Pilot symbol-assisted detection of CPM schemes operating in fastfading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes     

The BER analysis of OFDMA and SC‐FDMA under pilot‐assisted channel estimation and pilot jamming in rayleigh slow‐fading channel

In this paper, the authors derived the analytical bit error rate expressions for orthogonal frequency division multiple access and single‐carrier frequency‐division multiple access (SC‐FDMA) in Rayleigh slow‐fading channel for binary phase‐shift keying/quadrature phase‐shift keying/16‐quadrature amplitude modulations under pilot jamming and pilot symbol‐assisted channel estimation. Beginning with the bit error rate analysis from the general case of pilot symbol‐assisted channel estimation technique in Rayleigh slow‐fading channel, the expressions are first modified for different modulations and then further customized to account for the Zero‐Forcing equalization in frequency or time direction with application respectively to orthogonal frequency division multiple access or SC‐FDMA without and with pilot jamming. Piecewise‐linear interpolation is used for its simplicity. The simulation results match perfectly with the theoretical predictions except for some discrepancies with SC‐FDMA, which imply that the generalized equations developed here have to be further modified to account for system‐specific features like discrete Fourier transform precoding for SC‐FDMA. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of the Channel Estimation Algorithm for Advanced Terrestrial DMB System

This paper describes a channel estimation algorithm for the advanced terrestrial digital multimedia broadcasting (T-DMB) transmission system which is fully backward compatible with the conventional T-DMB standard. The advanced T-DMB has enhanced features which provide higher transmission data rate for increasing program channel capacity and better multimedia A/V service quality than the conventional T-DMB system by adopting a hierarchical modulation and scalable audio/video CODEC. To support the higher data rate transmission for the advanced T-DMB, high performance channel estimation and equalization techniques should be adopted into the advanced T-DMB receivers. In this paper, we propose a new channel estimation technique for the Advanced T-DMB to compensate channel distortion under dynamic multipath environment.      

The Performance Analysis of Backward Compatible Modulation With Higher Spectrum Efficiency for DAB Eureka 147

Based on the standard of digital audio broadcasting (DAB) Eureka 147 system to improve structures of transmitter/receiver, this paper proposes a physical layer transmission technique capable of boosting the spectrum efficiency up to two times of that of the DAB-Eureka 147 system while the backwards compatibility is guaranteed. The proposed transmission technique comprises the development of both the modulation and demodulation schemes. In the developed modulation scheme, differential 16-level amplitude/ phase shift keying (D16 APSK) is adopted to replace the differential quadrature-phase-shift-keying (DQPSK) used in the DAB Eureka 147 system. In the developed demodulation scheme, on the other hand, a detector for two-level differential amplitude-shift-keying (DASK) signal is proposed which can be implemented with rather low hardware costs. The performance is presented by the Simulink platform in multipath fading channel model.     

Nakagami衰落信道上组合SC/MRC的性能分析

研究Nakagami衰落信道上组合发射机选择合并(SC)/接收机最大比合并(MRC)天线分集系统的性能.使用矩生成函数方法,推导采用组合SC/MRC天线分集和相干检测的MPSK(M进制相移键控)、MQAM(M进制正交幅度调制)、MPAM(M进制脉冲幅度调制)、BFSK(二进制频移键控)、最小相关BFSK(BFSKmin)、差分编码BPSK(DE-BPSK)和预编码MSK(最小频移键控)等几种M进制数字调制方式在Nakagami衰落信道上的误符号率性能,获得了M进制数字调制系统误符号率性能的精确数学表达式.数值计算结果阐明了发射天线和接收天线数目以及衰落参数对数字调制系统误符号率性能的影响.     

Optimum Pilot Symbol Assisted Modulation

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.     

Pilot tone aided coherent GMSK systems for sound/data mobilebroadcasting

A Gaussian minimum-shift keying (GMSK) modem with built-in fade canceler is proposed narrowband mobile digital broadcasting systems. The proposed scheme combines DC suppressing line code and high-pass filters to create a spectral null at the carrier frequency of the transmit GMSK signal spectrum. This enables an unmodulated carrier pilot tone to be transmitted with the digital broadcast signal without mutual interference. In the receiver, the recovered pilot is used to coherently demodulate the received signal without phase ambiguity. The pilot can be also be used to track and cancel out the random phase noise induced by fast fading. The scheme is applied to a 16 kb/s BT=0.25 GMSK signal with B_v=800 Hz, and its performance over a fast Rayleigh fading channel is investigated using computer simulation. The results demonstrates that the proposed coherent modem is capable of significantly outperforming conventional differential detection in fast fading environments such as a broadcasting channel for mobile reception     

