent with the transmitted high‐rate codeword. Moreover, we derive an analytical bound to predict the average bit error probability performance of TC‐STLD over Rayleigh frequency‐flat fading channels. The analytical results are verified by Monte Carlo simulation results, which show that the derived analytical bounds closely predict the average bit error probability performance at high signal‐to‐noise ratios (SNR). Simulation results also show that TC‐STLD with 1 additional bit achieves an insignificant SNR gain of approximately 0.05 dB over the conventional STLD, while TC‐STLD with 2 additional bits achieves an SNR gain of approximately 0.12 dB.     

Achievable sum‐rate analysis of correlated two‐antenna MIMO uplink channels

This paper analyzes the achievable sum‐rate of correlated two‐antenna multiple‐input multiple‐output (MIMO) uplink channels. Most of previous works have considered the case when a single user has multiple transmit antennas (i.e. multi‐antenna single‐user scenario). This paper considers the case when two‐antenna MIMO uplink channels comprise two users with a single transmit antenna (i.e. single‐antenna two‐user scenario). The analytic and simulation results show that the achievable sum‐rate of correlated single‐antenna two‐user MIMO uplink channels highly depends on the angle difference between the receive correlation coefficients of two users. It is also shown that the achievable sum‐rate of correlated single‐antenna two‐user MIMO uplink channels is larger than that of correlated two‐antenna single‐user MIMO uplink channels and can even be larger than that of independent and identically distributed Rayleigh two‐antenna MIMO uplink channels. Copyright © 2009 John Wiley & Sons, Ltd.