Combined channel coding and constant amplitude continuous phase modulation

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.

Continuous phase modulation (CPM) is known for its attractive spectral properties. Furthermore, CPM has the property that the modulation signal maintains a constant envelope, so CPM is effective for satellite communications. Recently, generalized nonlinear CPM (GNCPM), which can achieve a larger minimum Euclidean distance than ordinary CPM, was introduced. In this paper, we propose a convolutional coded GNCPM to improve the bit error rate (BER) performance of uncoded GNCPM without expanding bandwidth. Combination CPM with convolutional coding causes an increased number of phase trajectory patterns which can cause the bandwidth expansion. Therefore, in our proposed model, to control the bandwidth, we pay attention to the phase trajectory pattern which is already owned by uncoded GNCPM and change the modulation index appropriately, depending on the input symbols, to keep the number of phase trajectory patterns the same as in uncoded GNCPM. First, we consider the most suitable assignment of the modulation index which can increase the Euclidean distances without bandwidth expansion. Next, we theoretically derive the upper bound on the error event probability of the proposed model in additive white Gaussian noise (AWGN). The performance of the proposed convolutional GNCPM, obtained by computer simulation, shows that the proposed model can improve BER performance without bandwidth expansion. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(8): 42–50, 1998

In the orthogonal frequency division multiplexing (OFDM) transmission system, when the digital symbols are transmitted in the wireless channel, it would be affected by a lot of noise interference due to the unsatisfactory condition characteristics of the wireless channel itself, therefore, the symbol error and bit error would be generated. To achieve a certain bit error rate (BER) under the condition of known signal-to-noise ratio (SNR), convolutional channel coding and block interleaver should be utilized to further reduce the BER. Moreover, convolutional code is almost utilized in all wireless communication systems. This paper proposes a convolutional code channel estimation method in multiple-input single-output (MISO)-based OFDM (MISO-OFDM) system with frequency-shift m-sequence (FSMS) as guard interval (GI) for avoiding inter-symbol interference (ISI). The proposed space-frequency block code (SFBC) MISO-OFDM system achieves higher transmit diversity gains and better BER performance. Simulation results verify that the proposed iterative threshold channel estimation (ITCE) method in octal representation generation vector (ORGV) convolutional code 4 × 1 MISO-OFDM system provides good BER and normalized mean squared error (NMSE) performance with significant coding gains in both static and dynamic multipath channels.

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. We focus on the ubiquitous inner differential encoder (used, in particular, to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum-likelihood (ML) coherently detected antipodal modulation over the additive white Gaussian noise (AWGN) channel for this construction are advantageous as compared to the stand-alone outer convolutional code. This is in spite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of an ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a rather dramatic decrease, as demonstrated here, in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand-alone convolutional code. The advantage of the examined serially interleaved concatenated code, given in terms of bit and/or block error probability which is decoded by a practical suboptimal decoder, over the optimally decoded standard convolutional code is demonstrated by simulations, and some insights into the performance of the iterative decoding algorithm are also discussed. Though we have investigated only specific constructions of constituent inner (rate 1) and outer codes, we trust, hinging on the rational of the arguments here, that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes.

A decomposition approach to continuous phase modulation (CPM), mostly due to the work of Rimoldi (1988), is significant in the design of combined coding and communication signaling scheme. In this paper the generalized decomposition model is developed and applies to the multi-h CPM. It is shown that any multi-h CPM can also be realized by a continuous phase encoder (CPE) concatenated with a memoryless modulator (MM). Moreover, depending on the manner that the modulation indexes are selected for each symbol interval, the CPE can be either a linear or nonlinear feedback convolutional encoder, in which both the CPE and MM are time-variant. Finally, some applications are employed to verify the advantage of the proposed decomposition model, namely, (1) natural trellis representation of the CPE for M-ary single-h CPM with different modulation indexes that have the same denominator P, (2) a reduction of the number of states of the MLSD receiver for conventional multi-h CPM, (3) asymmetrical multi-h CPM has no gain over conventional multi-h CPM, (4) nonlinear CPM has a CPE that is nonlinear.

The detection of convolutional codes over rings suitable for continuous phase modulation (CPM) are presented based on the Rimoldi's Decomposition of CPM. Because the ring convolutional codes are on the same ring as the inner codes of CPM, We can use reduced state sequence detection (RSSD) to analyze and detect the overall encoder. Numerical result shows the detection complexity of this RSSD is significantly reduced with a very small degradation in error performance.

