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     

Coherent and Noncoherent Detection CPFSK

Continuous phase frequency shift keying (CPFSK) is potentially an attractive modulation scheme for use on channels whose performance is limited by thermal noise. In this paper results for the performance available with CPFSK are given for coherent detection and noncoherent detection with arbitrary modulation indices and arbitrary observation intervals. This work serves two purposes. First, it provides interesting, new results for the noncoherent detection of CPFSK which indicate that the performance of such a system can be better than the performance of coherent PSK. Secondly, it provides a complete analysis of the performance of CPFSK at high SNR as well as low SNR and thereby unifies and extends the results previously available.     

Performance Analysis of Transmit Beamforming

Performance Analysis of Transmit Beamforming Using the theory of random matrices, a performance analysis is given for uncoded binary transmission over multiple-input multiple-output channels, under the assumption that transmitter beamforming is used. In particular, exact finite antenna expressions are found for the average bit-error rate (in the case of ergodic channels) for both noncoherent and coherent detection. Expressions for the outage probability (in the case of quasi-static channels) are also given.     

Performance analysis of a wireless multirate direct-sequence CDMAusing fast Walsh transform and decorrelating detection

We analyze the performance of a flexible multirate scheme for direct-sequence code division multiple-access (CDMA) mobile radio systems. The proposed scheme uses a variable processing gain serial pseudonoise modulation as a multirate strategy. To reduce the interference effects, the CDMA system utilizes the coherent fast Walsh transform transmission technique. The proposed scheme can be used in the reverse link (mobile-to-base station) of the upcoming third-generation wide-band CDMA system (has the feature of coherent reverse link). We analyze the system performance with and without using a decorrelating multiuser detector. The uncoded bit-error probability (BEP) with and without decorrelating detection on a multipath fading channel is derived analytically. In addition, the validity of the analysis results is demonstrated by computer simulations using the IMT-2000 vehicular multipath channel model. In order to make sure that the proposed processing techniques do not distort the soft values at the demodulator output, the proposed multirate scheme is also simulated in case of using turbo codes. The turbo-coded BEP is calculated for different user data rates and different number of decoding iterations     

Minimum Euclidean distance for combinations of short rate 1/2 convolutional codes and CPFSK modulation

Continuous phase frequency shift keying (CPFSK) is a constant amplitude modulation method with good spectral sidelobe properties. Good error probability properties can be obtained with coherent maximum-likelihood detection. In this paper we study the Euclidean distance properties of signals formed by a conventional rate1/2convolutional encoder followed by a binary or4-level CPFSK modulator. The minimum Euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length. The optimum detector is discussed for rational modulation index values. The best obtainable codes are found for the case of short rate1/2codes with binary or4-level CPFSK modulation. Lists of the best codes are given. Among the results are that the noncatastrophic rate1/2convolutional codes with optimum free Hamming distance do not in general give the best Euclidean distance with CPFSK.     

多进制CPFSK的减少状态格状图

连续相位调制的最佳相干解调的误码性能取决于其最小平方欧氏距离。本文在不减少其最小平方欧氏距离的前提下，提出了多进制ＣＰＦＳＫ的减少状态格状图，从而减少了维持比的译码复杂度。     

Limiter-discriminator detection of a coherent optical heterodyneM-ary CPFSK receiver

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, ΔνT. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at ΔνT=1% and ΔνT=2%, respectively, for M=4, 8, and 16     

Digital FM double errors

This paper evaluates the double-error probability (average probability of two consecutive bit errors) in digital FM for a noncoherent limiter/discriminator receiver with either integrate and dump or sample and hold (S&H) bit detection. A remarkably simple relationship is found relating the S&H double-error probability to the optimum coherent CPFSK bit error probability of Osborne and Luntz (1974)     

