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Abstract
Techniques to improve the BER performance of 16-level QAM transmission over Rayleigh fading channels for PCM systems are presented, simulations were carried out with a carrier frequency of 1.9GHz, data rate of 64 kbit/s and mobile speed of 30mph. The residual BER was reduced by over an order of magnitutde, by introducing circular constellation coupled differential amplitude and phase encoding, compared with a square QAM constellation. When an oversampling and interpolation technique was combined with circular constellation with differential encoding another order of magnitude reduction in residual BER was obtained. By expanding the number of QAM levels to 64, and on using the two extra bits gained for block coding, the BER was reduced 10-6 for channel SNRs in excess of 35 dB. Decreasing the data throughput to 48 kbit/s using 3/4 rate RS(60, 44, 12) code, 16 level QAM, interleaved over 40ms, transmitted over a Rayleigh fading channel yielded a BER of 10-6 for channel SNRs above 25 dB.
... As an alternative to ADPSK, the classic Differential Amplitude Phase Shift Keying (DAPSK) was proposed by Webb, Hanzo and Steele [187] in 1991. An example of 16-DAPSK is portrayed in Fig. 14(b). ...
... In other words, if the DAPSK's differential encoding process is to be represented by s n = x n−1 s n−1 , the transmitted symbols Nonetheless, the phase of 16-DAPSK's data-carrying symbol x n−1 is still drawn from the original 8PSK constellation diagram. It was proposed in [187] that the detection of DAPSK's data-carrying amplitude may be carried out by testing the amplitude change between consecutive received samples |y n |/|y n−1 |, while the data-carrying phase may be detected by testing the phase change ∠y n − ∠y n−1 . In summary, the fundamental difference between the ADPSK and the DAPSK is that the ADPSK aims for maintaining the mapping regime of a Star QAM constellation for the datacarrying symbols, while the DAPSK aims for maintaining a Star QAM constellation for the transmitted symbols. ...
... In 1995, Rohling and Engels [190] proposed the application of DAPSK in digital terrestrial video broadcasting, where the authors compared the performance of the CDD aided DAPSK to that of the coherent QAM in the presence of realistic channel estimation errors. Despite the satisfactory performance of CDD aided DAPSK in AWGN and block fading channels, it was observed by the authors of [187] that the DAPSK performance degrades and eventually an error floor is formed, as the Doppler frequency is increased. It was suggested by the authors of [187] that both oversampling and channel coding may be invoked for mitigating this problem. ...
Sixty years of coherent versus non-coherent tradeoff as well as the twenty years of coherent versus non-coherent tradeoff in Multiple-Input Multiple-Output (MIMO) systems are surveyed. Furthermore, the advantages of adaptivity are discussed. More explicitly, in order to support the diverse communication requirements of different applications in a unified platform, the 5G New Radio (NR) offers unprecendented adaptivity, abeit at the cost of a substantial amount of signalling overhead that consumes both power and the valuable spectral resources. Striking a beneficial coherent versus non-coherent tradeoff is capable of reducing the pilot overheads of channel estimation, whilst relying on low-complexity detectors, especially in high-mobility scenarios. Furthermore, since energy-efficiency is of salient importance both in the operational and future networks, following the powerful Index Modulation (IM) pholosophy, we conceive a holistic adaptive pholosophy striking the most appropriate coherent/non-coherent, single-/multiple-antenna and diversity/multiplexing tradeoffs, where the number of RF chains, the Peak-to-Average Power Ratio (PAPR) of signal transmission and the maximum amount of interference tolerated by signal detection are all taken into account. We demonstrate that this intelligent tripple-fold adaptivity offers significant benefits in next-generation applications of mmWave and Terahertz solutions, in space-air-ground integrated networks, in full-duplex techniques and in other sophisticated channel coding assisted system designs, where powerful machine learning algorithms are expected to make autonomous decisions concerning the best mode of operation with minimal human intervention.
... 11 According to the survey of [4, Table X], some channel models assume that the number of multipath components obeys the Poisson distribution having the mean of 1.8, 1.9, 9, 10 and 18. the DUC [41], as well as the ADSM [48] square matrices to nonsquare matrices. Here, we also plotted the MED of the star-QAM [76] constellations having L = 2, 4, 8, · · · , 2 10 for reference. In Rayleigh fading scenarios, the reciprocal of MED, i.e., 1/MED, correlates with the effective SNR that achieves a specific BER [13]. ...
... Fig. 5 shows our BER comparisons for the proposed scheme Diff. star 256−QAM [76] Coherent BLAST (PCSI) [9] Coherent SM P = 1 (PCSI) [25] Conv. S−DOSTC (PSK) [38] Conv. ...
... Similar to Fig. 6, in Fig. 7, we compared the proposed N- Diff. star 4096−QAM [76] Coherent BLAST P = 4 (PCSI) [9] Coherent GSM P = 2 (PCSI) [25] Conv. N−DUC P = 4 (DFT b., α c ) Fig. 7, the N-DUC scheme having the P = 4 DFT basis and the ADSM scheme having the P = 2 GSP basis achieved a similar trend to the coherent SM and BLAST schemes. ...
