Performance of joint multilevel/AES‐LDPCC‐CPFSK schemes over wireless sensor networks

In wireless sensor networks, data encryption and channel coding are considered together for ensuring secure and robust communication. In order to achieve this purpose, we introduce a new joint scheme, namely ‘Multilevel/Advanced Encryption Standard‐Low Density Parity Check Coded‐Continuous Phase Frequency Shift Keying (ML/AES‐LDPCC‐CPFSK)’. AES algorithm is the most powerful and widely used symmetric key cryptography in providing secure data transmission. LDPC codes have very large Euclidean distance and use iterative decoding algorithms. In this study, we have increased error performance employing multilevel structure to AES and LDPC. In all communications systems, phase discontinuities of modulated signals result in extra bandwidth requirements. CPFSK, which is a special type of continuous phase modulation, is a powerful solution for this problem. In this paper, we simulate error performance of ML/AES‐LDPCC‐CPFSK for regular LDPC codes. Simulation results are drawn for 4CPFSK, 8CPFSK and 16CPFSK over wireless cooperative sensor networks. Using this scheme, we are able to improve bit error performance, channel throughput, security level of communication and reduction in complexity compared with related schemes such as various turbo code structures. Copyright © 2009 John Wiley & Sons, Ltd.     

一种差分高阶调制联合LDPC编码方案及其FPGA实现

针对复杂环境中通信系统误码率高和硬件实现复杂度高的问题,提出基于正交频分复用( Orthogonal Frequency Division Multiplexing, OFDM)时域差分和 16 进制幅度差分相移键控( 16 Multilevel Differential Amplitude and Phase Shi...     

Blind equalization of multilevel turbo coded‐continuous phase frequency shift keying over MIMO channels

In this paper, multilevel turbo coded‐continuous phase frequency shift keying (MLTC‐CPFSK) is introduced and its bit error performance in multiple input multiple output (MIMO) fading channels are investigated considering a blind maximum likelihood channel estimation. Multilevel turbo coded signals with continuous phase modulation (CPM) provides low spectral occupancy and is suitable for power and bandwidth‐limited channels. Besides, antenna diversity is one of the best method to combat with multipath fading effects. The performance of 2LTC for 4‐ary CPFSK over AWGN, Rician (for Rician channel parameter K=10 dB) and Rayleigh channels are given for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations. Channel capacities of 2LTC‐4CPFSK signals are obtained as ?5.26, ?7.65 and ?7.14 dB for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations, respectively. Baum–Welch (BW) algorithm is used to estimate the channel parameters. Bit error probabilities of 2 level turbo coded 4 CPFSK (2LTC‐4CPFSK) are drawn in the cases of no channel state information (CSI), BW estimation, and perfect CSI. Approximately 0.1 and 0.75 dB gains in E_s/N₀ are obtained using BW channel estimator for Rician and Rayleigh channels, respectively. Therefore, MLTC‐CPFSK with BW channel estimator has excellent performance in MIMO fading channels. Copyright © 2006 John Wiley & Sons, Ltd.     

M-ary nonlinear continuous phase frequency shift keying

The authors present a new approach for designing a continuous phase frequency shift keying (CPFSK) system which is a nonlinear mapping of the M-ary symbols into the N-ary CPFSK. Using this approach they have designed an M-ary nonlinear CPFSK (NCPFSK) system of simple structure. The proposed M-ary NCPFSK system is a modification of the multi-h CPM (MHCPM) scheme. The proposed modulation gives improved performance over conventional modulation schemes     

基于LDPC码的无线光通信副载波误码性能分析

为了研究信道编码技术对无线光通信副载波系统差错性能的影响,基于无线光通信链路噪声特性,建立了大气信道等效数学模型。采用低密度奇偶校验(LDPC)码作为信道编码方式引入无线光通信,在不同光强闪烁指数下对基于副载波相移键控调制无线光通信系统进行了差错性能仿真,比较分析了LDPC编码前后副载波调制系统的误比特率,并对二相相移键控及四相相移键控两种系统进行了对比。结果表明,副载波二相相移键控调制系统的差错性能优于四相相移键控系统,同时LDPC码在弱湍流信道具有优越的纠错能力,可以获得比未编码系统较高的编码增益,在无线光通信领域具有一定的应用价值。     

Partitioning of spreading sequences for increased minimum distanceusing CPFSK modulation