译码转发中继系统的广义最大似然非相干分组检测（英文）

This paper considers noncoherent cooperative decode-and-forward(DF) halfduplex multi-branch relay systems.Each relay branch is modeled as a probabilistic transition system at the last hop,and thus it can be considered as a relaying chain comprising multi-hop relays.An approximation to the generalized maximum likelihood(ML) noncoherent block detection is derived for uncoded M-ary modulation in a faded noisy environment.In particular,the derived noncoherent block detection in a noiseless case is equivalent to a multichannel reception with full diversity.Furthermore,the generalized detection is extended specifically to block coded M-ary phase shift keying(MPSK) modulation.For a DF three node relay system using block coded quadrature phase shift keying(QPSK),simulation results are provided to examine the end-to-end error performance of the noncoherent detection with considering the effects of network geometry and power allocation,respectively.It is shown that under a fixed power allocation,a proper relay placement can yield near full diversity for large signal-to-noise ratio.     

Why FSK and CPFSK have identical linewidth requirements

CPFSK is the most widely used modulation scheme in coherent optical transmission. Theoretical analyses so far predicted a much more stringent linewidth requirement compared to ASK and FSK systems with noncoherent IF-detection. In this paper we present a unified linewidth analysis of ASK, FSK, CPFSK, and DPSK receivers, with leads to the conclusion that the linewidth performance of these different schemes is to a large extent identical. The inclusion of post-detection filtering in the analysis is critical for obtaining these results, which are supported by practical system measurements on a 1 Gbit/s phase diversity CPFSK receiver     

Performance of wireless CDMA with M-ary orthogonal modulation andcell site antenna arrays

An antenna array-based base station receiver structure for wireless direct-sequence code-division multiple-access (DS/CDMA) with M-ary orthogonal modulation is proposed. The base station uses an antenna array beamformer-RAKE structure with noncoherent equal gain combining. The receiver consists of a “front end” beamsteering processor feeding a conventional noncoherent RAKE combiner. The performance of the proposed receiver with closed loop power control in multipath fading channels is evaluated. Expressions for the system uncoded bit-error probability (BEP) as a function of the number of users, number of antennas, and the angle spread are derived for different power control scenarios. The system capacity in terms of number of users that can be supported for a given uncoded BEP is also evaluated. Analysis results show a performance improvement in terms of the system capacity due to the use of antenna arrays and the associated signal processing at the base station. In particular, analysis results show an increase in system capacity that is proportional to the number of antennas. They also show an additional performance improvement due to space diversity gain provided by the array for nonzero angle spreads     

Average BER Analysis for Binary Signallings in Decode-and-Forward Dissimilar Cooperative Diversity Networks

In this letter, the average bit-error rate (BER) performance is analyzed for uncoded decode-and-forward (DF) cooperative diversity networks. We consider two typical networks: a single-relay cooperative network with the direct sourcedestination link and a two-relay cooperative network with the direct source-destination link, under dissimilar network settings, i.e., the fading channels of different relay branches may have different variances. We first derive a closed-form approximate average BER expression of binary signallings including noncoherent binary frequency shift keying (BFSK), coherent BFSK, and coherent binary phase shift keying (BPSK), for the singlerelay network. We then generalize our analysis to the two-relay network, and a closed-form approximate average BER expression for binary signallings is derived. We also show that our BER expressions can be considered as generalizations of previously reported results in the literature. Throughout our analysis, only one approximation, so-called the piecewise-linear approximation, is made. Simulation results are in excellent agreement with the theoretical analysis, which validates our proposed BER expressions.     

Noncoherent block-coded MPSK

For coherent detection, block-coded modulation is a bandwidth efficient scheme. In this paper, we propose theorems about the error performance of block-coded modulation using M-ary phase-shift keying (MPSK) for noncoherent detection. Based on these theorems, we propose a novel block-coded modulation scheme for noncoherent detection called noncoherent block-coded MPSK. The proposed scheme provides flexible designs of noncoherent block codes with different code rate, block length and error performance. Good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes. Moreover, noncoherent block codes of this new scheme can be decoded by multistage decoding, which has the advantage of low complexity and satisfactory error performance. In this paper, two algorithms of multistage decoding for noncoherent detection are proposed as well. The error performance of some designed codes and decoding algorithms is verified by computer simulation.     

