Trapping sets with short cycles are known to give a detrimental effect on the error floor performance of a low-density parity-check (LDPC) code. Unlike in binary LDPC codes., short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is crucial to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles.

Short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is important to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles. Finally, we propose a low-complexity algorithm for designing an NB-LDPC code with low error floor. Depending on the modulation scheme, the codes constructed by the proposed design algorithm have similar or slightly worse performance, compared with those constructed via the method by Poulliat et al. However, the proposed design algorithm does not require a cycle enumeration algorithm with high complexity, and therefore is feasible even in the case of large code length, say ≥5000.

In this study, the coverage of downlink cellular orthogonal frequency‐division multiple‐access networks transmitting one quadrature‐amplitude modulation symbol per hop is analysed. The coverage probability is first defined by using an upper bound on the bit error rate (BER) of a bit‐interleaved coded modulation system. Moreover then, the moment generating functions of the legacy Gaussian and Laplacian metrics (LMs) for soft‐decision decoding of an employed error‐correcting code are derived for computing the upper bound on the BER and the corresponding coverage probability of the networks. Numerical results demonstrate that due to the impulsive nature of the inter‐cell interference for moderate‐to‐small cell loads, the networks using the LM for soft‐decision decoding significantly outperform those employing the legacy Gaussian metric in terms of the achievable cell radius and the amount of the average transmit power reduction.

High data rate at high mobile speed will still be an essential requirement for the future 5G mobile cellular system. High frequency bands above 6 GHz are particularly promising for the 5G system because of large signal bandwidths such high frequencies can offer. And it was shown that by using high gain beamforming antennas, the problem of high propagation loss at high frequencies could be compensated almost completely. But, achieving high speed mobile cellular communications with beamforming antennas at such a high frequency is a daunting task and has not been demonstrated until now. In this paper, we describe a testbed built at Samsung Electronics, Korea, with adaptive beamforming antennas at 28 GHz, and demonstrate feasibility of high speed mobile cellular communications.

The extended min‐sum (EMS) and improved EMS (I‐EMS) algorithms for non‐binary low‐density parity‐check codes over GF( q ) significantly reduce the decoding complexity with an acceptable performance degradation, but they suffer from high latency because of many serial computations, including a sorting process. On the other hand, the trellis‐based EMS algorithm can greatly reduce the latency, but it does not solve the complexity problem in high‐order fields ( q ≥ 64). To improve the latency problem with low‐complexity advantages, the authors propose heap‐based EMS (H‐EMS) and heap‐based I‐EMS (HI‐EMS) algorithms that are modifications of the EMS and I‐EMS algorithms, respectively. The authors also propose double H‐EMS and double HI‐EMS algorithms trading off the latency against the performance by heaping messages twice. Numerical results show that the H‐EMS algorithm has 2.74–9.52 times lower latency than the EMS algorithm with a negligible performance degradation over a wide range of code rates, whereas the HI‐EMS algorithm has 1.20–1.62 times lower latency than the I‐EMS algorithm. Furthermore, the proposed algorithms may be employed regardless of the decoding schedules.

Multitone‐frequency and quadrature‐amplitude modulation (MFQAM) is a combination of multitone frequency‐shift keying and quadrature‐amplitude modulation (QAM). In this study, the authors consider MFQAM with active subcarriers grouped in balance, where the active subcarriers are divided into a specified number of groups and the same QAM symbol is conveyed by every subcarrier in each group. This grouping may make MFQAM have frequency diversity in itself. They first derive the joint probability density function of the correlator outputs of an MFQAM receiver. They then compute the channel capacity of a coded modulation (CM) system employing MFQAM over Rayleigh fading channels. As a result, they demonstrate that for a moderate code rate between 1/3 and 2/3, its normalised throughput is close to the channel capacity limit in the low signal‐to‐noise ratio region, contrary to a CM system employing the conventional modulation. They also evaluate the frame error rate (FER) performance of a CM system employing MFQAM when a non‐binary error‐correcting code is employed. Numerical results demonstrate that the normalised throughput of the CM system computed via the FER shows a similar trend to that obtained via the channel capacity.

