GMSK with frequency-selective Rayleigh fading and cochannelinterference

The author derives a formula for error probability of partial-response continuous-phase modulation with differential phase detector and limiter discriminator detector in a multipath Rayleigh fading channel, taking into account frequency-selective fading, cochannel interference, Doppler frequency shift, and additive Gaussian noise while the receiver rejects a specified amount of adjacent channel interference. A formula for the error floor is also presented. Numerical results are presented for Gaussian minimum shift keying with a premodulation normalized filter bandwidth of 0.25. Under mild channel conditions and low energy-to-noise ratios, the best detector is an optimized two-bit differential detection; otherwise the best detector is the limiter discriminator detector     

Differential detection algorithms for MSK signals over AWGN andfrequency-flat Rayleigh fading channels

Novel symbol-by-symbol differential detection algorithms are proposed for minimum-shift keying signals transmitted over additive white Gaussian noise and frequency-flat Rayleigh fading channels. They are derived as approximations to the maximum likelihood noncoherent detection strategy. Their error performance is assessed by computer simulation and is compared with that of other noncoherent detectors. It is shown that, with fading channels, the new algorithms outperform the traditional methods     

Noncoherent detection of convolutionally encoded continuous phasemodulation

The authors consider the error probability at large signal-to-noise ratios of rate-1/2 convolutionally encoded CPFSK (continuous-phase frequency-shift keying) with an optimum noncoherent detector on an additive white Gaussian noise channel. The performance is given in terms of a parameter called the minimum squared normalized equivalent Euclidean distance which plays the same role mathematically as the minimum squared normalized Euclidean distance used for coherent detectors. It is shown that by introducing convolutional coding the error performance is significantly improved. The authors propose a decoding algorithm for these convolutionally encoded CPM schemes which is based on a limited tree search algorithm and uses the maximum-likelihood decision rule for noncoherent detection. Computer simulations show that the degradation in error performance compared to the performance of the optimum coherent Viterbi detector is less than 1 dB with a relatively simple noncoherent detector on an additive white Gaussian noise channel for most of the schemes considered     

Examples of Continuous Phase Modulation Using Discriminator Detection

Continuous phase modulation (CPM) techniques for digital communication have been proposed to achieve narrow bandwidth and good bit error rate (BER) performance in coherent systems. These modulation schemes may also be used with noncoherent discriminator detection. However, in this case, the CPM schemes should be designed for noncoherent detection. Using a receiver proposed by Chung for GTFM and "modified GTFM" signals, we show that it is possible to slightly improve BER performance over that of previous GTFM noncoherent schemes. We also show that a form of GMSK can achieve discriminator detectability performance almost equal to that of classical binary FSK (modulation index = 0.7) but with a much narrower bandwidth.     

Serially Concatenated Space-Time Coded Continuous Phase Modulated Signals

We investigate the detection of space time codes (STC) modulated using continuous phase modulation (CPM), in quasi-static fading channels. A symbol-by-symbol iterative detector with an optimum front-end is derived, and its reduced-complexity implementation is considered. Also, we have introduced several full-rank STC-CPM systems, constructed by combining full-diversity STCs with simple, widely-used CPM schemes, and introducing a small frequency offset. According to the simulation results, the bit error rate (BER) performance of the detector for quasi-static fading is around 1 dB from the case without fading. Furthermore, a comparison of the performance of the proposed detector with results from previous work on STC-CPM showed an improvement in the range of 2-3 dB. Moreover, the detector is robust to the errors in estimating the channel state information (CSI), which is a desirable feature for practical implementation.     

Error rate performance of noncoherent detection of duobinary coded MSK and TFM in mobile radio communication systems

Two continuous phase constant envelope modulation schemes are considered for use in digital mobile radio communication systems. These two schemes, duobinary coded minimum shift keying (MSK) and tamed frequency modulation (TFM), use partial response signaling to achieve efficient power spectrum. Therefore, they are suitable candidates for the application of digital data transmission via mobile radio where spectrum efficiency is an important consideration. The mobile communication channel is characterized by fast Rayleigh fading and cochannel interference resulting from the reuse of the channels. The error rate performance of duobinary coded MSK and TFM has been studied under these environments with noncoherent detection. A closed form expression for the probability of error of duobinary coded MSK with discriminator detection has been derived and evaluated for different cases of fast and slow fading and cochannel interference. The probability of error of duobinary coded MSK and TFM with differential detection has been calculated by numerical integrations for different cases of slow and fast fading and cochannel interference.     

