On the Computational Cutoff Rate, R0for the Peak-Power-Limited Gaussian Channel

The "computational cutoff rate," R0, represents a practical measure of the maximum reliable data rate that can be achieved by coding over a given communication channel using a given modulation format, in contrast with the "channel capacity,"C, which represents an idealized theoretical limit on the achievable data rate. Moreover, designing signal sets with good error probabilities using the R0criterion results in a mathematical problem that is much more tractable than that obtained by using the probability of error itself as a criterion. Both of the above reasons establish the importance of R0in communications theory. This paper starts with a brief tutorial background, which reveals the origin and the significance of R0. Next, the problem of achieving R0over the additive white Gaussian noise (AWGN) dispersive or nondispersive channel, using quadrature-amplitude modulation (QAM) with a peakpower constraint, is addressed. The major result is that, for both cases, the optimum transmission signal set is chosen from a discrete distribution. The solution is derived in detail for the peak-power-limited nondispersive channel, where it is shown that the optimum QAM symbols are selected independently from a probability distribution that is uniform in the phase and discrete in the radius. The solution for the corresponding peak-power-limited dispersive channel is obtained only asymptotically, for large signal-to-noise ratio (SNR), where it is shown that the QAM symbols are selected independently from a uniform distribution within a disk in the complex signal space.     

基于预译码的极化码最大似然简化连续消除译码算法

针对极化码译码串行输出造成较大译码时延的问题,该文提出一种基于预译码的最大似然简化连续消除译码算法。首先对译码树节点存储的似然值进行符号提取并分组处理,得到符号向量组;然后比较符号向量组与该节点的某些信息位的取值情况,发现向量组中储存的正负符号分布规律与该节点的中间信息位的取值具有一一对应的关系;在此基础上对组合码中间的1～2 bit进行预译码;最后结合最大似然译码方法估计组合码中的剩余信息位,从而得到最终的译码结果。仿真结果表明:在不影响误码性能的情况下,所提算法与已有的算法相比可有效降低译码时延。     

一种分布式MIMO差分检测方法

本文提出一种无需信道估计的分布式MIMO差分编码及检测方法:发送端将发射符号进行相位差分调制后生成空时码矩阵进行发射,接收端利用前后接收量判断相位信息恢复出发送端数据信息.本文将该方法在不同信道传播时延场景下进行了仿真验证,仿真结果表明,在相同E_b/N₀情况下,不同信道传播时延对应的误码率性能不同:在信道传播时延从0.1T_s到0.9T_s的变化过程中,误码率随信道传播时延的增大先降低后升高,当信道传播时延为0.6T_s左右误码率达到最低,存在使系统误码率性能较好的信道传播时延.     

Distribution of the phase angle between two vectors perturbed byGaussian noise II

The Case I, Case II, and Case III distributions for the phase angle between two vectors perturbed by Gaussian noise are restated in terms of integrals with integrands containing only exponentials. Added to these are a Case IV distribution in which one of the vectors is noise free; and Case V, Case VI, and Case VII distributions for the instantaneous radian frequency that results when the time between the two vectors goes to zero. In addition, existing and new forms for the probability density functions corresponding to each of the distributions are given. The results are applied to digital FM with a limiter/discriminator receiver to easily obtain the bit error probability without coding and the corresponding probability density function needed in a Chernoff bound approach to study the bit error probability with coding     

正交空时分组码性能估计的一种方法

本文给出并证明了采用正交空时分组码传输的衰落信道条件下,接收机输出瞬时信噪比的一般表达形式,分析了瑞利衰落信道条件下接收机输出符号差错性能.给出了正交空时分组码的符号差错概率的最小距离球界,由此可以得到空时分组码关于发送天线数量的"地板效应".     

System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission

In this paper, closed-form analytical bounds on PMD-induced symbol error rate and outage probability in high-speed long-haul optical orthogonal frequency division multiplexed (OFDM) systems are derived, evaluated, and verified experimentally in order to assess the PMD tolerance of this modulation format. To obtain the analytical results, the PMD channel is modeled as a linear time-invariant system, whose end-to-end transfer function is used to upper-bound symbol error and outage probabilities in IM/DD optical OFDM transmission. The symbol error rate bounds predicted by the general analytical model are verified experimentally on a 10-Gb/s OFDM system with instantaneous DGD ranging between $Deltatau = 0$ and 120 ps . The outage probability bounds indicate that, if no RF guard bands are required, OFDM enables high-speed transmission with at least twice the PMD tolerance provided by an equivalent uncompensated OOK-based system at system outage probabilities $P_{{rm out, sys}}≪10^{-5}$ . If RF guard bands are required to mitigate effects of other distortions, it is shown that a penalty in the system PMD tolerance proportional to the intermediate RF subcarrier frequency, $f_{{rm RF}}$, is exerted. Consequently, a tolerance tradeoff exists in IM/DD OFDM systems, wherein $f_{rm RF}$ as well as baseband constellation size may be viewed as design parameters that can be optimized depending on specific system requirements.      

