Tamed Frequency Modulation Research Articles

Receiver structure and estimation of the modulation index for tamed frequency modulated (TFM) signals

Tamed frequency modulation (TFM) is a spectrally efficient constant amplitude continuous phase modulation (CPM) scheme which can be simply realized by using a frequency modulator (FM). In the implementation the modulation index of TFM is calibrated to have a nominal value of 0.5, but due to temperature variations it can drift causing time varying phase jitter. In this paper we present novel algorithms and performance results to measure and control the modulation index in a coherent receiver based on the joint reduced state sequence detector (RSSD) and per-survivor processing (PSP) carrier phase estimation. The modulation index estimator measures phase transitions in the receiver and derives estimates by comparing the result to the coding rule of the TFM signal. The estimator has acquisition and tracking ability, and the current estimate can be used to replace the nominal index value. Our simulation results show that the proposed coherent receiver with the novel modulation index estimator has less than 1 dB performance degradation compared to around 4.5 dB exploiting only the PSP carrier phase estimation.

Separable TFM signal and its equivalence principle

It is proved that tamed frequency modulation (TFM) is a phase-separable continuous phase modulation (CPM) signal, and its equivalence principle is deduced. A TFM demodulator with parameters M, L, h is equivalent to a CPM demodulator with parameters M1=5, L1=1, h1=h/3.

Tamed frequency modulation detection analysis with NEC receivers

Various PSK modulations as well as minimum shift keying (MSK) have achieved great improvements in the signal-to-noise ratio by utilising the nonredundant error correction (NEC) technique. The cost for this improvement is neither an increase in bandwidth nor an increase in transmission power, but some extra complexity in the receiver. The receiver is only equipped with a bank of differential detectors and a simple error detection/correction circuit, whose complexity depends on the correction capability that the transmit–receive system must have. Here, it is proved that it is possible to differentially detect correlative, nonsymmetric continuous-phase frequency modulations such as tamed frequency modulation (TFM) with NEC receivers. TFM has not been used as much as MSK until now owing to its generation difficulties, but its main advantages of constant envelope and of very high spectrum efficiency make it a perfect candidate to work upon. Hence, TFM is first contaminated with additive white Gaussian noise and is subsequently detected through a single-error-correcting NEC receiver. Both the theoretical analysis and the computer simulations show that substantial error probability reduction is achieved over differentially detected TFM systems.

Generalized concatenation of encoded tamed frequency modulation

A novel construction for encoded tamed frequency modulation (TFM) is introduced which is based on the principles of generalized concatenation. The inner TFM is partitioned into nested subsystems which increases the free Euclidean distances. In order to obtain a large distance among the nested TFM subsystems, the scrambler matrices have to be computed which transfer the original TFM into the equivalent TFM with better partitioning properties. Then outer convolutional codes with different error-correcting capabilities are used to protect the partitioning. The new concatenated and generalized concatenated constructions were simulated in an additive white Gaussian noise channel. A multistep decoding algorithm based on soft-output demodulation was used. We present various simulation results which show a significant coding gain in comparison with the best known trellis codes having the same trellis state complexity.

A GMSK Compatible Modulation with Improved Spectral Properties

For the controlled spectral shaping of modulation methods similar to Minimum Shift Keying (MSK), Gaussian filtered Minimum Shift Keying (GMSK) and Tamed Frequency Modulation (TFM), three optimization approaches with different degrees of intersymbol interference and envelope fluctuations are discussed. For a frequency division multiplex transmission with a bitwise correlating receiver, a weighting function for the transmitter's power spectral density which is a good measure for the Bit Error Rate (BER) caused by Adjacent Channel Interference (ACI) is proposed. Its application to a separate or also joint optimization of the transmitter and the receiving filter reducing ACI power by roughly 20 dB is presented. For a given receiving filter, a compatible modulation that outperforms GMSK in both bandwidth and power efficiency can be designed.

Reduced-complexity detection and phase synchronization of CPM signals

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes, expressed in terms of the number of matched filters and states of a Viterbi algorithm, is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes do not require an increased number of matched filters, and are perfectly suitable to be used in conjunction with these receivers. Based on the phase-locked loop (PLL) equivalent linear model, a method for optimizing the parameters of digital second-order PLL's is presented. Numerical examples, based on theoretical analysis and computer simulation, are provided for two specific formats in the CPM class: tamed frequency modulation (TFM) and a quaternary raised-cosine (RC) modulation.

Simple baseband synchronisation schemefor tamed frequency modulation

A novel carrier and clock synchronisation scheme for tamed frequency modulation is presented. It requires one complex sample per bit, like the digital Costas loop for offset in-phase and quadrature modulations, and is based on processing baseband samples of the phase of the received signal. The performance of the synchroniser is assessed by S-curves and simulated acquisition trajectories.

