Showing papers on "QAM published in 2009"

Subcarrier-index modulation OFDM

Abstract: A new transmission approach, referred to as subcarrier-index modulation (SIM) is proposed to be integrated with the orthogonal frequency division multiplexing (OFDM) systems. More specifically, it relates to adding an additional dimension to the conventional two-dimensional (2-D) amplitude/phase modulation (APM) techniques, i.e. amplitude shift keying (ASK) and quadrature amplitude modulation (QAM). The key idea of SIM is to employ the subcarrier-index to convey information to the receiver. Furthermore, a closed-form analytical bit error ratio (BER) of SIM OFDM in Rayleigh channel is derived. Analytical and simulation results show error probability performance gain of 4 dB over 4-QAM OFDM systems for both coded and uncoded data without power saving policy. Alternatively, power saving policy retains an average gain of 1 dB while using 3 dB less transmit power per OFDM symbol.

121.9-Gb/s PDM-OFDM Transmission With 2-b/s/Hz Spectral Efficiency Over 1000 km of SSMF

Abstract: We discuss optical multi-band orthogonal frequency division multiplexing (OFDM) and show that by using multiple parallel OFDM bands, the required bandwidth of the digital-to-analogue/ analogue-to-digital converters and the required cyclic prefix can significantly be reduced. With the help of four OFDM bands and polarization division multiplexing (PDM) we report continuously detectable transmission of 10 times121.9-Gb/s (112.6-Gb/s without OFDM overhead) at 50-GHz channel spacing over 1,000-km standard single mode fiber (SSMF) without any inline dispersion compensation. In this experiment 8 QAM subcarrier modulation is used which confines the spectrum of the 121.9 Gb/s PDM-OFDM signal within a 22.8 GHz optical bandwidth. Moreover, we propose a digital signal processing method to reduce the matching requirements for the wideband transmitter IQ mixer structures required for PDM-OFDM.

A Foundation in Digital Communication

Abstract: This intuitive yet rigorous introduction derives the core results of digital communication from first principles. Theory, rather than industry standards, motivates the engineering approaches, and key results are stated with all the required assumptions. The book emphasizes the geometric view, opening with the inner product, the matched filter for its computation, Parseval's theorem, the sampling theorem as an orthonormal expansion, the isometry between passband signals and their baseband representation, and the spectral-efficiency optimality of quadrature amplitude modulation (QAM). Subsequent chapters address noise, hypothesis testing, Gaussian stochastic processes, and the sufficiency of the matched filter outputs. Uniquely, there is a treatment of white noise without generalized functions, and of the power spectral density without artificial random jitters and random phases in the analysis of QAM. This systematic and insightful book, with over 300 exercises, is ideal for graduate courses in digital communication, and for anyone asking 'why' and not just 'how'.

Error vector magnitude to SNR conversion for nondata-aided receivers

Abstract: Error vector magnitude (EVM) is one of the widely accepted figure of merits used to evaluate the quality of communication systems In the literature, EVM has been related to signal-to-noise ratio (SNR) for data-aided receivers, where preamble sequences or pilots are used to measure the EVM, or under the assumption of high SNR values In this paper, this relation is examined for nondata-aided receivers and is shown to perform poorly, especially for low SNR values or high modulation orders The EVM for nondata-aided receivers is then evaluated and its value is related to the SNR for quadrature amplitude modulation (QAM) and pulse amplitude modulation (PAM) signals over additive white Gaussian noise (AWGN) channels and Rayleigh fading channels, and for systems with IQ imbalances The results show that derived equations can be used to reliably estimate SNR values using EVM measurements that are made based on detected data symbols Thus, presented work can be quite useful for measurement devices such as vector signal analyzers (VSA), where EVM measurements are readily available

Multi-Level, Multi-Dimensional Coding for High-Speed and High-Spectral-Efficiency Optical Transmission