Performance of trellis-coded CPM with iterative demodulation anddecoding

Interleaved trellis-coded systems with full response continuous-phase modulation (CPM) are considered. Upper bounds on the bit-error rate performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver, and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide good bit error performance. Finally, a noncoherent iterative receiver is proposed and is shown to perform close to the coherent iterative receiver     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

On differentially encoded star 16QAM with differential detectionand diversity

Star 16QAM is a modulation method that transmits 4 bits per symbol and has the advantage that it may be differentially encoded and detected. It is very robust to fast multiplicative Rayleigh fading and is suitable for mobile telephone systems and personal communication networks. The main contribution of this paper is the derivation and bit error probability simulation of the maximum likelihood differential detector using phase differences and amplitude ratios from L diversity branches for bit decisions. As a comparison, much simpler previously known post detection combining techniques are generalized for star 16QAM and optimized. The bit error probability is simulated for both diversity detectors on a multiplicative Rayleigh fading channel with additive white Gaussian noise. It is found that the bit error probability of the ML detector may also be obtained by the simple combining detector. This is also true for the error floor due to the maximum Doppler frequency. The diversity gain is almost 8 dB, measured in signal to noise ratio per diversity branch, at a bit error probability of 1 percent. The diversity detector can sustain an almost 3 times larger Doppler frequency again at a bit error probability of 1 percent. We also show that star 16QAM offers, at most, 3 subchannels with different bit error probabilities     

Suboptimum detection of trellis-coded CPM for transmission onbandwidth- and power-limited channels

The authors consider a communication scheme based on continuous phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM) for transmission over a channel affected by Gaussian noise and fading. This scheme provides a power saving due to the coding gain of TCM and a reduced bandwidth occupancy due to the features of CPM signals. Moreover, CPM provides constant-envelope signals. To keep the complexity of the receiver manageable and to be able to use interleaving/deinterleaving techniques to spread the fade bursts, suboptimal detection schemes must be used. Two such schemes, based on coherent and noncoherent detection of CPM, are considered. Their performance is evaluated by computing the computational cutoff rate of the discrete channel generated by CPM     

Performance of multiple-dwell pseudo-noise code acquisition with I-Q detector on frequency-nonselective multipath fading channels

Multiple-dwell pseudo-noise code acquisition with a noncoherent I-Q detector is analyzed for Rayleigh and Rician fading channels that takes into account the detection correlations resulting from multipath fading. Minimum mean acquisition times with optimized dwell times and thresholds are obtained, and the effects of multipath fading and frequency offsets are evaluated. In addition, a detailed comparison between I-Q and square-law detectors is conducted under various channel conditions.     

Trellis-coded CPFSK and soft-decision feedback equalization for micro-cellular wireless applications

In this paper, trellis-codedM-ary CPFSK with noncoherent envelope detection and adaptive channel equalization are investigated to improve the bit error rate (BER) performance of microcellular digital wireless communications systems. For the same spectral efficiency, the trellis-coded modulation (TCM) schemes studied outperform minimum shift keying (MSK) with noncoherent or differentially coherent detection in Rayleigh fading channels. For the case of frequency-selective fading channels, adaptive channel equalization is applied to mitigate the time-variant intersymbol interference (ISI). A new equalizer structure is proposed which, in its feedback path, makes use of fractionally spaced signal samples instead of symbol-spaced hard decisions on transmitted symbols. Computer simulation results indicate that the soft-decision feedback equalizer (SDFE) can significantly improve the system's performance.     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

A new performance bound for PAM-based CPM detectors

It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detectors with near optimum performance. It has recently been shown that the PAM representation also extends to CPM schemes with multiple modulation indexes (multi-h CPM). In this paper, we present a detector for multi-h CPM which is based on the PAM representation. We also give an exact expression for the pairwise error probability for the entire class of PAM-based CPM detectors (single- and multi-h, optimal, and reduced-complexity) over the additive white Gaussian noise (AWGN) channel and show that this bound is tighter than the previously published bound for approximate PAM-based detectors. In arriving at this expression, we show that PAM-based detectors for CPM are a special case of the broad class of mismatched CPM detectors. We also show that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other CPM detectors. These distance properties are especially useful in applications with greatly reduced trellis sizes. We give thorough examples of the analysis for different single- and multi-h signaling schemes. We also apply the new bound in comparing the performance of PAM-based detectors with other reduced-complexity detectors for CPM.     

