Multiple trellis coded frequency and phase modulation

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami- m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel     

Error probabilities of fast frequency-hopped MFSK withnoise-normalization combining in a fading channel with partial-bandinterference

An error probability analysis performed for an M-ary orthogonal frequency-shift keying (MFSK) communication system employing fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a frequency-nonselective, slowly Rician fading channel with partial band interference is discussed. Diversity is obtained using multiple hops per data bit. Noise-normalization combining is employed by the system receiver to minimize partial-band interference effects. The partial-band interference is modeled as a Gaussian process. Thermal noise is also included in the analysis. Forward error correction coding is applied using convolutional codes and Reed-Solomon codes. Diversity is found to dramatically reduce the degradation of the noise-normalization receiver caused by partial-band interference regardless of the strength of the direct signal component. Diversity offers significant performance improvement when channel fading is strong, and performance improvement is obtained for high modulation orders (M>2). Receiver performance is improved when diversity, higher modulation orders, and coding are combined     

Bit error rate performance of π/4-DQPSK in a frequency-selectivefast Rayleigh fading channel

The bit error rate (BER) performance of π/4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For π/4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) π/4-DQPSK operated at a carrier frequency of 850 MHz and C/I<20 dB, the BER will be dominated by CCI if the vehicular speed is below 100 mi/h. In this derivation, frequency-selective fading is modeled by two independent Rayleigh signal paths. Only one co-channel is assumed in this derivation. The results obtained are also shown to be valid for discriminator detection of M-ary DPSK signals     

Error probability of M-ary FSK with differential phasedetection in satellite mobile channel

Formulas are derived for the error probability of M-ary frequency shift keying (FSK) with differential phase detection in a satellite mobile channel. The received signal in this channel is composed of a specular signal, a diffuse signal, and white Gaussian noise; hence, the composite signal is fading and has a Rician envelope. The error probability is shown to depend on the following system parameters: (1) the signal-to-noise ratio; (2) the ratio of powers in the specular and diffuse signal components; (3) the normalized frequency deviation; (4) the normalized Doppler frequency; (5) the maximum normalized Doppler frequency; (6) the correlation function of the diffuse component, which depends on the normalized Doppler frequency and the type of the antenna; (7) the number of symbols; and (8) the normalized time delay between the specular and diffuse component (t _d/T) where 1/T is the symbol rate. Except for T_d/T, all normalized parameters are the ratios of the parameter value and symbol rate. The Doppler frequency depends on the velocity of the vehicle and the carrier frequency. The error probability is computed as a function of the various parameters. The bit error probability is plotted as a function of signal-to-noise ratio per bit and other system parameters     

Probability of error analysis for FHSS/CDMA communications in thepresence of fading

Expressions are found for the probability of error of a slow frequency-hopped spread-spectrum (FHSS) code-division multiple-access (CDMA) system using noncoherent M-ary frequency-shift-keyed (FSK) data modification in the presence of slow-nonselective Rayleigh or single-term Rician fading. The analysis is general enough for the consideration of the near/far problem under the specified channel conditions. Comparisons are made between the error expressions developed here and previously published upper bounds. It is found, under certain conditions, that the previous upper bounds on the probability of error may exceed the true probability of error by an order of magnitude     

Differential detection in quadrature-quadrature phase shift keying(Q2PSK) systems

A generalized quadrature-quadrature phase shift keying (Q² PSK) signaling format is considered for differential encoding and differential detection. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. Symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same E_b/N₀. However, the bandwidth efficiency of differential Q²PSK is substantially higher than that of quaternary DPSK. In differential detection, it is quite reasonable to suspect that errors tend to occur in pairs. It is shown that when the error is due to AWGN, the ratio of double error rate to single error rate can be very high, and the ratio may approach zero at high signal-to-noise ratio. In an attempt to improve the error rate performance, differential detection through maximum-likelihood decoding based on multiple or N symbol observations is considered     

Uncoded and coded performance of MFSK and DPSK in Nakagami fadingchannels

The author presents uncoded and coded performance results for noncoherent M-ary frequency-shift keying (MFSK) and differentially coherent binary phase-shift keying (DPSK) in a slow nonselective Nakagami-m (1960) fading channel. He gives simple expressions for the asymptotic slopes of probability of bit error for large signal-to-noise ratio and shows that the effective order of diversity compared to an uncoded Rayleigh channel is the product of two parameters, one for the channel and one for the code. He also compares the uncoded Nakagami-m results to those of the Rician channel in order to show performance differences between these two generalized fading channel models     