数字调幅广播系统中基于滑动窗口的二维信道估计

针对DRM数字广播系统,提出一种基于滑动窗口的二维信道估计方法.该方法首先对接收到的导频信号所在信道进行最小二乘估计,然后进行时间方向插值估计导频子载波上所有位置处的信道频率响应,最后通过一个滑动窗口在多径扩展域和多谱勒扩展域分别进行处理.对于快速时变信道,通过调整窗口的滑动步数,可以有效处理窗口内信道路径数和路径延迟可能变化的情况,从而显著降低了子载波间干扰和高斯白噪声的影响.理论分析和仿真表明,与现有信道估计相比,该方法具有估计精确、易于实现的优点.     

CD3-OFDM: a novel demodulation scheme for fixed and mobilereceivers

This paper describes a novel channel estimation scheme identified as coded decision directed demodulation (CD3) for coherent demodulation of orthogonal frequency division multiplex (OFDM) signals making use of any constellation format [e.g., quaternary phase shift keying (QPSK), 16-quadrature amplitude modulation (QAM), 64-QAM]. The structure of the CD3-OFDM demodulator is described, based on a new channel estimation loop exploiting the error correction capability of a forward error correction (FEC) decoder and frequency and time domain filtering to mitigate the effects of noise and residual errors. In contrast to the conventional coherent OFDM demodulation schemes, CD3-OFDM does not require the transmission of a comb of pilot tones for channel estimation and equalization, therefore yielding a significant improvement in spectrum efficiency (typically between 5-15%). The performance of the system with QPSK modulation is analyzed by computer simulations, on additive white Gaussian noise (AWGN) and frequency selective channels, under static and mobile reception conditions. For convolutional coding rate 1/2, the results indicate that CD3-OFDM allows one to achieve a very fast adaptation to the channel characteristics in a mobile environment (maximum tolerable Doppler shift of about 80 Hz for an OFDM symbol duration of 1 ms, as differential demodulation) and an E_b /N₀ performance similar to coherent demodulation (e.g., E_b/N₀=4.3 dB at bit-error rate (BER)=2·10 ^-4 on the AWGN channel). Therefore, CD3-OFDM can be suitable for digital sound and television broadcasting services over selective radio channels, addressed to fixed and vehicular receivers     

BER Analysis of Equalized OFDM Systems in Nakagami, <Emphasis Type="Italic">m</Emphasis> < 1 Fading

The orthogonal frequency division multiplexing (OFDM) transmission scheme is currently experiencing increased popularity due to advances in very large scale integration technology. It is used for a variety of broadband systems such as asymmetric digital subscriber lines, very-high-speed digital subscriber lines, digital video, and audio broadcasting, and wide local area network standards such as IEEE 802.11a, IEEE 802.11 g, and ETSI Hiperlan/2. However, propagation impairments can cause severe degradation in bit error rates (BER) for coherent detection. We derive a semi-analytical method to evaluate BER of a quadrature phase shift keying (QPSK)-OFDM system in Nakagami, m < 1 fading and additive noise where pilot-assisted linear channel estimation and channel equalization are used. This allows modeling of more severe fading environments than can be depicted by a Rayleigh distribution. Numerical simulations are used to validate the proposed methods. The techniques developed can be applied to other channel estimation techniques, modulation schemes and the performance evaluation of equalized single carrier narrowband systems.     

Solutions to Infinite Integrals of Gaussian Q-Function Products and Some Applications

Infinite integrals involving the products of two and three Gaussian Q-functions of different arguments are solved in closed-form. These solutions provide novel expressions in the error rate analyses of signals such as general rectangular quadrature amplitude modulation, differentially encoded quaternay phase shift keying and new solutions for the error rate of the repetition code. As an example, closed-form expressions for the average symbol error rates of general rectangular quadrature amplitude modulation and the repetition code are obtained for a Nakagami-m fading channel.     

Space-Time Trellis Codes Over Rapid Rayleigh Fading Channels With Channel Estimation---Part I: Receiver Design and Performance Analysis

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.     