By using continuous-phase frequency shift keying (CPFSK) in a direct-sequence code-division multiple-access (DS-CDMA) system, and by partitioning the spreading sequence so that differing patterns of plus and minus chips are multiplied onto successive data bits, the net phase change will differ from bit to bit, giving an apparent variation in modulation index similar to multi-h CPFSK. This gives similar coding gain effects as multi-h CPFSK when maximum-likelihood sequence detection is used. Improved probability of error performance in terms of increased minimum distance has been demonstrated when the spreading sequence of a CDMA system is properly overlaid on outgoing data bits in the CPFSK modulation scheme. At the best modulation index observed, h=5/7, a computer search shows ~1.4-dB advantage over binary phase shift keying, and a ~0.6-dB advantage over the best fixed-h CPFSK     

软切换链路下的混合编码与副载波调制方案

为了提高自由空间光/射频（FSO/RF）混合通信链路的性能，采用混合低密度奇偶校验（LDPC）编码与副载波相移键控/正交振幅调制（PSK/QAM）联合调制的方法，对不同传输比例下混合系统的误比特率性能进行了仿真分析，取得了不同信道条件下单链路和混合链路传输方案的误比特率数据。结果表明，在弱中强湍流条件下采用副载波二进制相移键控（BPSK）调制，相比开关键控（OOK）调制可获得大约4.4dB~5.2dB的增益。采用软切换的混合LDPC编码与副载波BPSK/16QAM调制方案，依据链路状态调整比例为1:1和3:1时，不同湍流强度下可获得大约0.3dB~7.4dB的性能增益。这一研究结果对于提高FSO/RF混合通信系统的全天候高效可靠传输性能具有重要的参考价值。     

Design of serial concatenated MSK schemes based on density evolution

We consider the design of convolutional codes and low density parity check (LDPC) codes with minimum-shift keying (MSK) when the receiver employs iterative decoding and demodulation. The main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum-likelihood decoding. We first show that the design is crucially dependent on whether the continuous phase encoder (CPE) is realized in recursive form or in nonrecursive form. We then consider the design of convolutionally coded systems and low density parity check codes with MSK to obtain near-capacity performance. With convolutional codes, we show that it is possible to improve the performance significantly by using a mixture of recursive and nonrecursive realizations for the CPE. For low density parity check codes, we show that codes designed for binary phase shift keying are optimal for MSK only if the nonrecursive realization is used; for the recursive realization, we design new LDPC codes based on the concept of density evolution. We show that these codes outperform the best known codes for MSK and have lower decoding complexity.     

Data to frequency mappings in various MSK schemes

Minimum shift keying (MSK) is a digital modulation scheme which is suited to demanding applications requiring good bandwidth efficiency and error performance. It can be regarded as continuous phase frequency shift keying (CPFSK) with two signalling frequencies. In general, there is no unique mapping from the input data polarity to the particular signalling frequency during a given bit interval. The simplest formulation maps zeros of the data (marks) to the lower frequency, and ones (spaces) to the higher frequency. Other formulations of MSK employ more complex mappings. The article summarises the most commonly encountered mappings, then shows how to convert from one formulation to another by manipulating the input or output data. It is, therefore, possible to establish communication between different MSK modems employing different formulations of MSK by simple processing of the data     

An improved algorithm for evaluating trellis phase codes (Corresp.)

A method is described for evaluating the minimum distance parameters of trellis-phase codes, including continuous phase frequency shift keying (CPFSK), partial-response FM, and, more importantly, coded continuous-phase modulation (CPM) schemes. The algorithm provides dramatically faster execution times and smaller memory requirements than previous algorithms. Results of sample calculations and timing comparisons are included.     

Serially concatenated continuous phase modulation with iterativedecoding

Serially concatenated and interleaved continuous phase modulation (CPM) with iterative decoding is investigated. An a posteriori probability (APP) algorithm for CPM is developed based on the classic APP algorithm for channel codes. The system is analyzed through upper bounds on the average bit error probability. For coded and interleaved minimum shift keying, the weight spectrum is computed, resulting in a transfer function bound. This is cumbersome for a general CPM system; instead, only the most significant error events contributing to the weight spectrum are identified. Simulations show that, firstly, these events give a satisfactory view of system performance when equal outer codes are used, and secondly, that remarkably good performance can be obtained for some simple systems. Finally, power spectral densities and bandwidths are computed, allowing for a bandwidth/performanee comparison of different combinations     

Fractional Multi‐bit Differential Detection Technique for Continuous Phase Modulation

A new low‐complexity differential detection technique, fractional multi‐bit differential detection (FMDD), is proposed in order to improve the performance of continuous phase modulation (CPM) signals such as Gaussian minimum shift keying (GMSK) and Gaussian frequency shift keying (GFSK). In comparison to conventional one‐bit differential detected (1DD) GFSK, the FMDD‐employed GFSK provides a signal‐to‐noise ratio advantage of up to 1.8 dB in an AWGN channel. Thus, the bit‐error rate performance of the proposed FMDD is brought close to that of an ideal coherent detection while avoiding the implementation complexity associated with the carrier recovery. In the adjacent channel interference environment, FMDD achieves an even larger SNR advantage compared to 1DD.     