In cellular systems, the interference has been the most critical issue that practically limits the performance of overall networks. Furthermore, the distribution of the inter-cell interference (ICI) in conventional cellular networks employing orthogonal frequency-division multiple-access (OFDMA) with quadrature amplitude modulation (QAM) tends to approach a Gaussian distribution, which is known to be the worst-case distribution of the ICI as additive noise resulting in poor channel capacity. Thus, a dramatic enhancement of the channel capacity for the cellular network is expected when the ICI could be designed properly so that it has a non-Gaussian distribution. In this context, a cellular OFDMA system with a novel modulation scheme, frequency and quadrature-amplitude modulation (FQAM), is proposed in this paper. The statistical distribution of the ICI is shown to deviate far from the Gaussian distribution for the proposed FQAM-based system. Accordingly, it is shown that the non-Gaussian distribution of the ICI incurred with FQAM results in significantly improved transmission rates for the cell-edge users. Also, from the measurement results using practically implemented FQAM-based OFDMA systems, it is verified that the transmission rate for the cell-edge users could be increased significantly over the conventional QAM-based OFDMA system.

The distribution of the intercell interference (ICI) in conventional cellular networks employing orthogonal frequency-division multiple-access (OFDMA) with quadrature-amplitude modulation (QAM) tends to approach a Gaussian distribution when all available subcarriers in each cell are fully loaded. Recently, it has been also shown that the worst-case distribution of the ICI as additive noise in wireless networks with respect to the channel capacity is Gaussian. Thus, the channel capacity in cellular networks is expected to be further enhanced when the ICI could be designed properly so that it has a non-Gaussian distribution. This observation motivates us to propose, in this paper, a downlink cellular OFDMA network employing a modulation scheme called frequency and QAM (FQAM). We also derive maximum-likelihood metrics for the binary or non-binary error-correcting codes employed in the proposed network and propose their practical sub-optimal versions. Numerical results demonstrate that the distribution of the ICI in the proposed network deviates far from the Gaussian distribution. As a result, the transmission rates for the cell-edge users in the proposed network are significantly improved. In addition, the measurement results using practically implemented FQAM-based OFDMA systems verify that the transmission rates for the cell-edge users can dramatically increase, compared with the conventional QAM-based OFDMA network.

A systematic, granulized piecewise linear approximation to the Jacobian logarithm is developed. This approximation reverts to the Jacobian approximation and the exact Jacobian logarithm at the far extremes. The utility of the derived approximation is demonstrated by applying it to the decoding of Turbo coded, MIMO/BICM-ID systems.

In this paper, we analyze the performance of soft decision decoded, synchronous, fast frequency-hopping spread-spectrum multiple-access networks using M-ary frequency shift keying in Rayleigh fading channels under the assumption that the number of frequency hopping slots is sufficiently large. The joint probability density function (pdf) of the absolute values of the correlator outputs is derived to compute the channel capacity and evaluate the soft decision decoding performance of the 3GPP Turbo and convolutional codes. Results indicate that soft decision decoding based on the derived pdf drastically outperforms traditional decoders based on the Gaussian approximation of the effect of the multiple access interference (MAI). The sensitivity of the derived soft decision decoder to estimation errors in system parameters and the required computational complexities of the derived soft decision decoding metrics are also investigated.

An approximate upper bound is derived to the maximum likelihood decoding threshold of weighted nonbinary repeat-accumulate (WNRA) codes over GF(q) with q-ary orthogonal modulation and coherent detection over the additive white Gaussian noise channel. As with binary RA codes, WNRA codes show the potential for achieving the channel capacity with decreasing code rate for large enough q.

Using a Gaussian approximation to the distribution of the message vectors under density evolution, we design irregular weighted nonbinary repeat-accumulate codes over GF(q) with q-ary orthogonal modulation. The resulting codes achieve a frame error rate of 10-1within 0.56 to 0.91 dB of channel capacity under the AWGN channel.

