Coherent continuous-phase frequency-shift keying: Parameter optimization and code design

Continuous-phase frequency shift keying (CPFSK) is a type of frequency shift keying (FSK) that maintains phase continuity from symbol to symbol. The bandwidth efficiency of a CPFSK waveform is characterized by its modulation index, number of frequency tones and channel coding rate. These parameters can be flexibly designed to meet different bandwidth and energy requirements in wireless communication systems. One special case of CPFSK, orthogonal FSK, could be applied when bandwidth constraints are loose. By increasing the number of frequency tones, the energy efficiency can be improved at the expense of spectral efficiency. In this dissertation, the general case of orthogonal FSK, orthogonal modulation is first studied. Capacity, convergence behavior and asymptotic error rates of coded orthogonal modulation are analyzed. In addition to coherent detection, we consider noncoherent detection as well, which is one benefit of CPFSK. More often, CPFSK is designed to achieve high spectral efficiency by reducing its modulation index. The general case of nonorthogonal CPFSK is then studied. Capacity, spectral efficiency and capacity approaching code design are discussed for both coherent and noncoherent CPFSK. In addition to the system design and information theoretic issues, channel estimation for noncoherent CPFSK is considered. An iterative channel estimation, demodulation and decoding algorithm is derived using the expectation maximization (EM) algorithm. Finally, we apply noncoherent CPFSK to frequency hopping (FH) networks, leveraging the results acquired throughout the dissertation. Simulations show FH networks with CPFSK modulation and channel estimation can achieve robust performance against partial-band and multiple-access interference.

An optical continuous phase FSK modulation scheme with an arbitrary modulation index over long-haul transmission fiber link

In this paper, in order to improve bit error performance, bandwidth efficiency and reduction of complexity compared to related schemes such as turbo codes, we combine low density parity check (LDPC) codes and continuous phase frequency shift keying (CPFSK) modulation and introduce a new scheme, called ‘low density parity check coded‐continuous phase frequency shift keying (LDPCC‐CPFSK)’. Since LDPC codes have very large Euclidean distance and use iterative decoding algorithms, they have high error correcting capacity and have very close performances to Shannon limit. In all communication systems, phase discontinuities of modulated signals result extra bandwidth requirements. Continuous phase modulation (CPM) is a powerful solution for this problem. Beside CPM provides good bandwidth efficiency; it also improves bit error performance with its memory unit. In our proposed scheme, LDPC and CPFSK, which is a special type of CPM, are considered together to improve both error performance and bandwidth efficiencies. We also obtain error performance curves of LDPCC‐CPFSK via computer simulations for both regular and irregular LDPC code. Simulation results are drawn for 4‐ary CPFSK, 8‐ary CPFSK and 16‐ary CPFSK over AWGN, Rician and Rayleigh fading channels for maximum 100 iterations, while the frame size is chosen as 504. Copyright © 2006 John Wiley & Sons, Ltd.

A combined source/channel coding and modulation technique is developed for the transmission of memoryless sources over an AWGN channel. Combined source/channel coding is implemented using the concepts of trellis coded quantization (TCQ) in conjunction with an Ungerboeck code defined for a continuous phase frequency shift keying (CPFSK) signaling scheme. The Viterbi algorithm is employed by the source encoder to find a minimum mean-square-error (MSE) path through the source code trellis. The resultant minimum distortion sequence is mapped to an appropriate set of CPFSK symbols for transmission. A mapping is pragmatically developed to simultaneously preserve the original branch labelings of both the source and channel code trellises. Source symbol recovery is performed by maximum likelihood sequence estimation. The total distortion is experimentally determined over a range of channel signal-to-noise ratios. Furthermore, it is demonstrated that the use of a CPFSK signaling scheme avoids the production of spectral line components in the transmitted waveform spectrum that are usually associated with joint source/channel coding schemes.