基于椭圆球面波信号的连续相位调制及其频谱性能分析

椭圆球面波信号（PSWF）是时频域最佳能量聚集性信号,探索性地将PSWF信号应用于连续相位调制（CPM）技术,对基于椭圆球面波信号的CPM调制信号产生过程进行了描述;给出了采用自相关函数法对基于PSWF的CPM调制信号功率谱密度计算方法;结合数值计算、分析对比了最小频移键控、正弦频移键控、高斯最小频移键控以及基于高斯函数的CPM调制信号功率谱密度及其信号占用带宽等特性。数值计算结果表明椭圆球面波信号相比矩形脉冲、升余弦脉冲、高斯脉冲及（类）高斯脉冲作为CPM的基带调频信号,可以获得频谱性能、能量聚集性较好的CPM信号。     

Nonlinear continuous phase frequency shift keying

A novel signal-space coded CPM (continuous phase modulated) signaling technique, called nonlinear CPFSK (continuous phase frequency shift keying) signaling, which guarantees the maximum constraint length allowed by the number of states is introduced. Nonlinear CPFSK signals use a suitably selected state transition matrix during all signaling intervals. The selected state transition matrix is realized by changing the modulation index of the signals, hence the modulation index used during any interval depends on the transmitted symbol as well as on the state of the system. Binary nonlinear CPFSK signaling schemes are constructed and analyzed. Numerical results indicate that nonlinear CPFSK signals can achieve attractive minimum distances compared with other existing CPM signaling formats     

Improved mapping policy for reducing error coefficient in CPFSK signals

An improved mapping policy is introduced that alternates between standard and inverted bit mapping functions at selected phase states to reduce the error coefficient of continuous phase frequency shift keying (CPFSK) signals. The proposed policy can be applied to many different forms of CPFSK signals. It is demonstrated that the mapping policy can significantly improve performance, particularly at lower to moderate SNR values.     

Design of Quasi‐Cyclic Low‐Density Parity Check Codes with Large Girth

In this paper we propose a graph‐theoretic method based on linear congruence for constructing low‐density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ)‐regular quasi‐cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit‐error‐rate performance with iterative decoding in additive white Gaussian noise channels.     

Semi‐random LDPC codes for CDMA communication over non‐linear band‐limited satellite channels

This paper considers the application of low‐density parity check (LDPC) error correcting codes to code division multiple access (CDMA) systems over satellite links. The adapted LDPC codes are selected from a special class of semi‐random (SR) constructions characterized by low encoder complexity, and their performance is optimized by removing short cycles from the code bipartite graphs. Relative performance comparisons with turbo product codes (TPC) for rate 1/2 and short‐to‐moderate block sizes show some advantage for SR‐LDPC, both in terms of bit error rate and complexity requirements. CDMA systems using these SR‐LDPC codes and operating over non‐linear, band‐limited satellite links are analysed and their performance is investigated for a number of signal models and codes parameters. The numerical results show that SR‐LDPC codes can offer good capacity improvements in terms of supportable number of users at a given bit error performance. Copyright © 2006 John Wiley & Sons, Ltd.     

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     

Soft-decision differential phase detection of turbo-coded M-ary CPFSK signals over Ricean channels

The performance of turbo codes is examined over the Ricean fading channel with soft-decision differential phase detection (DPD). M-ary continuous phase frequency-shift keying (CPFSK) signaling and puncturing of the coded sequence are considered to achieve bandwidth efficient communication. The effects of the number of phase decision regions, fading conditions, number of states of the constituent codes, and code rate are examined. A bit error rate upper bound is developed, which is useful at low values of bit error probability where computer simulations are lengthy. Significant gains using soft-decision DPD over hard-decision DPD and conventional noncoherent detection are reported.     

Space Time Codes for CPFSK With Arbitrary Number of Receive Antennas

In this letter, space time (ST) trellis codes are developed for systems with an arbitrary number of receiver antennas in quasi-static fading channels applying M-ary continuous phase frequency shift keying (CPFSK) modulation with M = 4 and 8 for h = 1/M. The maximizing minimum squared Euclidean distance criterion (MMSEDC) is applied in the code search algorithm when obtaining the ST codes. The results show that a significant performance gain can be obtained by using the ST codes from the MMSEDC code search algorithm compared to the ST codes obtained in X. Zhang and M.P. Fits (2003) for CPFSK modulation systems