A very simple design rule for parallel concatenated Turbo codes over GF(q) with q-ary orthogonal modulation is proposed. Unlike previously proposed exhaustive search methods, the proposed design rule allows straightforward and systematic code designs for any value of q ≥ 2 and any constraint length greater than 2.

An iterative algorithm employing decision feedback provided by either an equalizer or a channel decoder is proposed in order to compensate for the phase noise resulting from imperfect oscillators in orthogonal frequency-division multiplexing (OFDM) systems. In the proposed algorithm, the received OFDM symbol is partitioned into subblocks in the time domain and the estimate of the time-average of the phase noise at each subblock is used to compensate for the phase noise. A formula for the signal-to-interference-plus-noise ratio (SINR) after phase noise compensation is derived and its values are evaluated under a variety of conditions in order to demonstrate the efficiency of the proposed algorithm. Numerical results show that the proposed algorithm achieves performance close to that of an OFDM system without phase noise over a wide range of conditions, while requiring only one-half the complexity of the partial intercarrier interference reduction algorithm.

In this paper, we propose a novel class of unitary space-time constellations based on quaternary quasi-orthogonal sequences (QOSs), minimizing the maximum correlation between the signal matrices. The proposed design, owing to the underlying algebraic structure of the QOSs, allows for an efficient decoder structure while offering performance virtually identical to the unitary space-time constellation design by Hochwald et al.

In this paper, a distribution matching technique is proposed to process the extrinsic information produced by practical multiple-antenna detectors with iteratively demodulated, bit-interleaved coded modulation (BICM-ID). It is shown that significant gains may be achieved by appropriately processing the extrinsic information generated by practical multiple-antenna detectors before feeding it to the channel decoder. The validity of the proposed matching technique is shown via simulation results applied to Turbo-coded BICM-ID systems using (QRD)-M and list sphere detectors.

The probability density function (PDF) of the intercell interference for downlink cellular orthogonal frequency division multiple access networks under log-normal shadowing and multipath Rayleigh fading is derived. The derived PDF is observed to highly deviate from the Gaussian distribution, especially at moderate to small network loads. Based on the derived inter-cell interference statistics, the decoder performance can be significantly improved compared to the case when the traditional decoder optimized for the AWGN channel is employed. A simple suboptimum decoding algorithm that closely approximates the derived optimum decoder performance is also proposed.

Recently, a variety of full-rate, full-diversity quasi-orthogonal space-time block codes (QO-STBCs) have been designed. Though the quasi-orthogonality does reduce the decoding complexity from order of MQNto MQN/2for Q-ary QAM modulation with N transmit and M receive antennas, there is still need for improvement. Several simple suboptimum decoding algorithms were proposed but suffer quite severe performance losses over maximum likelihood (ML) decoding. Here, we propose a class of decoding algorithms for QO-STBCs based on interference cancellation with complexity on the order of MQN/2-1and performance virtually identical to that of ML decoding. A modification to the base algorithm is also developed with complexity approximately 1/radic(Q) times that of the base algorithm.

An efficient synchronization scheme based on a repetitive preamble structure for orthogonal frequency division multiplexing systems was proposed by Schmidl and Cox. However, standard autocorrelation based estimation algorithms result in a plateau in the timing metric due to the cyclic prefix (CP), resulting in a region of uncertainty. Several modifications, either to the preamble structure itself or the estimation algorithm, have been proposed to remedy this problem. In this paper, we present a maximum-likelihood (ML) symbol timing estimation algorithm taking into account the presence of the CP. The performance of its practical modification is evaluated via computer simulations.

A 180/spl deg/ carrier phase ambiguity is inevitable in digital communication systems employing binary phase-shift keying modulation and non-data-aided carrier phase recovery. Here, we propose a simple modification to standard regular RA codes by exploiting differential encoding inherent to inner encoder of RA codes resulting in a 180/spl deg/ rotationally invariant RA code.