In this paper, we present a novel method to construct nonbinary irregular LDPC codes whose parity check matrix has only column weights of 2 and t, where t ¿ 3. The constructed codes can be encoded in linear time and in a parallel fashion. Also, they can achieve near-Shannon-limit performance over both AWGN and Rayleigh fading channels with a moderate field size. Analysis based on nonbinary EXIT charts is presented. Codes constructed by the proposed method with block lengths ranging from 1, 000 bits to 10, 000 bits are simulated. Simulation results show that codes of rate 1/2 and length 10, 000 bits can achieve block-error-rate (BLER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> within 1.1 dB and 1.3 dB away from the Shannon limits of the AWGN and Rayleigh channels, respectively. In an AWGN channel, codes of rate r = 8/9 and length around 4,000 bits can achieve BLER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> within 1.1 dB from the Shannon limit, while codes of rate r = 15/16 and length around 9,000 bits can achieve BLER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> within 1.0 dB from the Shannon limit. We conjecture that to further lower the error floor (e.g., to a BLER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-10</sup> ), a column weight no less than 3 is preferred and may be necessary, especially for codes with high rate and over Galois fields of small to moderate sizes.

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi-h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, Delta nu T. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at Delta nu T=1% and Delta nu T=2%, respectively, for M=4, 8, and 16.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In order to understand the optimal parameter settings of spectrally efficient continuous phase modulation (CPM), we elaborate on our previous work on numerically optimized CPM. An empirical model is developed based on an expression for the effective bandwidth of CPM, an approximate expression for the smallest Euclidean distances of spectrally efficient CPM and observed properties of the numerically optimized phase pulses. We find that the optimized phase pulses, which resulted from a joint optimization of modulation index and phase pulse, share common properties for different alphabet sizes and different spectral efficiencies. These properties are described by three phase pulse parameters, and we show that they attain approximately equal values at the so-called saturation length. The model can predict the minimum Euclidean distance at the saturation length for a CPM system using an even-integer alphabet and jointly optimized modulation index and phase pulse, and it partly extends to less spectrally efficient CPM systems.

In this paper, we mainly studied the coding and decoding principles of convolutional codes and turbo codes and verified the coding and decoding process and bit error rate performance of the two codes. In different channel conditions (AWGN and Rayleigh fading channels), with different code rates (1/2 code rate and 1/3 code rate), the convolutional codes with different constraint lengths (3 and 7) and turbo codes are simulated and compared. We can know from the simulation results that the performance of the two codes in AWGN channel is better than that in Rayleigh channel. In these two channels, the performance of the two codes with small bit rate is better than that of the ones with large bit rate; the performance of turbo codes improves with the increase of the constraint length. The performance of convolution code decreases with the increase of the constraint length when the SNR is small, but it improves with the increase of the constraint length when the SNR is large.

Irregular-repeat-accumulate (IRA) codes are random-like codes having extremely good performance over AWGN channel. They can be viewed as special kinds of LDPC codes in the way their parity-check matrix are sparse. Like LDPC codes, they can be decoded using the messages-passing algorithm efficiently, while the existence of short length circles in their corresponding factor graph representation has a deleterious effect on the BER performance of the codes. Progressive edge-growth (PEG) algorithm is a famous method to construct factor graph without short circles. In this paper, we use PEG algorithm to construct the parity-check matrix of IRA codes firstly, and then deduce the interleaver design of the codes. Experimental results show significant improvement on the BER performance of the IRA codes with designed interleaver over the IRA codes with randomly choose interleaver.

In Forward Error Correction (FEC), redundant bits are added for detecting and correcting bit error which increases the bandwidth. To solve this issue we combined FEC method with higher order M-ary modulation to provide a bandwidth efficient system. An input bit stream is mapped to a bi-orthogonal code on different levels based on the code rates (4/16, 3/16, and 2/16) used. The jamming attack on wireless networks are mitigated by Chaotic Frequency Hopping (CFH) spread spectrum technique. In this paper, to achieve better data rate and to transmit the data in a secured manner we combined FEC and CFH technique, represented as Code and Chaotic Frequency Modulation (CCFM). In addition, two rate adaptation algorithms namely Static retransmission rate ARF (SARF) and Fast rate reduction ARF (FARF) are employed in CFH technique to dynamically adapt the code rate based on channel condition to reduce a packet retransmission. Symbol Error Rate (SER) performance of the system is analyzed for different code rate with the conventional OFDM in the presence AWGN and Rayleigh channel and the reliability of CFH method is tested under different jammer.

Relay selection is crucial in improving the performance of wireless cooperative networks. Most of previous works for relay selection use the current observed channel conditions to make the relay selection decision for the subsequent frame. However, this assumption is often not realistic given the time-varying nature of some mobile environments. In this paper, we consider finite state Markov channels in the relay selection problem. Moreover, we also incorporate adaptive modulation and coding, as well as residual relay energy in the relay selection process. The objectives of the proposed scheme are not only to increase spectral efficiency, mitigate error propagation, but also to maximize the network lifetime. Simulation results are presented to show the effectiveness of the proposed scheme.