Abstract: We review and study several single carrier based multi-level and multi-dimensional coding (ML-MDC) technologies recently demonstrated for spectrally-efficient 100-Gb/s transmission. These include 16-ary PDM-QPSK, 64-ary PDM-8PSK, 64-ary PDM-8QAM as well as 256-ary PDM-16 QAM. We show that high-speed QPSK, 8PSK, 8QAM, and 16QAM can all be generated using commercially available optical modulators using only binary electrical drive signals through novel synthesis methods, and that all of these modulation formats can be detected using a universal receiver front-end and digital coherent detection. We show that the constant modulus algorithm (CMA), which is highly effective for blind polarization recovery of PDM-QPSK and PDM-8PSK signals, is much less effective for PDM-8QAM and PDM-16 QAM. We then present a recently proposed, cascaded multi-modulus algorithm for these cases. In addition to the DSP algorithms used for constellation recovery, we also describe a DSP algorithm to improve the performance of a coherent receiver using single-ended photo-detection. The system impact of ASE noise, laser phase noise, narrowband optical filtering and fiber nonlinear effects has been investigated. For high-level modulation formats using full receiver-side digital compensation, it is shown that the requirement on LO phase noise is more stringent than the signal laser. We also show that RZ pulse shaping significantly improves filter- and fiber-nonlinear tolerance. Finally we present three high-spectral-efficiency and high-speed DWDM transmission experiments implementing these ML-MDC technologies.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 $\times$ 2 and 4 $\times$ 2 MIMO Systems

Abstract: This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 × 2) and the 4 transmit antenna, 2 receive antenna (4 × 2) MIMO systems. Presently, the best known STBC for the 2 × 2 system is the Golden code and that for the 4 × 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 × 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 × 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of M 4 for square QAM of size M. In this paper, a scheme that reduces its ML-decoding complexity to M 2?(M) is presented.

Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems

Abstract: An accurate blind frequency offset estimator adapted to QAM modulated signal is proposed. For coherent 100Gbit/s QAM PolMux transmission, frequency offset can be recovered with an accuracy of a few kHz.

Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique.

Abstract: We demonstrate a linearly field-modulated, direct-detected virtual SSB-OFDM (VSSB-OFDM) transmission with an RF tone placed at the edge of the signal band. By employing the iterative estimation and cancellation technique for the signal-signal beat interference (SSBI) at the receiver, our approach alleviates the need of the frequency gap, which is typically reserved for isolating the SSBI, and saves half the electrical bandwidth, thus being very spectrally efficient. We derive the theoretical model for the VSSB-OFDM system and detail the signal processing for the iterative approach conducted at the receiver. Possible limitations for this iterative approach are also given and discussed. We successfully transmit a 10 Gbps, 4-quadrature-amplitude-modulation (QAM) VSSB-OFDM signal through 340 km of uncompensated standard single mode fiber (SSMF) with almost no penalty. In addition, the simulated results show that the proposed scheme has an approximately 2 dB optical-signal-to-noise-ratio (OSNR) gain and has a better chromatic dispersion (CD) tolerance compared with the previous intensity-modulated SSB-OFDM system.

Performance of Decode-and-Forward Cooperative Communications Over Nakagami- $m$ Fading Channels

Abstract: In this paper, we analyze the symbol error rate (SER) performance of decode-and-forward (DF) cooperative communications over Nakagami-m fading channels. For the classical three-node cooperation model, the exact SER expressions for both M phase shift keying (PSK) and M quadrature amplitude modulation (QAM) are derived. For easy usage, we also provide asymptotic approximations for the SER. In the analysis, we first consider the cooperation scenario in which all the channels are uncorrelated. In practice, it may happen that a correlation exists between the source-destination and relay-destination channels, e.g., for user cooperation in the uplink of a cellular network. We then examine the SER in this scenario. In addition, by varying the parameters of the Nakagami-m fading channels in the analytical results, we obtain some perceptions of choosing a good relay for enhancing the cooperation and make clear about how the included Nakagami fading figures and channel variances affect the SER performance. In addition, the optimal power allocation is investigated based on the derived asymptotic SER expressions. Simulations are finally provided to verify the correctness of our analysis.