Trellis coding of quadrature frequency/phase modulated signals

The authors explore the trellis coding of continuous-phase quadrature frequency/phase modulated (CPQFPM) signal sets and continuous-phase FPM (CPFPM) signal sets, which are embodiments of the quadrature biorthogonal modulation (QBOM) technique. Conventional TCM and multiple TCM schemes with these modulation formats are examined using both the AWGN channel and the Rician fading channel design. Asymptotic coding gains in d²(free) are tabulated for trellis-coded rate 3/4, 5/6, and 6/7 QFPM schemes, in comparison with uncoded modulations (8AMPM, 32AMPM) and other trellis-coded modulations [TCM (2FSK/4PSK 16QAM, 64QAM), MTCM (2FSK/8PSK)] of equivalent throughput rate. Performance gains on the Rician fading channel are demonstrated by increased values of the design parameters for this channel, namely symbol diversity L_min and branch distance product P     

Bandwidth efficient coding for fading channels: code constructionand performance analysis

The authors apply a general method of bounding the event error probability of TCM (trellis-coded modulation) schemes to fading channels and use the effective length and the minimum-squared-product distance to replace the minimum-free-squared-Euclidean distance as code design parameters for Rayleigh and Rician fading channels with a substantial multipath component. They present 8-PSK (phase-shift-keying) trellis codes specifically constructed for fading channels that outperform equivalent codes designed for the AWGN (additive white Gaussian noise) channel when v⩾5. For quasiregular trellis codes there exists an efficient algorithm for evaluating event error probability, and numerical results which demonstrate the importance of the effective length as a code design parameter for fading channels with or without side information have been obtained. This is consistent with the case for binary signaling, where the Hamming distance remains the best code design parameter for fading channels. The authors show that the use of Reed-Solomon block codes with expanded signal sets becomes interesting only for large value of E_s/N₀, where they begin to outperform trellis codes     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Offset DPSK with differential phase detector in satellite mobilechannel with narrow-band receiver filter

An expression is derived for the error probability of M-ary offset differential phase-shift keying (DPSK) with the differential phase detector and narrowband receiver filter in the satellite mobile (Rician) channel, which includes as special cases the Gaussian and land mobile (Rayleigh) channels. The error probability is computed as a function of various system parameters for M=2, 4, and 8 symbols and third-order Butterworth receiver filter. Both symmetric and conventional DPSK systems are considered. The optimal normalized bandwidth is close to 1.0. Symmetric and conventional DPSK differ significantly in error probability only for M=2 and in the lower range filter bandwidth. In most cases, symmetric DPSK outperforms conventional DPSK. This was particularly noted when the time delay between the specular and diffused signal components was taken into account     

Bit error probabilities MDPSK over the nonselective Rayleigh fadingchannel with diversity reception

Data transmission using M-ary differential phase shift keying (MDPSK) over the nonselective Rayleigh fading channel with diversity reception is considered. While previous studies on error probability mostly assume no fading fluctuation, the author considers, exclusively, the case in which the fading process fluctuates from one symbol interval to the next. Exact bit error probability results for 2, 4, and 8 DPSK as well as tight upper bounds are derived. Some applications of the results are discussed     

FH-MFSK multiple-access communications systems performance in thefactory environment

A frequency-hopped (FH), M-ary frequency-shift-keyed (MFSK), spread-spectrum (SS) communication system operating over the factory radio channel is described. The performance of the system for Rayleigh, Rician, and log-normal multipath fading for factory environments is investigated. The statistics of these channels, based on recent channel modeling studies, are used to evaluate the performance of the FH-MFSK system. A quadrature rule is employed to calculate the channel error probabilities. The average bit error rate (BER) is formulated and is evaluated approximately using Stirling's formula. The numbers of simultaneous users in terms of the number of hopped frequencies, number of MFSK chips, receiver threshold, signal-to-noise ratio, and channel statistics at a fixed BER for Rayleigh, Rician, and lognormal fading channels are determined     

An improved π/4-QPSK with nonredundant error correction forsatellite mobile broadcasting