The sensitivity of the iterative decoder for repeat-accumulate (RA) codes to carrier phase and channel signal-to-noise ratio estimation errors is investigated, and efficient algorithms to estimate and correct these errors are developed. The behavior of RA codes with imperfect channel estimation is different from that of turbo codes, and correction algorithms specific to RA codes must be formulated. The proposed algorithms use the soft information generated within the iterative decoder, and thus, are not only hardware-efficient, but also offer excellent performance.

It is well known that turbo codes provide highly unequal error protection within a transmitted frame. Previous attempts to exploit this fact focused mainly on adding additional redundancy to provide extra protection for the error-prone bit positions. Here, instead, we use the error-detection capability of the cyclic redundancy check (CRC), which is almost always employed in practical systems. Once a frame is declared uncorrectable by the CRC, a process termed the error-prone bit processing procedure is activated in an attempt to correct the probable error patterns which are a priori identified as being error-prone.

The uplink performance of synchronous and asynchronous slow frequency-hop spread-spectrum multiple-access (SFHSS-MA) networks transmitting L bits per hop using binary differential phase shift keying (BDPSK) is analyzed under the additive white Gaussian noise (AWGN) and Rayleigh fading channels. Analytic expressions for the average conditional bit error probabilities given a hop is hit by K' interfering users are derived. Results show that SFHSS-MA networks using BDPSK achieve nearly twice the maximum normalized network throughput compared to networks using BFSK under both AWGN and Rayleigh fading channels.

Optimum values for the modulation order M, code rate r, and the number of frequency-hop slots q maximizing the network throughput are obtained based on simulations for frequency-hopped spread-spectrum multiple-access networks, where L Q-ary Reed-Solomon (RS) code symbols are transmitted per hop, and each Q-ary RS code symbol is transmitted using log/sub M/Q M-ary frequency-shift-keying-modulated signals. Network throughput is evaluated under additive white Gaussian noise and Rayleigh fading channels. For the case when the received RS symbol is not interfered by multiple-access interference (MAI), a closed-form expression for the symbol-error probability is derived, and for the case when the symbol is interfered by MAI, simulated symbol-error probabilities are used. It is shown that the optimum M is four or eight, irrespective of the channel environment and the number of users. The optimum code rate is determined primarily based on the channel environment and does not show much dependence on M or Q. It is also shown that for the case of synchronous hopping under Rayleigh fading at high signal-to-noise ratios, the difference in instantaneous power among the interfering users significantly improves the performance, compared with the case when there is no fading. We also consider the case when the receiver erases the symbols that are interfered and compare the performance with the case of the hard decisions receiver.

Optimization for system parameters including the modulation order, diversity order and traffic density to maximize the throughput of FHMA system with multi-level FSK is performed. Theoretical limit on the throughput and optimal system parameters are derived. The derived results can be applied to the conventional synchronous fast FHMA system with MFSK modulation based on the equivalent characteristic in multiple access channel model between both systems.

A novel frequency-hop spread-spectrum multiple-access network employing M-ary orthogonal Walsh sequence keying with noncoherent demodulation is proposed. The transmitted Walsh sequence is overlaid by a user-specific pseudonoise sequence to reduce the effect of multiple-access hits. Two Gaussian approximations for the multiple-access interference from both the dehopped slot and its neighboring slots are developed and are used to analyze the performance of the proposed network for synchronous and asynchronous hopping under nonfading and Rayleigh fading channels. The effect of imperfect hop timing synchronization at the receiver is also analyzed. It is shown that the proposed network offers significantly improved network throughput compared to networks based on traditional M-ary frequency-shift keying modulation.

Performance of robust soft decoding metrics is examined for use in convolutional coded asynchronous fast frequency-hop spread-spectrum multiple-access networks using binary frequency-shift keying under Rayleigh fading channels. For comparison, maximum-likelihood metrics based on a Gaussian approximation are derived. Significant gains are observed compared to hard decision decoding by using appropriate soft metrics.