Orthogonal frequency division multiplexing with subcarrier index modulation (SIM-OFDM) is recently proposed to enhance the performance of traditional OFDM. By incorporating the index modulation in OFDM, the data can be sent on the indices of subcarriers as well as the subcarriers themselves reducing the system complexity. In addition, the Peak to Average Power Ratio (PAPR) and Inter Carrier Interference (ICI) can be reduced by switching on /off some OFDM subcarriers in OOK fashion. In this paper, a comparative study of OFDM with SIM_OFDM and Enhanced SIM_OFDM methods in terms of complexity, spectral efficiency and bit error rate over AWGN channel using two power policies is presented. The simulation results showed that at bit error rate of 10-3, SIM_OFDM and ESIM_OFDM achieved gains in Eb/No of 1.1 dB and 2 dB over 4-QAM OFDM respectively under power reallocation policy. However, the results also showed that traditional OFDM has better spectral efficiency compared to both SIM_OFDM and ESIM_OFDM especially at high M-ary orders.

After the vision and the overall objectives of future wireless networks for 2020 and beyond have been defined, standardization activities for fifth generation (5G) wireless networks have been started. Although it is expected that 5G new radio (NR) will be based on cyclicly prefixed orthogonal frequency division multiplexing (CP-OFDM)-based waveforms along with multiple waveform numerologies, the sufficiency of CP-OFDM-based NR is quite disputable due to the continuing massive growth trend in number of wireless devices and applications. Therefore, studies on novel radio access technologies (RATs) including advanced waveforms and more flexible radio accessing schemes must continue for future wireless networks. Generalized frequency division multiplexing (GFDM) is one of the prominent non-CP-OFDM-based waveforms. It has recently attracted significant attention in research because of its beneficial properties to fulfill the requirements of future wireless networks. Multiple-input multiple-output (MIMO)-friendliness is a key ability for a physical layer scheme to satisfactorily match the foreseen requirements of future wireless networks. On the other hand, the index modulation (IM) concept, which relies on conveying additional information bits through indices of certain transmit entities, is an emerging technique to provide better spectral and energy efficiency. In this paper, considering the advantages of non-CP-OFDM-based waveforms and the IM concept, we present a framework, which integrates GFDM with space and frequency IM schemes to provide flexible and advanced novel RATs for future wireless networks. Several MIMO-GFDM schemes are provided through the proposed framework and their bit error ratio performances, computational complexities, and spectral efficiencies are analyzed. Based on the obtained results, a guideline for selecting the proper MIMO-GFDM scheme considering target performance criterion is given. It has been demonstrated that the proposed framework has a strong potential to engineer the space-frequency structure according to channel conditions and use cases, and it provides a great flexibility that can be easily tuned to address the required performance criterion.

Multicarrier transmission techniques like multicarrier code division multiple access (MC-CDMA) is the strongest contender for the future generation wireless networks which is supposed to cater to the need of very high data rate with mobility and at the same time combat multipath and intersymbol interference in a spectrally efficient manner. To enhance the spectral efficiency further, some form of adaptive modulation is being proposed (Wasantha et al. (2002)). In this paper, first of all, we simulate the performance of various single-h continuous phase modulation (CPM) schemes in an MC-CDMA system by varying the two CPM parameters - size of symbol alphabet (M) and modulation index (h). The parameter sets considered are {M=2, h=0.5}, {M=2, h=0.875}, {M=4, h=0.5} and {M=4, h=0.875}. Simulation results show that the higher order modulation schemes (M=4) need better channel conditions than the lower order schemes (M=2) for a given bit error rate (BER). Moreover, as expected (Xiong (2000)), h=0.875 (approximate optimum value) gives a better BER performance than h=0.5 for a given BER. Based on these simulation results, we then design two adaptive modulation based systems, one considering h=0.5 and the other with h=0.875, each with M=2 and 4. Results of the adaptive systems clearly indicate that the adaptive switching of the modulation formats in each of these two systems increases the system capacity per given bandwidth (spectrum efficiency) effectively without sacrificing the expected BER performance. Also, it is seen that the adaptive system with h=0.875 is superior to the h=0. 5 system, both in terms of BER performance and the number of simultaneous users, but obviously at the cost of reduced bandwidth efficiency as higher the value of h, the higher bandwidth it requires.