Performance of GMSK in a land mobile radio channel

Discriminator detection of Gaussian minimum shift keying (GMSK) in a cellular mobile-communication channel is analyzed. The channel is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). A closed-form expression for the probability of error is derived. Numerical computation is used to obtain the GMSK bit error rate (BER) performance for various combinations of channel parameters. These results show that GMSK gives slightly better performance compared to that for π/4-quadrature phase shift keying (QPSK) previously reported in the literature     

Soft-decision differential phase detection of turbo-coded M-ary CPFSK signals over Ricean channels

The performance of turbo codes is examined over the Ricean fading channel with soft-decision differential phase detection (DPD). M-ary continuous phase frequency-shift keying (CPFSK) signaling and puncturing of the coded sequence are considered to achieve bandwidth efficient communication. The effects of the number of phase decision regions, fading conditions, number of states of the constituent codes, and code rate are examined. A bit error rate upper bound is developed, which is useful at low values of bit error probability where computer simulations are lengthy. Significant gains using soft-decision DPD over hard-decision DPD and conventional noncoherent detection are reported.     

Multistage decoding for internally bandwidth efficient coded Poisson fiber-optic CDMA communication systems

We consider the structure and performance of a multistage decoding scheme for an internally bandwidth efficient convolutionally coded Poisson fiber-optic code division multiple access (CDMA) communication system. The decoder is implemented electronically in several stages in which in each stage, the interfering users' coded bit decisions obtained in the previous stage is applied for computing the likelihood of the coded symbols of the desired user. The first stage is a soft-input Viterbi decoder for the internally coded scheme, in which the soft-input coded symbol likelihood values are computed by considering the multiuser interference as a noise signal. The likelihood of coded symbol computed in each stage is then entered into the convolutional decoder for the next bit decisions. The convolutional codes that are used for demonstrating the performance of the multistage decoder are super orthogonal codes (SOCs). We derive the bit error rates (BERs) of the proposed decoder for internally coded Poisson fiber-optic CDMA systems using optical orthogonal codes (OOCs) along with both ON-OFF keying (OOK) and binary pulse position modulation (BPPM) schemes. Our numerical results indicate that the proposed decoding scheme substantially outperforms the single-stage soft-input Viterbi decoder. We also derive the upper bound on the probability of error of a decoder for the known interference case, which is the ultimate performance of a multiuser decoder, and compare the result with that of the soft-input Viterbi decoder.     

Performance bounds of rate-? convolutional codes with QPSK on Rayleigh fading channel

An analytic expression for the bit error probability upper bounds of rate-? convolutional codes in conjunction with QPSK modulation and maximum-likelihood Viterbi decoding on the fully interleaved Rayleigh fading channel is presented. The given expression is evaluated numerically for selected rate-? optimum convolutional codes together with QPSK.     

Sequence estimation over the slow nonselective Rayleigh fadingchannel with diversity reception and its application to Viterbi decoding

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented     

BER analysis of convolution coded QDPSK, in digital mobile radio

The bit error rate (BER) performance of convolutional coded quaternary differential phase-shift keying (QDPSK) with Viterbi decoding is theoretically investigated in Rayleigh fading environments. The probability density functions of the path and branch metric values of Viterbi decoding are derived. The BERs after decoding due to additive white Gaussian noise and cochannel interference are theoretically analyzed. Rate 1/2 codes and their symbol punctured high-rate codes are considered, and the symbol positions for deletion to minimize the BER after decoding are presented for the codes with a constraint length K=3-7. It is shown that Viterbi decoding considerably reduces the desired signal-to-interference power ratio as well as the signal energy per information bit-to-noise power spectrum density ratio necessary to achieve a certain BER. The spectrum efficiency of the cellular mobile radio system, achievable by the use of the symbol punctured codes, is also evaluated     