Fundamental performance limits of communications systems impaired by impulse noise

Abstract: In this paper, we investigate the ultimate performance limits, in terms of achievable information rate (IR), of communication systems impaired by impulse noise. We compare single carrier (SC) and multi-carrier (MC) transmission systems employing quadrature amplitude modulation (QAM) formats. More precisely, we consider SC schemes with coded modulations and MC systems based on orthogonal frequency division modulation (OFDM). For the MC schemes, we introduce a theoretically equivalent channel model which makes the computation of the IR feasible. This simple channel model will be referred to as interleaved MC. We show that, in the presence of impulse noise and except for systems operating at very high spectral efficiency, the IR of MC schemes is lower than that of SC schemes. More precisely, use of MC schemes may lead to an unavoidable fundamental loss with respect to SC schemes at typical coding rates, whereas MC schemes are to be preferred for very high coding rates or in uncoded systems. These results hold for additive white Gaussian noise (AWGN) and dispersive channels, either considering plain OFDM or MC schemes employing water-filling and bit-loading algorithms. In order to validate our theoretical results, we also obtain the bit error rate (BER) performance of SC and MC schemes through Monte Carlo simulations. A few trellis-coded modulation (TCM) and low-density parity-check (LDPC)-coded schemes are considered. The obtained SNR loss in the BER curves between the AWGN and impulse noise channels matches well with the corresponding IR gap.

On Optimal Quasi-Orthogonal Space–Time Block Codes With Minimum Decoding Complexity

Abstract: Orthogonal space-time block codes (OSTBC) from orthogonal designs have both advantages of complex symbol-wise maximum-likelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than two antennas for complex symbols. To increase the symbol rates, they have been generalized to quasi-orthogonal space-time block codes (QOSTBC) in the literature but the diversity order is reduced by half and the complex symbol-wise ML decoding is significantly increased to complex symbol pair-wise (pair of complex symbols) ML decoding. The QOSTBC has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair-wise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal-literal triangular lattices have been found by Su-Xia, where the optimality means the optimal diversity product (or product distance). QOSTBC has also been modified by Yuen-Guan-Tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair-wise ML decoding (the same complexity as complex symbol-wise decoding) and the optimal rotation angle for square and rectangular QAM constellations has been found. In this paper, we systematically study general linear transformations of information symbols for QOSTBC to have both full diversity and real symbol pair-wise ML decoding. We present the optimal transformation matrices (among all possible linear transformations not necessarily symbol rotations) of information symbols for QOSTBC with real symbol pair-wise ML decoding such that the optimal diversity product is achieved for both general square QAM and general rectangular QAM signal constellations. Furthermore, our newly proposed optimal linear transformations for QOSTBC also work for general QAM constellations in the sense that QOSTBC have full diversity with good diversity product property and real symbol pair-wise ML decoding. Interestingly, the optimal diversity products for square QAM constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. However, the optimal diversity products for (nonsquare) rectangular QAM constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. In this paper, we also present the optimal transformations for the co-ordinate interleaved orthogonal designs (CIOD) proposed by Khan-Rajan for rectangular QAM constellations.

Performance of Optimum Switching Adaptive $M$ -QAM for Amplify-and-Forward Relays

Abstract: Optimization of the switching thresholds for constant-power adaptive five-mode M-ary quadrature amplitude modulation (M -QAM) transmission with an amplify-and-forward (AF) relay network is developed. The optimization criterion is the maximization of spectral efficiency subject to an average bit-error-rate (BER) constraint. This approach results in a constant-BER variable-rate M-QAM AF relay system, which requires feedback of log2(N) bits for N modes. The performance analysis is based on an upper bound on the total effective SNR. Expressions are derived for the outage probability, the achievable spectral efficiency, and the error-rate performance for the AF cooperative system over both independent identically distributed (i.i.d.) and non-i.i.d. Rayleigh fading environments. The tightness of the upper bound is validated by Monte Carlo simulation. Adaptive five-mode M-QAM with optimum switching levels is shown to offer performance gains of 2-2.5 dB compared with fixed switching in terms of the transmit SNR to achieve specific spectral efficiency. Furthermore, the spectral efficiency of adaptive five-mode M-QAM with optimized switching comes within ~6 dB of the theoretical Shannon channel capacity. However, this performance gain, which is obtained by employing adaptive M -QAM under cooperative diversity, comes at the cost of increased system complexity that is incurred due to the additional complexity of transmitter and receiver design.