A large-scale differential-detection aided generalized spatial modulation (GSM) system is proposed, which relies on a novel Gram-Schmidt basis set and an adaptive low-complexity detector, and is evidently suitable for high-mobility millimeter-wave (mmWave) channels. We consider non-stationary time-varying mmWave channels and assume that the beam-angles remain relatively fixed, while the channel coefficients vary rapidly. In this scenario, it is a challenging task to find the accurate estimates of channel coefficients for digital beamforming, which becomes an even more severe problem, as the numbers of subarrays and subcarriers increase. Our analog-beamforming-aided nonsquare differentially-detected scheme achieves a higher transmission rate than the conventional coherent multiple-input multiple-output schemes because the pilot overhead and the complex-valued feedback are eliminated. Our simulation results following the IEEE 802.11ad specifications show that the performance of our proposed nonsquare differential GSM improved upon increasing the number of subarrays, where the maximum transmission rate of 16 [bps/Hz] was considered.
... Since for a JFTS channel, the 296 average capacity derived in [8] can only be expressed in terms 297 of infinite series summation, it is more appealing to obtain the 298 channel cutoff rate achievable using only variable rate M-ary 299 signaling. The channel cutoff rate can be calculated using [11] 300 ...
... The results obtained in (C.30) and (C.31) are put back in (11) 708 to obtain the final expressions in Proposition 3. high-speed mixed-signal IC design, and data networks. His research interests 819 include analog/digital CMOS circuit design, communication systems, and 820 biomedical instrumentation for molecular sensing and analysis. ...
... distribuand absence of channel magnitude and phase estimates.The channel cutoff rate R 0 of the communication link is 106 defined as a channel capacity related quantity such that 107 for any R c < R 0 , it is possible to construct a channel 108 code using block length n and coding rate R c capable of 109 maintaining an average error probability less than or equal 110 to 2 −n(R 0 −R c )[11]. Quantifying the channel cutoff rate is done using the Chernoff bound calculation. ...
Performance of common digital modulation techniques is analyzed over indoor wireless environments modeled through the recently proposed joint fading and two-path shadowing (JFTS) channel model. Mathematically tractable expressions for the instantaneous signal-to-noise ratio (SNR) statistics, average bit error rates (ABER) and achievable channel cutoff rates are derived. Analytical results are used to i) investigate the impact of different JFTS model parameters and different modulation techniques on bit error rates and cutoff rates and, ii) demonstrate how the JFTS channel model affects system performance in comparison to conventional empirical channel models. Finally simulation results are used to corroborate this analysis and evaluate the usefulness of such an analysis.
... Without differential encoding on amplitude, this transmission mechanism may be termed as absolute-amplitude DQAM, which may include Absoluteamplitude Differential Phase Shift Keying (ADPSK) [15], Twisted ADPSK (TADPSK) [16] and TADPSK associated with Joint Mapping (TADPSK JM ) [17], where TADPSK introduces a ring-amplitude-dependent phase rotation in order to increase the Star QAM constellation distances, while TADPSK JM jointly maps its bits to DQAM's phase index and ring-amplitude index in order to increase the correlation between the two terms. Moreover, as a popular alternative, Differential Amplitude Phase Shift Keying (DAPSK) [18] applies differential encoding both to the phase and to the ring-amplitude, which constitutes the family of differentialamplitude DQAM schemes that may also include the constellation variants of Twisted DAPSK (TDAPSK) and TDAPSK associated with Joint Mapping (TDAPSK JM ). In this paper, the notational form of M -DQAM(M A ,M P ) is used for all the DQAM schemes, where M , M A and M P refer to the number of modulation levels, ring-amplitudes and phases, respectively. ...
... In the absence of CSI, the DQAM's Conventional Differential Detection (CDD) suffers from a performance erosion compared to its coherent counterparts [18], [19]. In order to improve the CDD's performance, Multiple-Symbol Differ-ential Detection (MSDD) was conceived both for DPSK in [20]- [22] and for DQAM in [22]. ...
... By contrast, the DAPSK scheme [18], [37] invokes the differential encoding process in the same way as the classic DPSK as: ...