Corona Based Optimal Node Deployment Distribution in Wireless Sensor Networks

This paper shows the trade off between different modulation techniques such as multi level quadrature amplitude modulation, multi level phase shift keying, and multi level differential phase shift keying for upgrading direct detection optical orthogonal frequency division multiplexing systems with possible transmission distance up to 15,000 km and total bit rate of 2.56 Tb/s. The 2.56 Tb/s signal is generated by multiplexing 64 OFDM signals with 40 Gb/s for each OFDM. Variations of optical signal to noise ratio (OSNR), signal to noise ratio (SNR), and bit error rate (BER) are studied with the variations of transmission distance. Maximum radio frequency power spectrum, and output electrical power after decoder are measured for different multi level modulation techniques with carrier frequency. It is observed that multi level QAM has presented better performance than multi level PSK and finally multi level DPSK in optical OFDM systems. Maximum output power after decoder is enhanced with both 32-PSK, and 64-QAM. Quadrature signal amplitude level at encoder is upgraded with 64-QAM. It is noticed that OSNR, SNR, and BER are improved using 4-QAM OFDM system than either QPSK or 4-DPSK.     

Precise BER analysis of dual-channel reception of QPSK in Nakagami fading and cochannel interference

A precise bit error rate analysis is performed for bandwidth-efficient dual-channel quadrature phase shift keying in Nakagami fading with Nakagami-faded asynchronous interfering signals. In contrast to previous works, the analysis accounts for the dependencies between the quadrature carriers owing to nonRayleigh fading and cochannel interference. The impact of the interfering users' fading severities on the desired user bit error rate is investigated. A comparison of the bit error performance for binary phase shift keying and quadrature phase shift keying is given.     

Analysis of equal gain diversity on Nakagami fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L -branch equal-gain (EG) diversity combiners in Nakagami (1960) fading channels is derived. The bit error rate for a matched filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase shift keying (CPSK) and differential coherent phase shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. Bit error rates for EG combining on Rayleigh fading channels are obtained for L>2. These results are presented as a special case of the more generalized Nakagami fading model     

The error performance of Gray encoded QPSK and 8-PSK schemes in afading channel with cochannel interference

Closed-form BER (bit error rate) expressions are derived for Gray-encoded QPSK (quadrature phase shift keying) and 8-PSK schemes using coherent detection in a slow Rayleigh fading narrowband channel with fading cochannel interference. Earlier work has been limited to deriving the approximate BER using the canonical Stein (1961) receiver concept. The symbol error rate (SER) for the QPSK scheme is also derived. The desired signal and the cochannel interferer are both PSK signals, modulated by different baseband pulses with identical signaling rate     

Performance of Single and Multichannel Coherent Reception under Rician Fading

In the present work, simple closed-form series solutions for the average error rate of several coherent modulation schemes such as, binary phase shift keying (BPSK), binary frequency shift keying (BFSK), differential binary phase shift keying (DBPSK), quadrature phase shift keying (QPSK), offset-QPSK, minimum shift keying (MSK), and square M-ary quadrature amplitude modulation (M-QAM), operating over frequency non-selective slow Rician fading channel and corrupted by additive white Gaussian noise (AWGN) are derived. Further, to improve the link quality, receiver antenna space diversity is considered, where multiple independent and identically distributed (i.i.d.) as well as uncorrelated signal replicas are combined before successive demodulation. The proposed linear predetection combiner follows optimum maximal ratio combining (MRC) algorithm. Starting from a novel unified expression of conditional error probability the error rates are analysed using probability density function (pdf) based approach. The derived end expressions, consisting of rapidly converging infinite series summations of Gauss hypergeometric function, are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity, non-fading AWGN and Rayleigh fading. Symbol or, bit error probabilities (SEP/BEP) are graphically displayed against signal to noise ratio (SNR) per bit per channel for all the digital modulation schemes stated above with different values of diversity order L and varying values of the channel specular-to-scatter ratio or, the Rician parameter K, as found from the measured statistics of mobile and indoor wireless channels. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size M, numerical results are plotted for various values of M. Selected simulation results are also provided to verify the analytical deductions. The series solutions presented in current text realize a trade-off between precision and complexity and offers valuable insight into the performance evaluation over a fading channel in a unified manner.     