Distribution of L-values in gray-mapped M 2 -QAM: closed-form approximations and applications

Abstract: In this paper we develop closed form approximations for the probability density function (PDF) of the reliability metrics (L-values) in bit-interleaved coded modulation (BICM). The expressions are valid for M2-ary quadrature amplitude modulations (M2-QAM) with binary reflected Gray mapping when the metrics are calculated using the so-called max-log approximation. Based on the developed expressions, we also propose two simple Gaussian mixture approximations that are analytically tractable. We apply our developments to efficiently calculate the BICM capacity, and to develop bounds on the coded bit-error rate when a convolutional code is used. The coded performance of a hybrid automatic repeat request (HARQ) based on constellation rearrangement is also evaluated.

Polarization QAM modulation (POL-QAM) for coherent detection schemes

Abstract: A new polarization constellation diagram leads to polarization QAM modulation formats. At 28Gbaud (112Gb/s) POL-QAM 6-4 with six QPSK modulated states-of-polarization enables 1.7-dB higher sensitivity than PDM-QPSK by applying coded-modulation with an inner RS(511,455) FEC.

Signal Remodulation of OFDM-QAM for Long Reach Carrier Distributed Passive Optical Networks

Abstract: The passive optical network (PON) using orthogonal frequency-division multiplexing (OFDM) is a subject of many research works recently. The OFDM signal is especially good for long reach (LR)-PON due to its high tolerance to chromatic dispersion and high spectral efficiency. We study, for the first time, the possibility of using OFDM for signal remodulation in LR-PONs. Three different colorless optical networking unit (ONU) architectures, electroabsorption modulator-based, reflective semiconductor optical amplifier-based and injection-locked Fabry-Perot laser diode-based ONUs, are tested and compared. Error-free operations are achieved in 100-km fiber transmission without dispersion compensation.

Laser Linewidth Tolerance of Decision-Aided Maximum Likelihood Phase Estimation in Coherent Optical $M$ -ary PSK and QAM Systems

Abstract: This letter extends the decision-aided (DA) maximum likelihood (ML) phase estimation in an M -ary phase-shift keying (PSK) system to quadrature amplitude modulation (QAM) signals. The block length effect is simulated for both M-ary PSK and QAM systems, and also investigated in M -ary PSK systems through analysis. Our results show that the tolerance of DA ML to laser linewidth for square 16-QAM can be increased by >10 times compared to the block Mth power scheme.

ML performance analysis of the decode-and-forward protocol in cooperative diversity networks

Abstract: We analyze the maximum-likelihood (ML) performance of the decode-and-forward protocol in a cooperative diversity network which consists of a source, a relay, and a destination with a direct path signal, but which is not equipped with cyclicredundancy- check (CRC) codes. In this system, due to a symbol error at the relay, the ML receiver at the destination needs to consider all the possible symbol detection scenarios at the relay as well as at the destination. Therefore, the ML detection metric is given by a linear combination of exponential functions, which prevents the use of the classical minimum Euclidean distance rule. Adopting the max-log approximation, we approximate the ML detection rule which makes the ML performance analysis tractable. In order to facilitate the derivation of decision regions, we simplify the ML detection rule in the two-dimensional real space such that two metric values of two adjacent constellation points are sequentially compared. Then we obtain decision regions in a form without union and intersection. Finally, based on the decision regions, we derive a very accurate closedform BER approximation for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM). The obtained BER expression can serve as the error performance upper-bound of the decode-and-forward protocol in cooperative diversity networks.