Iterative channel estimation and decoding of pilot symbol assistedturbo codes over flat-fading channels

A method for coherently detecting and decoding turbo-coded binary phase shift keying (BPSK) signals transmitted over frequency-flat fading channels is discussed. Estimates of the complex channel gain and variance of the additive noise are derived first from known pilot symbols and an estimation filter. After each iteration of turbo decoding, the channel estimates are refined using information fed back from the decoder. Both hard-decision and soft-decision feedback are considered and compared with three baseline turbo-coded systems: (1) a BPSK system that has perfect channel estimates; (2) a system that uses differential phase shift keying and hence needs no estimates; and (3) a system that performs channel estimation using pilot symbols but has no feedback path from decoder to estimator. Performance can be further improved by borrowing channel estimates from the previously decoded frame. Simulation results show the influence of pilot symbol spacing, estimation filter size and type, and fade rate. Performance within 0.49 and 1.16 dB of turbo-coded BPSK with perfect coherent detection is observed at a bit-error rate of 10^-4 for normalized fade rates of f_dT_s=0.005 and f_dT_s=0.02, respectively     

Effect of channel estimation error on M-QAM BER performance inRayleigh fading

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider     

Error probability minimizing pilots for OFDM with M-PSK modulation over Rayleigh-fading channels

Orthogonal frequency division multiplexing (OFDM) with pilot symbol assisted channel estimation is a promising technique for high rate transmissions over wireless frequency-selective fading channels. In this paper, we analyze the symbol error rate (SER) performance of OFDM with M-ary phase-shift keying (M-PSK) modulation over Rayleigh-fading channels, in the presence of channel estimation errors. Both least-squares error (LSE) and minimum mean-square error (MMSE) channel estimators are considered. For prescribed power, our analysis not only yields exact SER formulas, but also quantifies the performance loss due to channel estimation errors. We also optimize the number of pilot symbols, the placement of pilot symbols, and the power allocation between pilot and information symbols, to minimize this loss, and thereby minimize SER. Simulations corroborate our SER performance analysis, and numerical results are presented to illustrate our optimal claims.     

Pairwise error probability evaluation of multiple symbol trellis-coded continuous phase frequency shift keying in a slow fading channel

This article evaluates the pairwise error probability (PEP) of multiple symbol trellis-coded modulation applied to continuous phase frequency shift keying (MTCM/CPFSK) in a slow fading environment with and without channel state information (CSI). The fading amplitude is assumed to be constant during an error event and distributed as Rician. For the case with CSI, the PEP is approximated using the Gauss-Chebysev formula and a tight upper bound is presented. For the case without CSI, a simplified upper bound is derived by using the improved Chernoff bound technique. Simulation results are also presented.     

Pilot symbol assisted BPSK on Rayleigh fading channels withdiversity: performance analysis and parameter optimization

The loss due to imperfect channel estimation is derived for pilot symbol assisted binary phase-shift keying (BPSK) on fading channels with diversity. The presented approach, which holds for both narrow-band and spread spectrum communication, further provides an analytical optimization of pilot symbol spacing. The loss due to channel estimation is demonstrated to be low if the maximum Doppler frequency is significantly less than the bit rate     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.     

Performance analysis of APSK modulation for DVB‐S2 transmission over nonlinear channels

For increased bandwidth efficiency and receiver performance, standards for satellite broadcasting systems are evolving by utilizing efficient transmission techniques. The second‐generation digital video broadcasting for satellites (DVB‐S2) adopts the amplitude phase shift keying (APSK) modulation for enhanced performance over nonlinear channels. In this paper, we derive error rate bounds for APSK modulated symbols and generalize the bounds to the case of distorted constellation, which occurs when the maximum transmission amplitude is saturated by the soft‐limiter type channel. The derived bound is shown to significantly improve the previously known result, to accurately predict both the symbol error rate and bit error rate in the entire signal‐to‐noise ratio (SNR) region of interest. Using the derived formula, the optimal input power level for the soft‐limiter channel is determined, and the corresponding minimal error rates for 16‐ and 32‐APSK are quantified. The result is also interpreted in terms of optimal input back‐off (IBO) for nonlinear power amplifiers by evaluating the performance degradation as a function of IBO. Copyright © 2009 John Wiley & Sons, Ltd.     

双发射天线选择正交空时码分集系统性能分析

针对任意Nakagami衰落信道,分析了多输入多输出(MIMO)系统中采用双发射天线选择正交空时码的平均误码率(ASER)性能。利用矩生成函数方法,推导出采用相干检测的二进制相移键控/二进制频移键控(BPSK/BFSK)、多进制相移键控(MPSK)和多进制正交幅度调制(MQAM)的精确ASER闭合解析式,对不同条件下的系统性能做了数值仿真,验证了分析结果的正确性。