Optimization of trellis coded TFM via matched codes

A matched code is a convolutional code chosen in such a way that when combined with modulation with memory the resulting receiver for the coded modulation has the smallest possible number of states. In the paper, the matched coding technique is applied to coded tamed frequency modulation (TFM) schemes and a formal procedure is developed to find the best combination of a code and a modulation. The optimization criterion is the maximum free Euclidean distance for a given code rate and a given number of states in the Viterbi receiver used for the coded modulation. A search for the best codes was carried out for code rates 1/2 and 2/3, and for receivers with up to 256 and 64 states, respectively. Good coding gains (more than 7 dB for rate 1/2) were achieved. Some of the best codes were catastrophic, yet the coded modulation was not. The codes obtained using the matched coding approach were in many cases better than those obtained using traditional optimization techniques. >

Multiple differential detection of continuous phase modulation signals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B/sub 1/T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Differential detection of correlative encoded continuous phase modulation schemes using decision feedback

We generalise a differential detection technique, introduced elsewhere for a Gaussian minimum shift keying (GMSK) scheme, to include any correlative encoded continuous phase modulated (CECPM) signalling format. The proposed symbol-by-symbol receivers employ decision feedback to partially remove the effects of the destructive intersymbol interference (ISI) which corrupts the differentially detected CECPM signal. After achieving wider eye opening with the decision feedback, the outputs of the two or more differential detectors are jointly utilised to further improve the performance. As a typical example of the CECPM family of signals and because of its excellent spectral characteristics, the new receiver configurations employing up to 3-bit differential detectors have been applied to a tamed frequency modulation (TEM) signal. Bit error rate (BER) performance evaluation results have indicated that performance improvements of more than 5 dB (at BER = 10-4) over a conventionally differential detected TFM scheme are possible. As compared with a limiter/discriminator receiver employing maximum likelihood sequence estimation (MLSE), the proposed receivers offer gains of more than 2 dB(at BER = 10 -4).

Symbol synchronization for digital signals with multisegment trajectory: digital data transition tracking loop

The symbol synchronizer presented is an all-digital data transition tracking loop which permits simple implementation and voltage control of the loop bandwidth. The equivalent loop integration constant is changed by changing the threshold level of a comparator at the output of the loop phase error detector. Phase error probability distribution function, its variance, and the average probability of cycle slipping are analyzed analytically for the general case. The theory of finite Markov chains is used to analyze statistical properties of the tracking error, primarily with regard to the phase error distribution and its variance, the average probability of the cycle slipping, the synchronizer time response, and bandwidth. As an example, numerical results for generalized tamed frequency modulation (GTFM with B=0.62 and r=0.36) are presented and discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model of error generation in tamed frequency modulation

In digital communication systems a knowledge of the transmission error statistics is necessary in the design of appropriate error control procedures, such as retransmission protocols or error-correcting codes. The probability of occurrence of different error patterns has been measured for a TFM (tamed frequency modulation) demodulator subject to additive white Gaussian noise. Good agreement is obtained with a theoretical model of the error generation process.

Carrier Phase and Clock Recovery for Continuous Phase Modulated Signals

This paper presents an analysis of a synchronization circuit to be used for carrier-phase and symbol-timing recovery in continuous phase modulation systems. M -ary modulation formats with arbitrary pulse shaping and rational modulation indexes are assumed. Circuit performance is expressed in terms of variances of phase and timing errors. Numerical results are provided for some important cases, including minimum shift keying and tamed frequency modulation. Theoretical results are found in good agreement with computer simulations.

The Hybrid Transmission Scheme of a 900 MHz Digital Land Mobile Radio System

The hybrid transmission scheme of MATS-D uses different transmission principles on both directions of a duplex radio link. Based on the analysis of the radio transmission characteristics and of multiple-access methods, the two directions are designed independently from each other. In the downlink (from base station to mobile station) a combination of TDM and CDM is applied. In the uplink (from mobile station to base station) single channel per carrier FDMA with generalized tamed frequency modulation (GTFM) is employed. Both transmission schemes have been implemented. Measurements with fading generators as well as field tests were carried out. Experimental results are presented for the performance of both transmission schemes, expressed in terms of the bit error rate versus the signal-to-noise ratio and the signal-to-interference ratio.