An adaptive serial search pseudonoise (PN) code acquisition scheme is proposed, in which the detection threshold is scaled by the instantaneous received power measured prior to PN code correlation. We observe that the proposed scheme achieves significantly improved mean acquisition times compared to the conventional nonadaptive schemes under Rayleigh fading and pulsed Gaussian noise jamming. Furthermore, the proposed scheme is shown to be optimum under pulsed Gaussian noise jamming in the sense that it forces the worst case jamming fraction to unity.

The performance of frequency-hop spread-spectrum multiple-access networks using orthogonal M-ary frequency-shift keying modulation with noncoherent detection is analyzed under tone jamming, Rayleigh fading, and additive white Gaussian noise. A simple Gaussian model is derived for the multiple-access interference giving accurate fit to the simulation results with appropriately chosen correction terms. This approximation is then used to analyze the performance of the network under additional tone jamming. Both cases when the jamming tones fade and when they do not are considered.

The performance of asynchronous slow frequency-hop spread-spectrum multiple-access networks where each user transmits L, M-ary symbols per hop using M-ary frequency-shift keying (FSK) modulation with noncoherent demodulation is investigated. Expressions for the decision variables are derived for a given multiple FSK (MFSK) symbol within a hop hit by K' interfering users under additive white Gaussian noise and Rayleigh fading channel models. For the special case when M=2, an accurate analytic approximation for the average error probability is derived as a function of L and K' and semianalytic Monte Carlo simulations are performed to estimate the probability of error for M larger than 2. The results are used to investigate the dependence of the average symbol error probability on L and M. Finally, the effect of enforcing phase transition between the MFSK symbols within a hop is investigated.

Uncoded antijamming capability of the multicarrier direct-sequence spread-spectrum system proposed by Kondo and Milstein (see ibid. vol.44, p.238-46, 1996 ) is analyzed. Joint pulse/partial-band noise jamming is considered with various subcarrier demodulator output combining schemes. We find that full-band pulse jamming maximizes the error probability for all cases considered. With Rayleigh fading and maximal-ratio combining, the multicarrier system achieves performance very close to that of the single-carrier system without fading even with a very small number of subcarriers.

Unlike traditional trained channel equalizers, not much work has been done to theoretically characterize the convergence properties of blind channel equalizers due to their inherent nonlinearity. It is only recently that convergence properties of some well-known algorithms such as the generalised Sato algorithm (GSA) and the constant modulus algorithm (CMA) have been analytically derived. In this paper, the convergence properties of the stop-and-go algorithm proposed by Picchi and Prati (1987) are analyzed. The derived mean squared error and the coefficient trajectories are compared with simulation results to verify the validity of the analytical results.

Capture phenomena in slotted ALOHA packet radio networks employing spread-spectrum modulation is considered. Probability of capture with both delay and power capture mechanisms are derived and compared with power- and delay-only capture models. Significant improvements in the capture probability is observed. The improvement over the delay-only capture model increases with decreasing arrival-time randomization overhead.

In this paper, we derive error probability expressions for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) spread direct-sequence spread-spectrum (DSSS) systems employing random spreading sequences with RAKE receivers. The derived expressions accurately take into account the effect of interpath interference which usually has been neglected in previous analyses. Selection, equal gain, and maximal ratio techniques are considered for diversity combining. Two possible finger assignment strategies, one based on the instantaneous amplitudes and another based on the average powers of the multipath components, are considered for the assignment of multipath components to the available demodulating fingers in the RAKE receiver. Also, various simple, and in many cases, closed-form approximations for the error probabilities are derived and their accuracies are assessed.