Generic error probabilities

This paper presents new forms for an error probability associated, with the phase angle between two vectors perturbed by Gaussian noise. An interesting consequence of the underlying generic form is a new expression for the symbol error rate in MDPSK that is very similar to its counterpart for MPSK. The generic error probability is further shown to contain as special cases MPSK, MDPSK, CPFSK, and digital FM; and to give a new expression for the Marcum Q-function. The generic error probability also simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK     

基于记忆因子的连续相位调制信号最大似然调制识别

为解决有记忆非线性的连续相位调制(CPM)信号调制方式识别精度低的问题,该文提出一种基于记忆因子的CPM信号最大似然调制识别新方法。该方法定义具有时齐马尔科夫性的映射符号,通过计算其后验概率构造记忆因子,进一步结合CPM分解和EM算法,推导出时间可分离,信道参数可估计的CPM信号似然函数。该调制识别方法所需符号数目少,适用信噪比范围广,识别CPM信号种类多且精度高,对相位误差鲁棒性强。仿真结果证明,当符号数目为200,信噪比为0 dB,相位误差任意时,该方法对8种CPM信号的识别率可达95%以上。     

A Novel Ternary CDMA Code for TPSK Modulation Scheme

In code division multiple access (CDMA), two or more chips are grouped together to form symbols and each symbol is transmitted during the symbol period. The phase shift keying (PSK) modulation techniques map the digital baseband data into two or more possible signals by varying the phase of a radio frequency (RF) carrier. The recently proposed PSK scheme called ternary PSK (TPSK) scheme can convey three possible symbols. In this paper, a novel ternary based CDMA sequence so-called large area synchronous even ternary (LAS-ET) sequence is introduced to increase spectrum efficiency in TPSK scheme. Its sequence duty ratio and cross-correlation are analyzed. The performance analysis of this sequence is compared with the large area synchronous (LAS) sequence in term of symbol error rate and chip error rate (CER) over various channel models. It is shown that TPSK scheme in LAS-ET sequence outperforms LAS sequence in terms of CER evaluation. At the same time, the spectrum efficiency is doubled when a pair of chips in LAS-ET sequence is mapped into one symbol.     

Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

A new viewpoint for adopting the lattice reduction in communication over multiple-input multiple-output (MIMO) broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided (LRA) precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior (signal-to-noise ratio (SNR) $longrightarrow infty$) of the symbol error rate for the LRA precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum rate is analyzed. It is shown that the LRA method, using the Lenstra–Lenstra–LovÁsz (LLL) algorithm, achieves the optimum asymptotic slope of symbol error rate (called the precoding diversity).      

A new approximation to the symbol error probability for codedmodulation schemes with maximum likelihood sequence detection

The power efficiency of coded modulation schemes in additive white Gaussian noise depends on the signal space distribution of their most common error events. Symbol error probability calculation allowing for the pairwise interaction of these error events is discussed. Two optimality criteria are considered for detectors. The first minimizes the probability of symbol error for each symbol decision. This is called the symbol-to-symbol detector. The second (which is superior) is the maximum likelihood sequence detector (MLSD). A lower bound for the symbol-to-symbol detector and an approximation to the MLSD symbol error probability are described. The theoretical performance difference between these two detectors is given. The results are more accurate than minimum squared Euclidean distance predictions, especially at low and intermediate signal-to-noise ratios. The MLSD symbol error probability approximation is obtained for considerably less cost than computer simulation and gives more insight into the signal space structure of the scheme being analyzed. Numerical results are presented for a continuous phase modulation (CPM) example     

Error rate analysis of MDPSK/CPSK with diversity reception undervery slow Rayleigh fading and cochannel interference

The distribution of the phase noise due to additive white Gaussian noise (AWGN) and cochannel interference (CCI) is analyzed for differential phase detection (DPD) and coherent phase detection (CPD) in a very slow nonfrequency selective Rayleigh fading environment. The effects of modulation timing offset between the desired signal and the CCI and of the overall channel filter response are considered. Simple closed-form expressions are derived for ideal selection diversity reception. The derived phase noise distributions are used for evaluating the bit error rate (BER) performance of 2-16DPSK/CPSK assuming square-root raised cosine Nyquist transmit/receive filters. It is found that the BER performance of CPSK is less sensitive to CCI modulation timing offset than DPSK, and that increasing the filter rolloff factor can improve the BER performance due to CCI. Finally, the accuracy of the BER approximation that uses the symbol error rate is discussed     

