Analysis and design of short block OFDM spreading matrices for use on multipath fading channels

We consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels. The main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver. We pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized. This formulation allows us to find explicit solutions for the optimal spreading matrices. The performance is validated for the uncoded channel as well as for the coded channel employing turbo-iterative decoding. We further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing (OFDM) do not gain any diversity advantage over traditional diagonal OFDM.     

Approximation power of biorthogonal wavelet expansions

This paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions. The Strang-Fix conditions imply that the error for an orthogonal wavelet approximation at scale a=2^-i globally decays as a^N, where N is the order of the transform. This is why, for a given number of scales, higher order wavelet transforms usually result in better signal approximations. We prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone. We also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero. These results strengthen Sweldens earlier analysis and confirm that the approximation power of biorthogonal and (semi-)orthogonal wavelet expansions is essentially the same. Finally, we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines. We also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error     

正交循环码M进制扩频接收机的研究

该文提出了一种基于正交循环码的M进制扩频接收机方案,发端将一条原型扩频码循环移位构成M个扩频码,实现M进制扩频,接收端利用时频变换域正交匹配滤波器实现了非相干解扩解调。该方案不仅减少了需要的扩频码数目,而且有效地降低了接收机的计算复杂度。该文对所提出的系统在单用户和多用户条件下的误码性能进行了理论分析和仿真,并比较了3种M进制解扩方法的运算量。结果表明:正交循环码M进制扩频系统的计算复杂度和误码特性均优于传统的M进制系统。     

Channel interference reduction using random Manchester codes forboth synchronous and asynchronous fiber-optic CDMA systems

We propose the random Manchester codes (RMC) to improve the bit error probability (BEP) performance in both synchronous and asynchronous fiber-optic code-division multiple-access (CDMA) systems. The spreading sequences used in the synchronous and asynchronous systems are modified prime sequence codes and optical orthogonal codes (OOCs), respectively. Thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration in the BEP analyzes. The results show that the proposed systems can support a larger number of simultaneous users than other systems with similar system complexity under the same bit-error probability constraint     

The study of a BOCC m-ary spread spectrum scheme

M-ary spread spectrum technique has been found wide applications in wireless communications, but it needs too many orthogonal spreading codes, and its despreading/demodulation is quite complex computationally, which limit its wider applications. This paper proposes a novel scheme for Code Division Multiple Access （CDMA） communication systems based on M-ary spread spectrum, where only one prototype spreading code is assigned to each user and the codes for different users are orthogonal or quasi-orthogonal with each other. The M spreading codes of each user to represent K bits data are generated by circularly shifting the assigned code and reversing its polarity. The spreading codes generated like that are called as BiOrthogonal Cyclic Codes （BOCCs）. At the receiver of the system, a transform domain matched-filter implemented by means of Fast Fourier Transform （FFT） is employed to despread and demodulate the received signals, which has very low computational complexity. The results of simulation experiments and bit-error performance analysis show that the proposed scheme is practical and very useful in many cases.     

High Diversity Transceiver for Low Power Differentially Encoded OFDM System

In this work, we investigate differentially encoded blind transceiver design in low signal‐to‐noise ratio (SNR) regimes for orthogonal frequency‐division multiplexing (OFDM) signaling. Owing to the fact that acquisition of channel state information is not viable for short coherence times or in low SNR regimes, we propose a time‐spread frequency‐encoded method under OFDM modulation. The repetition (spreading) of differentially encoded symbols allows us to achieve a target energy per bit to noise ratio and higher diversity. Based on the channel order, we optimize subcarrier assignment for spreading (along time) to achieve frequency diversity of an OFDM modulated signal. We present the performance of our proposed transceiver design and investigate the impact of Doppler frequency on the performance of the proposed differentially encoded transceiver design. To further improve reliability of the decoded data, we employ capacity‐achieving low‐density parity‐check forward error correction encoding to the information bits.     

Residual Correlation for Generalized Discrete Transforms

We have undertaken a systematic investigation of the performance of a complete set of discrete orthogonal transforms Gr(n). The criterion of performance is that defined by Hamidi and Pearl, namely the Residual Correlation. This criterion measures the proportional correlation left in by a transform which is suboptimal, in the sense of not completely decorrelating the signal as in the case of the Karhunen-Loeve transform. The family of orthogonal transforms Gr(n), as defined by Ahmed and Rao, ranges from the discrete Walsh transform DWT, to the discrete Fourier transform DFT, as r varies from r = 0 to r = n - 1. Our study is applied to Markov-1 signals only.     