Modulation and Detection for Simple Receivers in Rapidly Time-Varying Channels

We investigate the performance degradation of basic modulation schemes in a rapidly time-varying channel using a first-order autoregressive channel model. Various performance metrics are used to indicate the relative advantages of each modulation scheme. We find that noncoherent frequency-shift keying (FSK) is suitable for operating at very high mobility and high signal-to-noise ratio, ideal for some military applications. We then propose a partially coherent detector for FSK and differential phase-shift keying that exploits partial channel knowledge to enable the receiver to operate effectively in both fast and slow fading. The maximum-likelihood rule obtained for the partially coherent FSK turns out to be a linear combination of coherent and noncoherent detection rules. Results demonstrate that significant performance improvement can be achieved over the best of coherent and noncoherent FSK detection. The detector is robust to estimation errors present in the channel statistics. We also propose a few adaptive schemes that employ various combinations of modulation schemes to increase the robustness of the system in fast fading     

Decorrelating detector with diversity combining for single user frequency-selective rayleigh fading multipath channels

Diversity combining techniques are applied in mobile radio communications as a means of performance improvement in a fading multipath environment. Adaptive equalizers which incorporate diversity combining were shown to combat intersymbol interference (ISI) caused by multipath provided that the fading is sufficiently slow. However, for fast fading rates, noncoherent techniques are often desirable. In this paper, we examine the performance of several coherent and noncoherent detectors that make use of diversity combining. In particular, the decorrelating filter is shown to provide reliable performance for a frequency-selective Rayleigh fading multipath channel with ISI. Numerical and simulation results are presented for a channel with two independent Rayleigh fading paths. Signal design issues which arise in the implementation of the decorrelating detector and the zero-forcing equalizer are discussed.     

Multiuser detectors with disjoint Kalman channel estimators forsynchronous CDMA mobile radio channels

We compare performance of several multiuser detectors for differentially encoded data combined with simple, disjoint, decision-directed Kalman channel estimators over flat Rayleigh fading channels. Simpler detectors with noncoherent differential detection are also compared. Different performance trends relative to the case of perfect channel estimation are observed. We find that in the presence of channel mismatch, the linear decorrelator is the most robust detector in terms of the bit-error rate and the near-far resistance. Parameter adjustment for fading channel modeling and estimation in the decision-directed mode are also discussed     

Probability of error analysis of digital partial responsecontinuous phase modulation with noncoherent detection in mobile radiochannels

An analysis is presented of noncoherent detection of constant-envelope digital partial-response continuous-phase modulation (PRCPM) in fast Rayleigh fading that characterizes land mobile radio channels. Closed-form expressions for the probability of error are derived for limiter discriminator detection, and both 1- and 2-bit differential detection. Numerical results are presented for cases of practical interest to researchers and designers of land mobile radio systems. The expressions derived for the probability of error are general and can be used for all PRCPM schemes     

Error floors in the satellite and land mobile channels

In a satellite mobile channel (SMC) and land mobile channel (LMC) because of fading and nonlinear power amplifiers, constant envelope modulation and noncoherent detection methods may outperform other schemes. It is shown how to compute the error floor for four noncoherent digital communication systems in satellite and land mobile channels. Differential phase shift keying (DPSK) with differential phase detection (DPD) or frequency shift keying (FSK) with DPD, limiter discriminator integrator detection. (LDID), or limiter discriminator detection (LDD) are studied. The error floor is the residual error probability when SNR is infinity, i.e. the error probability in the system is limited by the error floor. The error floor is computed as a function of Doppler frequency, modulation index, and ratio of powers in the specular and diffuse signal components for DPSK-DPD, FSK-DPD, FSK-LDID and FSD-LDD systems     

Performance of channel coded noncoherent systems: modulation choice, information rate, and Markov chain Monte Carlo detection

This paper investigates performance of channel coded noncoherent systems over block fading channels. We consider an iterative system where an outer channel code is serially concatenated with an inner modulation code amenable to noncoherent detection. We emphasize that, in order to obtain near-capacity performance, the information rates of modulation codes should be close to the channel capacity. For certain modulation codes, a single-input single-output (SISO) system with only one transmit antenna may outperform a dual-input and single-output (DISO) system with two transmit antennas. This is due to the intrinsic information rate loss of these modulation codes compared to the DISO channel capacity. We also propose a novel noncoherent detector based on Markov Chain Monte Carlo (MCMC). Compared to existing detectors, the MCMC detector achieves comparable or superior performance at reduced complexity. The MCMC detector does not require explicit amplitude or phase estimation of the channel fading coefficient, which makes it an attractive candidate for high rate communication employing quadrature amplitude modulation (QAM) and for multiple antenna channels. At transmission rates of 1 ~ 1.667 bits/sec/Hz, the proposed SISO systems employing 16QAM and MCMC detection perform within 1.6-2.3 dB of the noncoherent channel capacity achieved by optimal input.