A new correlator receiver architecture for noncoherent optical CDMAnetworks with bipolar capacity

A new correlator receiver architecture based on a modified version of unipolar-bipolar correlation is proposed for noncoherent optical fiber code-division multiple-access (CDMA) networks. For this architecture, the receiver average bit-error rate (BER) performance is numerically evaluated as a function of the received optical power for noncoherent transmission and direct detection with the number of simultaneous users as a parameter. The BER performance is also evaluated by a closed-form formula that is developed in this paper. Comparison of the results from the latter with numerical results show that, the formula provides a good approximation to the system performance. Furthermore, the closed form solution suggests that the system can achieve the same capacity as a CDMA system using coherent detection     

Optimal binary communication with nonequal probabilities

Optimal signal energies are derived for optimal binary digital communication systems with arbitrary signal probabilities and correlation with both coherent and noncoherent detection. The resulting bit-error probability (BEP) is computed and compared with the BEP of the same systems with equal signal energies. One of the conclusions is that for the coherent system with nonnegative correlation, and for the noncoherent system with arbitrary correlation, the optimal signals are on-off keying (OOK), i.e., the signal with probability p/spl les/0.5 has energy E/p, while the second signal has zero energy, where E is the average signal energy. The proposed system is also better than a system with source coding and equiprobable signals.     

Performance analysis of space-time MMSE multiuser detection for coded DS-CDMA systems in multipath fading channels

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.     

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     

On Trellis Coded Noncoherent Space-Time Modulation

Unitary space-time modulation (USTM) is well-tailored for noncoherent space-time modulation. Trellis coded USTM (TC-USTM) can obtain significant coding gains over uncoded USTM for the noncoherent block fading channel. Conventional TC-USTM schemes expand the signal set of uncoded USTM by a factor of two. In this letter, we propose a new TC-USTM scheme in which the size of USTM set is not limited to be just double for uncoded USTM. However, in TC-USTM schemes, because signals of the same trellis branch are transmitted over the same fading coefficients, one trellis branch can only obtain one temporal diversity. In this letter, we also propose a new trellis coded noncoherent space-time modulation scheme by interleaving space-time signals. The proposed scheme can enlarge temporal diversity at the price of increased complexity and delay. Simulation results demonstrate the excellent error performances of codes found by computer searches for both schemes.     

A novel demodulator/detector for digital and analog signals on LMRchannels

The design, implementation, and performance of an all-digital demodulator/detector suitable for differential phase-shift keying (DPSK), continuous-phase frequency-shift keying (CPFSK), frequency-shift keying (FSK), and analog FM are discussed. In this modulator/detector, two detectors, one noncoherent and another differentially coherent, operate simultaneously to provide data detection and automatic frequency control (AFC). Test results indicate that the system provides improved performance over the conventional analog quadrature detector for two-period raised-cosine (2RC) CPFSK modulation in additive white Gaussian noise (AWGN) and Rayleigh fading channels. Being all-digital, the demodulator/detector is well suited for integrated circuit implementation. In addition, the system performs as well as the analog quadrature detector for analog FM voice transmissions, thereby maintaining full compatibility with analog land mobile radio (LMR) transmissions     

Theoretical analysis and performance limits of noncoherent sequencedetection of coded PSK

A theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded M-ary phase-shift keying (M-PSK) is presented. A method for the numerical evaluation of the pairwise error probability-for which no closed-form expressions exist-is described, the classical union bound is computed, and results are compared with computer simulations. An upper bound on this pairwise error probability is also presented. This upper bound may be effectively used for the definition of an equivalent distance, which may be useful in exhaustive searches for optimal codes. Using this bound, it is proven that, in the general coded case, the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large. In the case of differentially encoded M-PSK, a simple expression of the asymptotic bit-error probability is derived, which is in agreement with simulations for high as well as low signal-to-noise ratio (SNR)