多带OFDM-UWB系统的抗干扰研究

根据超宽带通信系统存在严重窄带干扰的特点,提出基于正交扩展与交织的抗干扰方法。该方法充分利用超宽带系统子载波和子带之间的频率分集性,将子载波传输的编码比特流扩展到相应子带的所有子载波上,然后再将扩展的数据流在系统所有的子带间进行交织,由此增强了系统抗窄带干扰的顽健性。理论分析和仿真结果表明,扩展与交织能降低系统误比特率1~2个数量级或者改善信干比5~10 dB,大大提高了系统的抗窄带干扰能力。     

Cooperative Diversity Based Multi-Carrier CDMA System with Decode and Forward Relays in Rayleigh Fading channels

Cooperative communication is one of the major diversity techniques which exploit spatial diversity through a virtual antenna array. In addition to cooperation, transmitting the same symbols through different sub carriers (Multi-Carriers) introduces frequency diversity as well. The objective of this paper is to investigate cooperative diversity performance in Multi-Carrier Code Division Multiple Access (MC-CDMA) systems with orthogonal and non-orthogonal spreading codes. We evaluate the Symbol Error Rate (SER) of cooperative transmission in frequency-selective Rayleigh faded uplink channel. We focus on the use of despreading-combining (DC) receiver and coherent detection with Maximal Ratio Combining for the above selected criteria respectively. It is shown that the orthogonal spreading code cancels Multiple-Access Interference (MAI) and the performance is completely independent of the length of the spreading code. The approximate SER derived here for the the transmission scheme is well matched with the increasing number of users in the system. Hence the Gaussian approximation is acceptable for systems which are operating with their maximum user capacities at lower SNR values.     

OTFS技术研究现状与展望

正交时频空（orthogonal time frequency space,OTFS）技术是近年来出现的一种新型多载波调制技术。在 OTFS 技术中,数据信号在时延—多普勒域产生,经过逆偶有限傅里叶变换实现信号的时频二维扩展,以解决正交频分复用（orthogonal frequency division multiplexing,OFDM）技术在时频双选信道下干扰严重的问题。介绍了OTFS技术的基本原理,通过仿真验证其相比于OFDM技术的优势。对其研究现状进行分析总结,指出 OTFS 技术中的多址接入、信道估计和线性接收机等研究方向目前有待解决的问题。对 OTFS 技术在雷达—通信一体化系统中的应用前景进行分析和展望。     

Discrete multiple tone modulation with coset coding for thespectrally shaped channel

A discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample. This discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes     

Application Specific Efficient VLSI Architectures for Orthogonal Single- and Multiwavelet Transforms

In this paper, efficient VLSI architectures for orthogonal wavelet transforms with respect to common applications are presented. One class of orthogonal wavelet transforms is the singlewavelet transform which is based on one scaling and one wavelet function. An important application of this transform is signal denoising for which an efficient VLSI implementation and layout is derived in this paper. Contrary to singlewavelets, orthogonal multiwavelets are based on several scaling and wavelet functions. Since they allow properties like compact support, regularity, orthogonality and symmetry, simultaneously, being impossible in the singlewavelet case, multiwavelets are well suited bases for image compression applications. With respect to an efficient implementation of these orthogonal wavelet transforms, approximations of the exact rotation angles of the corresponding wavelet lattice filters are used. The approximations are realized by elementary CORDIC rotations. This method reduces the number of shift and add operations significantly with no influence on the good performance of the transforms. VLSI architectures for the computationally cheap transforms and related implementation aspects are discussed and design examples from architectural level down to layout are given.     

A symbol-by-symbol channel estimation receiver for space-time block coded systems and its performance analysis on the nonselective rayleigh fading channel

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.     

A new spreading scheme for convolutionally coded CDMA communicationin a Rayleigh-fading channel

There has been increased interest in the use of direct-sequence code-division multiple-access (DS/CDMA) for wireless communication systems. We find that the asymptotic bit-error probability (BEP), P_b, of a convolutionally coded code-division multiple-access (CDMA) system in a frequency-selective Rayleigh-fading channel depends on the length of the shortest error event path and the product of symbol distances along that path. Based on this observation, we propose a new spreading scheme that maximizes the length of the shortest error event path. It is shown that the proposed scheme yields an improvement of 1.0-1.3 dB at P_b=10^-5 over the conventional convolutionally coded CDMA system, and even a higher improvement can be achieved as the required BEP is decreased     

On lapped orthogonal transforms [signal coding applications]

The energy compaction performance of several lapped orthogonal transforms (LOTs) are presented. It is shown that the LOT outperforms the conventional block transforms for all the cases considered. The performance of the poorly performing block transforms for high correlation sources increased dramatically in their LOT versions. It is found that the energy compaction performance of the LOT versions of the different block transforms considered is about the same. Therefore, the choice of LOT is based on the efficiency of the transform algorithm. The LOT is an alternative to the block transforms for signal coding applications. Also, the blocking effect is reduced with the increase in the computational complexity of the transform algorithm     