The attractive properties of the digital constant amplitude modulation scheme CPM (continuous phase modulation) have been demonstrated in a previous paper in this journal.1 This concerned both the power and spectral efficiency of the large family of CPM schemes over the Gaussian channel.In this paper the considered channel can be both bandlimited or band‐ and amplitude‐limited at the same time. Analytical results as well as simulations are presented for a number of selected CPM schemes.In today's increasing demand for bandwidth, CPM is an attractive candidate for future satellite applications because of its spectral efficiency. In addition to this comes the fact that the transmitted signal has a constant amplitude and good detection performance when optimal coherent detection is performed.

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.

We consider the serial concatenation of a convolutional code and a continuous phase modulation separated by a random interleaver. It is shown that the continuous phase modulator has the same behavior as a recursive systematic convolutional code in serial turbo codes. The interleaver gain produced by the modulator and the random interleaving depends only on the minimum Hamming distance of the outer code. A soft-input soft-output detection algorithm is described and applied in an iterative joint detection-decoding scheme. Simulated performance over Gaussian and Rayleigh channels shows a dramatic gain over both uncoded modulation and classic detection.

Multi-h full response CPM (continuous-phase modulated) signals are analyzed at preselected numbers of states in contrast to the standard method of analyzing them at preselected numbers of modulation indices. Optimal multi-h phase codes which produce the highest minimum Euclidean distance are presented according to the number of states. Three orders of multi-h signaling are considered in the optimal code search. Numerical results are presented for binary CPFSK (continuous-phase frequency shift keying) and binary 1RC (1 raised cosine) signals at number of states from four through 12. >

The method of multiple trellis-coded modulation is applied to continuous phase modulation (CPM). Double trellis-coded quaternary CPM schemes using convolutional codes with an effective rate of 2/4 are considered. Tables of optimum codes and minimum Euclidean distances are given for several frequency impulses and ratios of trellis-branches-per-symbol-interval, which have to be processed by a Viterbi-decoder. The results are clearly superior to single trellis-coded schemes with 1/2-rate codes. These improvements are accomplished by a proper selection of double-channel symbols. This method also offers improved receiver implementation properties. For a further reduction of complexity, a modified decision-feedback-sequence estimation is proposed. >

Background theory and specific coding designs for combined coding/modulation schemes utilizing convolutional codes and continuous-phase modulation (CPM) are presented. In this paper the case of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r = 1/2</tex> coding onto a 4-ary CPM is emphasized, with short-constraint length codes presented for continuous-phase FSK, double-raised-cosine, and triple-raised-cosine modulation. Coding buys several decibels of coding gain over the Gaussian channel, with an attendant increase of bandwidth. Performance comparisons in the power-bandwidth tradeoff with other approaches are made.

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

Continuous phase modulation (CPM) has been widely used in telecommunication and aeronautical telemetry system due to its high power and spectral efficiency. Non-coherent detection is a kind of feasible CPM detection method if there is large phase noise or residual carrier frequency offset. Near-optimal non-coherent sequence detection, which is based on Viterbi algorithm, has a performance close to that of maximum-likelihood sequence detection (MLSD). However, near-optimal non-coherent detection of CPM is very complicated to be implemented, and it is even more difficult to achieve a high speed due to feedback in the process of calculating branch metrics, add-compare-select (ACS), updating the beginning phase and phase reference symbol. In this paper, we first review near-optimal non-coherent detection of CPM, and then we present a high speed design of FPGA implementation for near-optimal non-coherent detection of a 64 state, 4-ary, length-3T raised cosine (3RC) CPM on Xilinx XC7VX690T device. In our scheme, the frequency pulse truncation is used to simplify the CPM detection. We propose a feedback processing in parallel for different states of CPM trellis to achieve a low latency. Furthermore, we develop a recursive implementation architecture for the process of updating the beginning phase. We achieve the CPM bit rate of 25Mbps for the on-chip processing clock of 100MHz. The results of simulation shows near-optimal non-coherent detection performs much better the coherent detection when residual carrier frequency offset or phase noise exists. It is found that the implementation can achieve a degradation in the Eb/N0 from computer simulation of as small as 0.3 dB for an average BER=10-5.

The paper considers a wireless transmission system in a multiple-user environment. It involves a combination of non-binary convolutional codes with Continuous-Phase Modulation (CPM) for transmission in an uplink channel using the Frequency Division Multiple Access (FDMA) method. For a more efficient available band utilization, the distances between individual system user carriers are decreased. In order to reduce the bit error rate (BER) a concatenation of CPM with convolutional codes over a ring has been used and a low-complexity iterative algorithm for inter-carrier interference (ICI) cancellation was employed on the receiver side. BER results obtained in computer simulations are presented for the proposed solution.