Mean-Square Crosstalk in Tamed Frequency Modulation

An analytical expression for evaluating the mean-square crosstalk between adjacent channels in coherent tamed frequency modulation (TFM) systems is presented. Numerical results are obtained and compared to previous crosstalk results for minimum shift keying (MSK); the substantial superiority of TFM is confirmed. An equivalent white Gaussian noise model for crosstalk is included and used to estimate performance degradation as a function of frequency separation between channels. The crosstalk results are also used to show that TFM is about 0.9 dB more sensitive to tone jamming than MSK.

Optimization of Generalized Tamed Frequency Modulation Bit Error Rate Performance Subject to a Bandwidth Constraint

This paper deals with the optimization of coherent generalized tamed frequency modulation (GTFM). The optimization is carried out over certain parameters of the modulation scheme to give the best BER (bit error rate) performance, subject to a bandwidth constraint. The optimization is done by an algorithm which uses the upper bound on the squared Euclidean distance as a metric of the BER performance and the power spectra at a certain frequency as a metric of the bandwidth. It is concluded that when the modulation index is not restricted to 0.5, a theoretic improvement of 1.9 dB over the BER performance of GTFM is achievable, with equal bandwidths as a basis of comparison.

Generalized tamed frequency modulation and its application for mobile radio communications

Continued investigation of tamed FM (TFM) has led to an extension called generalized tamed FM (GTFM). The very narrow spectral property of a GTFM signal meets the stringent requirements on bandwidth utilization in modern mobile radio applications. The principle of GTFM is first described. It is then shown that the generation of GTFM signals can be made very simple by the use of an ROM table-lookup technique. By an appropriate choice of parameters in GTFM signal generation at the transmitter, a joint optimization for coherent and noncoherent detection with regard to BER performance in the presence of additive white Gaussian noise can be achieved. For mobile radio applications, the robustness of the detection scheme to fast fading is important. A low-complexity noncoherent receiver is presented, comprising a frequency discriminator and a simple maximum-likelihood sequence estimator. This receiver performs well in a fast fading environment. Computer simulated results of BER performance of this scheme are given. These results are confirmed by experimental measurements.

Generalized Tamed Frequency Modulation and Its Application for Mobile Radio Communications

Continued investigation of tamed FM (TFM) has led to an extension called generalized tamed FM (GTFM). The very narrow spectral property of a GTFM signal meets the stringent requirements on bandwidth utilization in modern mobile radio applications. The principle of GTFM is first described. It is then shown that the generation of GTFM signals can be made very simple by the use of an ROM table-lookup technique. By an appropriate choice of parameters in GTFM signal generation at the transmitter, a joint optimization for coherent and noncoherent detection with regard to BER performance in the presence of additive white Gaussian noise can be achieved. For mobile radio applications, the robustness of the detection scheme to fast fading is important. A low-complexity noncoherent receiver is presented, Comprising a frequency discriminator and a simple maximum-likelihood sequence estimator. This receiver performs well in a fast fading environment. Computer simulated results of BER performance of this scheme are given. These results are confirmed by experimental measurements.

Noncoherent Detection of Tamed Frequency Modulation

Continuous-phase, constant-envelope digital modulation schemes are useful in various applications where a high spectrum utilization as well as immunity to nonlinear distortion is required. From this point of view, typical efficient schemes are digital partialresponse frequency modulation methods. The aim of this work is to investigate noncoherent detection in order to avoid the RF carrier recovery problem. In this paper we select for analysis tamed frequency modulation (TFM) as a particularly representative member of this class, but a similar analysis could be carried out for other partialresponse digital FM systems. After an evaluation of the optimal noncoherent detection and of differential phase detection of TFM, we propose a demodulation method based on a simple and efficient baseband processing of the output of a frequency demodulator. It turns out that the power loss with respect to coherent or optimal demodulation of TFM is on the order of 2 dB. The baseband processing here proposed is in some way equivalent to a partial recovery of the carrier phase and could be improved by using a more complex baseband processing such as a decoding scheme based on the Viterbi algorithm.

Design and implementation of a high efficiency TFM digital modem

Abstract A TFM (Tamed Frequency Modulation) tranceiver (excluding the RF portion) is implemented and tested. The transmitter features digital synthesis of phase path function, which gives accurate modulation results without the need of complicated feedback control, and a unique AGC function, which guarantees the balance of I‐ and Q‐channels to minimize the distortion of final TFM signal. At the receiver, a four‐phase Costas Loop is used successfully to recover the 10.7 MHz IF carrier, and correct sample timing is derived from the envelope of baseband signals. The final decision of received data is achieved by using simple logic circuit and the proof of why it can be done in this way is given. Finally, the error performance has been measured under different signal‐to‐noise ratios and the bit error rate (BER) is found to be only 1–2 db worse than theoretically predicted value which didn't take any synchronization effects into consideration.