Differential phase noise distribution of Rayleigh faded DPSK signal with selection diversity

Closed-form expressions for the distribution of differential phase noise due to additive white Gaussian noise (AWGN) are derived for predetection selection diversity with independent, equal power very slow Rayleigh fading signals. Also investigated are the effects of fading correlation and unequal powers between diversity antennas on practical two-branch diversity reception. The derived phase distribution is used to calculate the average symbol error rate of 8 DPSK as an example.<>     

On the Binary DPSK Communication Systems in Correlated Gaussian Noise

Using the recently developed probability density function we obtain "directly" the error rate expressions for the binary differential phase-shift keyed (DPSK) systems when the noise values at the sampling instants in adjacent time slots are statistically dependent. Two cases are considered: One corresponding to equal SNR at each of the two sampling instants, and the other to unequal SNR's. The consideration of the former case, together with the assumption of unequal a priori symbol probabilities P0and P1results in an error rate expressionP_{E} =1/2[1 + (P_{0} - P_{1})rho] exp (-h^{2})where ρ is the noise correlation coefficient, and h²is the SNR. This expression shows clearly why PEis independent of noise correlation when the source symbols are equi-probable provided intersymbol interference is assumed absent. We then obtain the error probability expression in terms of unequal SNR's (at the two sampling instants) and the correlation coefficient ρ. Since intersymbol interference in a binary DPSK system gives rise to unequal SNR's, this expression provides a useful formula for estimating the system performance under such circumstances.     

Bit error rate of binary and quaternary DPSK signals with multipledifferential feedback detection

A differentially coherent detection scheme with improved bit error rate (BER) performance is presented for differentially encoded binary and quaternary phase shift keying (PSK) modulation. The improvement is based on using L symbol detectors with delays of 1, 2, . . ., L symbol periods and on feeding back detected PSK symbols. Exact formulas for the bit error probability are derived for the case that correct symbols are fed back. The effect of symbol errors in the feedback path on the BER is determined by computer simulations     

Importance Sampling Evaluation of Digital Phase Detectors With Carrier Phase Tracking: A Large Deviations Approach

This paper applies large deviations theory (LDT) to the design of efficient importance sampling (IS) simulation of $M$-ary digital phase detectors subject to random carrier phase drift within symbol interval. Phase tracking is accomplished by extended Kalman–Bucy filters or dedicated stochastic nonlinear filters. The LDT approach relies essentially on the properties of the receiver's error sets, which present unique topological features in an N-dimensional space. We show how to derive the referred topological properties for the particular phase modulating sequences and receiver solutions adopted. The proposed methodologies lead to very high simulation gains both for the assessment of the error floors induced by the random phase drift and for the scenarios where simultaneous random phase and channel noise preclude the derivation of the error regions.      

Further results on the bit error probabilities of MDPSK over thenonselective Rayleigh fading channel with diversity reception

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as π/2-2DPSK and π/4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems     

Analysis of minimum selection H-S/MRC in Rayleigh fading

We analyze the error performance of an improved hybrid selection/maximal-ratio combining (H-S/MRC) technique called minimum selection H-S/MRC in flat Rayleigh fading for coherent digital modulation schemes. Here the minimum number of diversity branches are selected such that their combined signal-to-noise ratio is above a given threshold. We derive a closed-form expression for the distribution of the number of selected branches. This distribution is used to obtain the symbol error probability.     

Optimal designs for space-time linear precoders and decoders

We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error     

Sample size required in error-rate measurement on fading channels

This paper presents analytical and numerical results on the sample size required to achieve a specified root mean square (RMS) error in estimating the error rate for flat fading channels having complex Gaussian statistics. The analysis shows that for the large sample sizes normally used in estimating error rates, k, the required sample size normalized to the required sample size for independent symbol fading, can be expressed in the form k=1+dβ where d is the symbol rate normalized to the Doppler spread of the channel. For a given modem, β is a function of the error probability and the order of diversity. It is shown that if the Doppler spread measure used is proportional to the RMS Doppler spread, P will be relatively insensitive to the shape of the Doppler power spectrum. Numerical results are presented for Lth order diversity reception of binary phase shift keying (PSK), differential PSK, and frequency shift keying (FSK) signals and for five different Doppler power spectra. Ideal maximal ratio combining is assumed for the PSK modem, and square law combining is assumed for the DPSK and FSK modems