A Rate-1 Space-Time Diversity Method for Rotated 4-QAM Constellations

We propose a rate-1 space-time transmit diversity technique. We obtained second-order diversity by transmitting the real and imaginary parts of the symbols from two antennas. With four transmit antennas, we can add Alamouti coding to reach fourth-order transmit diversity. There is no need to detect symbols jointly in either of these applications. It is possible to use both Alamouti coding and Hadamard spreading diversity with the proposed method, thereby obtaining eighth-order (or even higher) transmit diversity. However, joint detection of the symbols is again required at this point. The proposed technique is a suitable space-frequency coding method for OFDM systems. We used computer simulations to compare our technique with the Alamouti coding, quasi-orthogonal space-time block coding (QOSTBC), and orthogonal space–time block coding (OSTBC) methods. We also compared its performance to that of Hadamard spreading diversity. Alamouti coding performs better than the proposed technique at the second order of transmit diversity, but is also limited to that order. The proposed technique performs better than OSTBC at the same order of the transmit diversity. QOSTBC performs slightly better than the proposed technique at the same order of transmit diversity. However, when all methods have the same detection complexity, the proposed technique performs better than both QOSTBC and Hadamard spreading diversity.     

Multidimensional parallel combinatory transform domain communication system

Transform domain communication system is an adaptive anti‐interference system that can dynamically generate interference‐orthogonal waveforms. As a spread spectrum system, its low spectrum efficiency limits potential practical applications. In TDCS, cyclic code shift keying is an orthogonal modulation, whose symbols can be regarded as scalars in different dimensions. However, the constellation is restricted by signal time‐bandwidth product. In this study, extending constellation is proven to be a valid approach to improve spectrum efficiency. The combinatory of multidimensional vectors is designed mathematically to increase the variety of the scalars with the minimum orthogonality damage. On the basis of the design, an efficient modulation scheme, namely, multidimensional parallel combinatory transform domain communication system, is proposed, whose fundamental modulation symbols can be represented by the combinatory of a series of cyclic code shift keying symbols with phase shift keying modulation. Compared with the existing methods, multidimensional parallel combinatory transform domain communication system can achieve a considerably higher spectrum efficiency. The bit error rate performance is also improved to various extents. Theoretical spectrum efficiency and bit error rate of the proposed method are derived for additive white Gaussian noise and typical multipath fading channels. System with different spectral conditions and channel estimation methods is also simulated and analyzed to confirm the practical usability.     

Optimum spreading bandwidth for selective RAKE reception overRayleigh fading channels

Building on the developments in the performance analysis of generalized selection combining (GSC), this paper examines the optimum spreading bandwidth for a fixed-complexity GSC diversity receiver operating over independent identically distributed Rayleigh paths. For this purpose, the study considers three performance criteria: (1) average combined signal-to-noise ratio (SNR) at the GSC output; (2) average bit error probability (BEP); and (3) outage probability of the instantaneous combined SNR at the GSC output. For the average BEP criterion, results are presented for both coherent and noncoherent combining. For the average combined SNR and some instances of the average BEP optimization problem, an accurate approximate estimate of this optimum bandwidth in the form of a solution of a transcendental equation is provided. In other cases, where the optimization is not easily tractable in an analytic fashion, a numeric-search procedure is used to find this optimum bandwidth for different performance criteria and system parameters of interest. Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a set of system parameters and a particular performance criterion of interest     

随机信号Haar小波包变换的性能研究

本文研究了Ｈａａｒ小波包库内各种正交基对应的正交变换用于对随机数字信号进行处理的问题，提出了一种小波包基的编码方案，并且从方差分布、均方误差、率失真函数的角度对各种Ｈａａｒ小波包基对就的正交变换在数据压缩、广义维纳滤波和变换编三中的性能进行比较，总结了其规律。     

Differentially amplitude and phase-encoded QAM for the correlatedRayleigh-fading channel with diversity reception

This paper studies the differentially amplitude and phase-encoded (DAPE) quadrature amplitude modulation (QAM) transmission over correlated Rayleigh channels with diversity reception. Operating over two successive received symbols, the optimum and an asymptotic maximum-likelihood (AML) differentially coherent receiver are developed and compared with a conventional switched diversity combining (SDC) grid receiver. It is shown that the AML and SDC grid receivers are much simpler in complexity than the optimum receiver in that no channel side information is required in their realization. An exact expression of the bit-error probability (BEP) is obtained for the SDC grid receiver. Based on a union bound argument, a BEP upper bound for the AML receiver is also derived and verified by simulation. Numerical results on 16- and 64-point constellations show that the AML receiver exhibits an almost optimum performance and the SDC grid receiver with a small level of diversity is nearly optimum. It is also shown by simulation that the conventional equal-gain diversity receiver is almost optimal for demodulating a 16-point DAPE QAM signal