EXIT-based evolutionary optimization of continuous phase modulation waveforms

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

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.

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.

Existing space-time codes have focused on multiple- antenna systems with linear modulation schemes such as phase- shift keying and quadrature amplitude modulation. Continuous phase modulation (CPM) is an attractive scheme for digital transmission because of its constant envelope which is needed for power efficient transmitters. Recent research has shown that space-time coded CPM can achieve transmit diversity to improve performance while maintaining the compact spectrum of CPM signals. However, these efforts mainly combine space- time coding (STC) with CPM to achieve spatial diversity at the cost of a high decoding complexity. In this paper, we design space-time block codes (STBC) for binary CPM with modulation index h = 1/2 and derive low-complexity receivers for these systems. The proposed scheme has a much lower decoding complexity than STC CPM with the Viterbi decoder and still achieves near-optimum error performances.

Constant envelope and high spectral efficiency are among the key properties which make continuous phase modulation (CPM) a preferred choice for many applications. Numerous methods are available for designing concatenated CPM systems to achieve additional coding gains. In this paper, we propose a new serial concatenated CPM scheme. Our design uses a multi-alphabet binary CPM as an inner code, a modified turbo code as an outer code, and specially designed interleavers. The extrinsic information transfer (EXIT) chart technique has been employed to assist the outer code design. Using soft decision decoding, we show that our design gives noticeable improvements compared with previous concatenated CPM schemes over additive white Gaussian noise (AWGN) channel.

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

Frequency-domain equalization for continuous phase modulation (CPM) is investigated. A discrete representation of the CPM signal is obtained by using the Gram-Schmidt orthonormalization procedure. The CPM discrete signal representation admits frequency-domain equalization for the purpose of mitigating intersymbol interference. General full- and partial-response CPM waveforms, and specific examples of MSK and GMSK with BT=0.3 are considered. Frequency-domain equalization is shown to be effective for CPM on severe frequency-selective fading channels.

The purpose of this paper is to provide a detailed description and experimental and simulated performance results for some of the current Raytheon satcom high efficiency tactical waveforms, namely the dual-h quaternary continuous phase modulated (CPM) waveforms and the shaped phase shift keying (SPSK) waveforms. The emphasis is on the performance in terms of adjacent channel interference (ACI), bit error rate (BER), coding gain over conventional waveforms, and the ability of the radio to acquire these waveforms while being subjected to a Doppler frequency of /spl plusmn/1200 Hz. This paper first introduces the mathematical representation of the dual-h quaternary CPM waveform. Then the principle of the data demodulation including carrier and symbol timing acquisition and tracking using the MIL-STD-188-181B-specified preamble is illustrated. Finally, with the use of computer simulations, the spectral envelope and bandwidth efficiency of these efficient waveforms are compared to conventional counterparts.

This paper considers the performance of a speech transmission scheme with application to cellular digital mobile radio systems. The source coder is embedded DPCM and modulation scheme belongs to a class of Partial Response Continuous Phase Modulation Both quantizing noise and transmission errors contribute to the overall mean squared error. The performance measure is audio signal to noise ratio. It is seen that in a fading environment space diversity is very effective in bringing down the threshold of channel signal to noise ratio to maintain the required audio signal to noise ratio. The number of channels the system can support is evaluated under various conditions.

The performance of constant envelope digital partial response continuous phase modulation (PRCPM) with two-bit differential detection and offset receiver diversity is theoretically analyzed in fast Rayleigh fading AWGN (additive white Gaussian noise) channels. A simple closed-form expression for the probability of error is derived and evaluated for cases of practical interest to researchers and designers of land mobile radio systems. It is shown that the dynamic BER performance is considerably improved using the offset diversity scheme. Thus, many new PRCPM signals having compact power spectra can be used in future mobile radio systems. >

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.

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.

Summary form only given. Future mobile radio systems are expected to provide high-quality voice and high-speed data transmission and to be integrated into the digital communication networks in several countries. The performance of some digital modulation techniques that are relevant for future mobile radio systems is studied. These techniques are characterized by having a constant envelope signal to reduce the effect of nonlinearity and fading and a compact RF power spectrum to reduce adjacent channel interference. Most digital partial-response continuous-phase modulation (PRCPM) techniques such as 2 RC, 2 SRC, 2 RC, 3 SRC, GMSK, and GTFM have the above properties. Discriminator detection of these techniques is analyzed in fast Rayleigh fading characterizing land mobile radio channels. Approximate closed-form expressions for the probability of error are derived and numerical results are presented for land mobile radio systems. >

Continuous phase modulation (CPM) with noncoherent detection over a one-symbol interval is discussed. In order to obtain good performance with this simple demodulation strategy, the phase function of the modulation scheme has to be designed properly. An approach to shaping the purchase function to achieve noncoherent orthogonal performance for various values of the modulation index (h) is presented. Using the Gram-Schmidt orthogonality procedure, an entire family of orthogonal phase functions for h>or=0.68 is derived. All CPM schemes with these phase functions produce the same performance as noncoherent orthogonal signaling. For h=1 the phase function reduces to that of the FSK phase function. It is shown that there are CPM schemes that give the same SNR performance as noncoherent orthogonal FSK but have some spectral advantages over the FSK modulation format. >

We introduce a space-time (ST) continuous phase modulation (CPM) and its companion noncoherent receiver. Through careful selection of an underlying differential code, the defining characteristics of the CPM transmissions are effectively maintained. Using a set of interference suppressed statistics and taking advantage of the ST differential encoding, the receiver first performs low complexity block detection. Channel estimates are then obtained at a rate notably higher than the CPM symbol rate, enabling a second-stage coherent sequence detector to refine the initial decisions. Simulation results for two CPM formats, with two and four transmit antennas, validate the proposed ST-CPM scheme.