QAM and PSK codebooks for limited feedback MIMO beamforming

Abstract: This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

The Equivalence of Semidefinite Relaxation MIMO Detectors for Higher-Order QAM

Abstract: In multi-input multi-output (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient high-performance approach. For BPSK and QPSK, it has been found that SDR can provide near-optimal bit error probability performance. This has stimulated a number of recent research endeavors that aim to apply SDR to the high-order QAM cases. These independently developed SDRs are different in concept, structure and complexity, and presently no serious analysis has been given to compare these methods. This paper analyzes the relationship of three such SDR methods, namely the polynomial-inspired SDR (PI-SDR) by Wiesel , the bound-constrained SDR (BC-SDR) by Sidiropoulos and Luo, and the virtually-antipodal SDR (VA-SDR) by Mao Rather unexpectedly, we prove that the three SDRs are equivalent in the following sense: The three SDRs yield the same optimal objective values, and their optimal solutions have strong correspondences. Specifically, we establish this solution equivalence between BC-SDR and VA-SDR for any 4q -QAM constellations, and that between BC-SDR and PI-SDR for 16-QAM and 64-QAM. Moreover, the equivalence result holds for any channel, problem size, and signal-to-noise ratio. Our theoretical findings are confirmed by simulations, where the three SDRs offer identical symbol error probabilities. Additional simulation results are also provided to demonstrate the effectiveness of SDR compared to some other MIMO detectors, in terms of complexity and symbol error performance.

Useful integrals for performance evaluation of communication systems in generalised η - μand κ - μ fading channels

Abstract: The author obtains closed-form expressions for the averages of the Gaussian Q-function and product of two Gaussian Q-functions over the generalised η−μ and κ−μ distributions. These results can be useful in many practical applications when evaluating error rate performances of communication systems operating in radio channels modelled by the η−μ and κ−μ distributions. The formulas are obtained in terms of Appell's (F1(·) and Φ1(·)) and Lauricella's (FD3(·) and Φ1(3)(·)) hypergeometric functions. As examples of application, the average symbol error rates of general order rectangular quadrature amplitude modulation (QAM) in η−μ and κ−μ radio channels are evaluated.

A Fixed-Complexity Smart Candidate Adding Algorithm for Soft-Output MIMO Detection

Abstract: We present a soft-output multiple-input multiple-output (MIMO) detection algorithm that achieves near max-log optimal error rate performance with low- and fixed-computational complexity. The proposed smart ordering and candidate adding (SOCA) algorithm combines a smart-ordered QR decomposition with smart candidate adding and a parallel layer-by-layer search of the detection tree. In contrast to prior algorithms that use smart candidate adding, the proposed algorithm has fixed computational complexity, and it never visits a node more than once. Results indicate that the SOCA algorithm has an attractive performance-complexity profile for both fast and slow fading 4 × 4 and 8 × 8 MIMO channels with quadrature amplitude modulation (QAM) inputs.

A low complexity hierarchical QAM symbol bits allocation algorithm for unequal error protection of wireless video transmission

Abstract: A low complexity hierarchical quadrature amplitude modulation (QAM) symbol bits allocation algorithm for unequal error protection of video transmission over wireless channels is proposed in this paper. An unequal error protection (UEP) scheme using hierarchical QAM, which takes into consideration the non-uniformly distributed importance of intracoded frame (I-frame) and predictive coded frame (P-frame) in a group of pictures (GOP), is first proposed. In order to optimally allocate the hierarchical QAM's high priority (HP), medium priority (MP) and low priority (LP) symbol bits to the H.264/AVC video, a generic solution for optimal allocation of hierarchical QAM's high priority (HP), medium priority (MP) and low priority (LP) symbol bits to the H.264/AVC video is then proposed. Finally, a low complexity symbol bits allocation algorithm, namely ranking search algorithm, which reduces the computational complexity of the proposed optimal symbol bits allocation algorithm, is proposed. Simulation results show that our proposed UEP scheme outperforms the classical equal error protection (EEP) scheme and also the previous UEP scheme.

Cascaded two-modulus algorithm for blind polarization de-multiplexing of 114-Gb/s PDM-8-QAM optical signals

Abstract: An 8-QAM optical signal is generated for the first time using a parallel I/Q modulator followed by a phase modulator with binary drive signals. Blind polarization de-multiplexing of 60 and 114-Gb/s PDM-8-QAM signals is demonstrated using a new cascaded two-modulus algorithm.

Design of rotated QAM mapper/demapper for the DVB-T2 standard

Abstract: Signal Space Diversity (SSD) has been lately adopted into the second generation of the terrestrial digital video broadcasting standard DVB-T2. While spectrally efficient, SSD improves the performance of QAM constellations over fading channels thanks to an increased diversity. In this paper, flexible mapper and demapper architectures for DVB-T2 standard are detailed. A detection based on the decomposition of the constellation into two-dimensional sub-regions in signal space associated to an algorithmic simplification constitute the main novelty of this work. They enable to strongly decrease the complexity of the demapper. The design and the FPGA prototyping of the resultant architecture are then described. Low architecture complexity and measured performance demonstrate the efficiency of the detection method.