Performance evaluation and implementation of convolution coded OFDM modem in wireless underwater acoustic communication

High‐data transmission rate and reliable communication in underwater acoustic channel is challenging because of limited bandwidth, multipath propagation, and Doppler shift, which results in poor bit error performance. Under this constraint, this paper explains the simulation results of underwater wireless acoustic data transmission system by using quadrature phase shift keying modulation with convolution encoder at the transmitter and proposed Viterbi decoder at the receiver. The decoder algorithm in comparison with MATLAB inbuilt function shows asserting improved results. This paper evaluates the performance of convolution coded orthogonal frequency division multiplexing modem, which is studied over typical underwater channel through an extensive computer simulation and a semirealistic experimentation. The performance of convolution coded orthogonal frequency division multiplexing system is measured in time domain plots, bit error rate curves, and number of bit errors per frame over additive white Gaussian noise and Rayleigh channel conditions.     

A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding

Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rateP_bfor a constraint length 3 decoder has been plotted versus the channel transition probabilitypand shows close agreement with the improved bound on the bit error probability.     

Adaptive trellis-coded multiple-phase-shift keying for Rayleighfading channels

An adaptive scheme for trellis-coded modulation of MPSK signals, called adaptive trellis-coded multiple-phase-shift keying (ATCMPSK), is proposed for slowly Rayleigh fading channels. The adaptive scheme employs a slightly modified rate 1/2 convolutional encoder and the corresponding Viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions. During poor channel conditions, trellis-coded QPSK (TCQPSK) together with repetition schemes are employed. As channel conditions improve, higher rate schemes such as trellis-coded 16 PSK are used. An interleaving/deinterleaving method suitable for the adaptive scheme is proposed. Theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived, and are compared against simulation results. Simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions. It is shown that ATCMPSK results in considerable improvement in bit-error-rate (BER) performance of MPSK signals. Under ideal conditions, gains in the range of 3-20 dB are achieved over conventional fixed rate pragmatic trellis-coded schemes     

Encoded 16-PSK: a study for the receiver design

The authors present the results of a design study of the receiver in a digital transmission system using the combined coding and modulation schemes known as Ungerboeck codes. Specifically, they examine the design of the receiver for encoded 16-PSK (phase shift keying) modulation, presenting first the traditional structure for the optimum receiver and then a simpler structure. The decoding depth of the Viterbi algorithm, the quantization of the metrics inside the Viterbi processor, and the phase jitter in the recovered carrier are considered. The impact of branch and path metric quantization inside the receiver is discussed, showing that a reasonable number of bits (8) is sufficient to obtain nearly optimum performance when the code complexity is limited. The effect of imperfect carrier recovery inside the receiver is studied, providing accurate analytical estimates of the error event probability as well as an upper bound to the symbol error probability. Results of a detailed simulation, including carrier and bit timing recovery blocks, show that the effects of imperfections on the bit error probability are very small, even at low signal-to-noise ratios. On the whole, results show the robustness of the Viterbi algorithm with respect to fairly rough quantizations of the metrics and indicate that carrier recovery is not as critical as expected     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

Performance of phase-invariant trellis coding for differentially-encoded coherent M-PSK signals on Rayleigh fading channels

Rate(n-1)/n phase-invariant trellis coding with unquantised maximum-likelihood Viterbi decoding for differentially-encoded coherent M-ary (M-2/sup n/) PSK signals on Rayleigh fading channels is considered. The simulated bit error probability performance of the trellis-coded modulation is presented for four- and eight-state linear and nonlinear codes for constraint lengths 3 and 4, respectively, with coding gains of at least 2.5 dB at a bit error rate of 10/sup -3/.<>     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.     

Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

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