An improved π/4-quadrature phase-shift keying (QPSK) receiver that incorporates a simple nonredundant error correction (NEC) structure is proposed for satellite and land-mobile digital broadcasting. The bit-error rate (BER) performance of the π/4-QPSK with NEC is analyzed and evaluated in a fast Rician fading and additive white Gaussian noise. (AWGN) environment using computer simulation. It is demonstrated that with simple electronics the performance of a noncoherently detected π/4-QPSK signal in both AWGN and fast Rician fading can be improved. When the K-factor (a ratio of average power of multipath signal to direct path power) of the Rician channel decreases, the improvement increases. An improvement of 1.2 dB could be obtained at a BER of 10^-4 in the AWGN channel. This performance gain is achieved without requiring any signal redundancy and additional bandwidth. Three types of noncoherent detection schemes of π/4QPSK with NEC structure, such as intermediate frequency band differential detection, baseband differential detection, and FM discriminator, are discussed. It is concluded that the π/4-QPSK with NEC is an attractive scheme for power-limited satellite land-mobile broadcasting systems     

Hybrid block-convolutional rate-½ coding strategy forconstant envelope (CE)Q2PSK

The authors address the problem of trellis coding on multidimensional signal space for incorporation into a 4D quadrature-quadrature phase-shift keying (Q²PSK) communication system. A low-complexity rate-½ hybrid block-convolutional coding scheme is proposed, to be utilised in a constant envelope (CE)Q²PSK system configuration. The encoder and decoder designs have been structured to facilitate simple implementation with standard components. The bit error rate performance of the proposed coding scheme is studied by means of simulation on a non-frequency selective Rician fading channel assuming coherent detection. The benefits of the use of channel state information (CSI) in conjunction with maximum-likelihood Viterbi decoding are also considered     

Performance of fast frequency-hopped MFSK receivers with linear andself-normalization combining in a Rician fading channel withpartial-band interference

An error probability analysis is performed for both self-normalized and conventional M-ary orthogonal frequency-shift-keying (MFSK) noncoherent receivers using fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a Rician fading channel with partial-band interference. The self-normalization receiver uses a nonlinear combination procedure to minimize performance degradation due to partial-band interference. The performance of the conventional receiver is significantly degraded by worst-case partial-band interference regardless of the modulation order or number of hops per data symbol used, while the self-normalization receiver can provide a significant immunity to worst-case partial-band interference for many channel conditions when diversity is used, provided the signal-to-thermal-noise ratio is large enough to minimize degradation due to nonlinear combining losses. The improvement afforded by higher modulation orders is dependent on channel conditions     

Asymptotic performance of M-ary orthogonal signals inworst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E_b/N_I) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E_b/N _I(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E_b/N₀) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E_b/N₀ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication     

On the symbol error probability of maximum-selection diversityreception schemes over a Rayleigh fading channel

The symbol error probability of two selection schemes, namely, maximum signal-to-noise ratio (Mγ) selection and maximum output (MO) selection, for M-ary multidiversity reception over a Rayleigh fading channel are discussed. The symbol error probability of the MO scheme is lower than that of the Mγ scheme. The more diversity receptions that are used, the larger is the difference. A simple expression of crossover average signal-to-noise ratio (per bit) is presented as a guideline for increasing the number of diversity receptions     

Error probability of binary phase shift keying in Nakagami-m fadingchannel with phase noise

The error performance of coherent detection of binary phase shift keying (BPSK) signals with noisy phase reference is analysed for a flat Nakagami-m fading channel and in the presence of additive white Gaussian noise (AWGN). By assuming Gaussian and Tikhonov probability density functions (PDFs) for the phase error, closed-form expressions for the average bit error rate (BER) are derived     

Error probability of digital modulation in satellite mobile, landmobile, and Gaussian channels with narrow-band receiver filter

It is shown how to derive formulas for the error probability for M-ary differential phase shift keying with differential phase detection (DPD) and M-ary frequency shift keying with DPD, limiter-discriminator detection and limiter-discriminator-integrator detection in the satellite mobile channel (SMC) with narrowband receiver filter if such formulas are available for the Gaussian channel. The modification of the formulas involves only a redefinition of the noise power and autocorrelation function. Since the SMC contains as special cases the land mobile (Rayleigh) channel and the Gaussian channel, the derived formulas are valid for these channels as well. In fact the formula for the land mobile channel is in many cases reduced to a closed form, which does not contain an integral. The author computes the error probability for the four systems, and compares their performance assuming a third-order butterworth filter and M=2,4,8 symbols