A multilevel coded modulation approach for hexagonal signal constellation

Abstract: We propose a new coded modulation called hexagonal shell modulation (HSM). The HSM has a signal constellation composed of shell-like tiling of hexagons and thus has a lower peak-to-average power ratio (PAR) than a standard square quadrature amplitude modulation (QAM) with comparable bandwidth efficiency and minimum Euclidean distance. The main challenge is that HSM has a non-power-of-two number of constellation points, and thus assignment of binary information to HSM is not straightforward. We resolve this by applying a multilevel coded modulation (MLC) scheme where a ternary set partitioning combined with binary-input ternary-output (BITO) turbo codes is employed to fully exploit the property of the nonpower- of-two constellation points. Throughout this letter, we focus on an 18-ary HSM with the information rate of 3 bit/symbol as a specific example. It is shown that this system outperforms the standard square 16-QAM with the same rate when PAR is constrained.

Exact error probability analysis of rectangular QAM for single- and multichannel reception in nakagami-m fading channels

Abstract: In this contribution, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) for single- and multichannel diversity reception over independent but not-necessarily identically distributed Nakagami-m fading channels. The diversity branches may hence exhibit identical or distinctive power levels and their associated Nakagami indexes need not be the same. Our work extends previous results pertaining to nondiversity reception of M-ary rectangular QAM over Rayleigh fading channels and multichannel reception of M-ary square QAM over Nakagami-m fading channels. For a given number L of diversity branches and a corresponding set of arbitrary real-valued Nakagami indexes not less than 1/2, our SEP results are expressed in terms of Gauss's hypergeometric function 2F1 and Lauricella's multivariate hypergeometric function FD (L) of L variables, both of which can be efficiently evaluated using standard numerical softwares.

All-Optical Waveform Sampling in High-Speed Optical Communication Systems Using Advanced Modulation Formats

Abstract: We review techniques to characterize optical data with very high fidelity using the principle of optical sampling based on four-wave mixing in a highly nonlinear fiber. This approach results in sub-ps time resolution without artifacts in the impulse response and also excellent sensitivity allowing statistical analysis. In particular we describe implementations aimed at differentially phase encoded data (such as DQPSK) with all-optical balanced detection, formats requiring the complete signal field recovery (such as QAM) with phase-sensitive sampling, and signals requiring real-time recovery with all-optical real-time sampling. The all-optical approach to characterize optical waveform is shown to be very attractive and practical way to capture the details of various kinds of data and is, in principle, also scalable to extremely high baud rates.

Exact BER analysis of distributed alamouti's code for cooperative diversity networks

Abstract: We analyze the bit-error rate (BER) performance of the distributed Alamouti's code for cooperative diversity networks consisting of a source, two relays and a destination node over Rayleigh fading channels. It is assumed that the relays adopt the amplify-and-forward protocol. Firstly, assuming the existence of the direct path component from the source to the destination, we derive the exact BER expression in a one-integral form for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM) constellations. We also present a series expansion of a very accurate BER approximation, which does not require any numerical calculation, and we prove this series is convergent. Secondly, considering the system where the direct path component does not exist, we obtain the exact BER expression in a one-integral form and a series expansion of the exact BER expression. Numerical results confirm that the two exact BER expressions in a one-integral form perfectly match the simulation results and the two series expressions of BER are very accurate, even with a small truncation window.

Performance Analysis of Cooperative Communication Systems with Imperfect Channel Estimation

Abstract: This paper investigates the effects of channel estimation errors on the symbol-error-rate (SER) performance of a cooperative communication system operating in an amplify-and-forward (AF) mode. A pilot symbol assisted modulation scheme with linear minimum mean square estimation (LMMSE) is used for the channel estimation. An accurate and easy-to-evaluate SER expression is presented for uncoded cooperative communication systems with quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. Numerical simulations are conducted to verify the correctness of the proposed analytical formulation. It is shown that the performance loss caused by channel estimation errors increases mainly with the normalized maximum Doppler frequency.