The main concern of this paper is to estimate the symbol error probabilities of synchronous and asynchronous frequency-hop spread-spectrum multiple-access (FHSS-MA) networks through semi-analytic Monte Carlo simulations. We concentrate on systems transmitting one M-ary (M/spl ges/2) FSK modulated symbol per hop with noncoherent demodulation. The usual practice when analyzing the performance of such networks is to upper-bound the probability of symbol error when a hop is hit by K/sup '//spl ges/1 interfering users with (M-1)/M or 1. Previous work on the derivation of accurate approximations to this probability for the case when M=2 has indicated that the aforementioned bound not only gives excessively pessimistic results but may also lead to wrong tradeoff decisions. Using the simulated values for the error probabilities, we show that a similar argument holds for the cases when M>2 as well. Also, by employing a normalized throughput measure that takes into account the bandwidth and time expansion associated with the modulation order M, we find that there exists an optimum value of M that achieves the maximum possible throughput for the cases when binary and M-ary error correcting codes are employed. Throughput results are also given for the case when the signals from the active users in the network suffer from independent Rayleigh fading.

The performance of a frequency-hop spread-spectrum system employing carrier jitter against one-dimensional tone jamming (n=1 band multitone jamming) is investigated. First, noncoherent BFSK signaling under continuous-wave (CW) tone interference with arbitrary frequency offset is analyzed. A closed-form expression is derived for the error probability when there is one interfering CW tone and the background noise is negligible. When the background noise is significant, an expression involving one numerical integration is derived for the probability of error. It is shown that an interfering CW tone with power less than that of the signal can still cause errors with significant probability for certain ranges of carrier offsets. Next, the authors apply these results in analyzing the performance of a FHSS communications system under one-dimensional tone jamming when the communicator pseudorandomly jitters his carrier frequency from hop to hop. Two different methods of carrier jittering are considered. It is found that one of the schemes offers approximately a 3 dB gain in signal-to-noise ratio over a system without carrier jittering while the other scheme offers no significant gain.>

The optimal arrival-time distribution that maximizes the delay-capture probability in spread-spectrum packet radio networks is derived. It is shown that using the optimal arrival-time distribution, the capture probability converges to a finite value as the number of contending users increase. Normalized throughput and average delay is computed for slotted ALOHA random access packet radio networks employing direct-sequence spread-spectrum modulation. It is shown that large performance improvements may be expected by optimizing the arrival-time distribution compared to the uniform arrival-time distribution assumed by Davis and Gronemeyer (1980). Three practical realizable modifications are considered which are shown to provide performance close to the optimum.>

The performance of robust metrics (metrics that can be computed from the outputs of the matched filters only) with convolutional coding and diversity under worst-case partial-band noise jamming is analyzed. Both binary and dual-k convolutional codes employing these metrics with diversity are compared via Union-Chernoff bounds. The performances of metrics considered in the literature that assume perfect side-information are given for comparison purposes. It is found that there exist very good robust metrics that provide performance comparable to metrics using perfect side-information. Among the robust metrics considered, the self-normalized metric offers the best performance and achieves performance practically identical to that of the square-law-combining metric with perfect side-information for M=8.>

The performance of Reed-Solomon codes in an asynchronous frequency-hop spread-spectrum multiple-spectrum (FHSS-MA) network is discussed. When q denotes the number of frequency slots available to the network and r denotes the rate of the Reed-Solomon code, optimal (q,r) pairs that meet a given performance criterion with minimum bandwidth expansion (q/r) for a given number of active users are obtained. It is shown that the optimal code rate rapidly converges to a constant value and the optimum number of slots increases approximately linearly as the number of active users increases. This suggests that one should fix the code rate and increase the number of slots to accommodate the increasing number of users in the network under a given performance criterion with minimum bandwidth expansion.>

Expressions are developed for the probability of error for asynchronous frequency-hop spread-spectrum multiple-access networks using Markov hopping patterns and binary frequency shift keying (BFSK) with one symbol transmitted per hop. The expressions are exact when there is one interfering user and orthogonal BFSK is used. They provide excellent approximations when there are more than one interfering user. It is also shown that the error probability when Markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used. By computing the channel capacity and the associated throughput, a simple hard decision receiver is shown to perform much better than a receiver using perfect side-information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop.>