Turbo detection performed by exchanging extrinsic information between the soft-decision QAM detector and the channel decoder is beneficial for the sake of exploring the bit dependency imposed both by modulation and by channel coding. However, when the soft-decision coherent QAM detectors are provided with imperfect channel estimates in rapidly fading channels, they tend to produce potentially unreliable LLRs that deviate from the true probabilities, which degrades the turbo detection performance. Against this background, in this paper, we propose a range of new soft-decision multiple-symbol differential sphere detection (MSDSD) and decision-feedback differential detection (DFDD) solutions for differential QAM (DQAM), which dispense with channel estimation in the face of rapidly fading channels. Our proposed design aims for solving the two inherent problems in soft-decision DQAM detection design, which have also been the most substantial obstacle in the way of offering a solution for turbo detected MSDSD aided differential MIMO schemes using QAM: 1) how to facilitate the soft-decision detection of the DQAM's amplitudes, which - in contrast to the DPSK phases - do not form a unitary matrix, and 2) how to separate and streamline the DQAM's soft-decision amplitude and phase detectors. Our simulation results demonstrate that our proposed MSDSD aided DQAM solution is capable of substantially outperforming its MSDSD aided DPSK counterpart in coded systems without imposing a higher complexity. Moreover, our proposed DFDD aided DQAM solution is shown to outperform the conventional solutions in literature. Our discussions on the important subject of coherent versus noncoherent schemes suggest that compared to coherent square QAM relying on realistic imperfect channel estimation, MSDSD aided DQAM may be deemed as a better candidate for turbo detection assisted coded systems operating at high Doppler frequencies.
... To achieve a higher bandwidth efficiency, differential amplitude/phase-shift keying (DAPSK) modulation, see e.g. [4], is introduced. To make use of the diversity of multiple transmit antennas, differential unitary space-time modulation (DUSTM) [5], [6], and differential space-time block coding (DSTBC) [7], are proposed. ...
... Another more bandwidth-efficient modulation scheme for single antenna wireless communication systems is MDAPSK modulation [4]. MDAPSK, where both amplitude and phase are differentially encoded, may be viewed as a combination of differential amplitude-shift keying (DASK) and DPSK, which are independent of each other (cf. ...
... 16DAPSK (y = 2) modulation, which is also referred as 16-star quadrature-amplitude modulation (QAM) [4], is a popular example of MDAPSK modulation. The single constellation for 16DAPSK is shown in Fig. 2 In the first stage of the receiver, differential decoding involves as shown in Fig. 2.9. ...
... For this reason, typically Star QAM constellations are preferred for DQAM design. Furthermore, the classic Differential Amplitude Phase Shift Keying (DAPSK) was proposed by Webb et al. [4] in 1991, where differential encoding was invoked for both the Star QAM ring-amplitude and phase. In 2000, Fischer et al. [2] carried out the capacity comparison of ADPSK, of DAPSK and of their twisted-constellationbased counterparts both in AWGN channels and in quasi-static fading channels. ...
... The performance of the CDD aided DAPSK was compared to that of the coherent QAM in [5]- [7], where the DAPSK was shown to be particularly advantageous, when its coherent QAM counterpart suffered from a realistic channel estimation error. However, it was observed in [4] that the performance of CDD aided DAPSK degrades and eventually an error floor is formed in Rayleigh fading channels, when the Doppler frequency is increased. In order to further improve the CDD's performance, the classic Decision-Feedback Differential Detection (DFDD) that was originally proposed for DPSK in [8], [9] was further developed for DAPSK in [10]- [12]. ...
... For an M -DAPSK(M A ,M P ) scheme [4], [31], differential encoding is invoked both for the phase Ω n = ω n−1 Ω n−1 and for the ring-amplitude Γ n = γ n−1 Γ n−1 by: ...
Differential amplitude phase-shift keying (DAPSK), which is also known as star-shaped quadrature-amplitude modulation, has implementational advantages not only due to dispensing with channel estimation but as a benefit of its low signal detection complexity as well. It is widely recognized that separately detecting the amplitude and the phase of a received DAPSK symbol exhibits lower complexity than jointly detecting the two terms. However, since the amplitude and the phase of a DAPSK symbol are affected by correlated magnitude fading and phase rotations, detecting the two terms completely independently results in a performance loss, which is particularly significant for soft-decision-aided DAPSK detectors relying on multiple receive antennas. Therefore, in this contribution, we propose a new soft-decision-aided DAPSK detection method, which achieves optimum DAPSK detection capability at substantially reduced detection complexity. More specifically, we link each a priori soft-input bit to a specific part of the channel's output, so that only a reduced subset of the DAPSK constellation points has to be evaluated by the soft DAPSK detector. Our simulation results demonstrate that the proposed soft DAPSK detector exhibits lower detection complexity than that of independently detecting the amplitude and the phase, whereas the optimal performance of DAPSK detection is retained.
... M ODULATION schemes, in great number and variety, have been developed and analyzed in uncountable works. Examples of modulation formats are pulse amplitude modulation (PAM), square/rectangular quadrature amplitude modulation (QAM), phase shift keying (PSK), Star-QAM [1], and amplitude-PSK (APSK) [2]. Square-QAM, (or just QAM), is the de-facto-standard in existing wireless communication systems. ...
... , c K ), x ∈ (0, 1), and let the magnitude for the nth signal point be r n = f P (n/N ). 1 We also want to ensure that f P (x) is positive and growing. This is e.g. ...
Quadrature amplitude modulation (QAM), deployed in billions of communication devises, exhibits a shaping-loss of ( dB) compared to the Shannon-Hartley theorem. With inspiration gained from special (leaf, flower petal, and seed) packing arrangements (so called spiral phyllotaxis) found among plants, we have designed a shape-versatile, circular symmetric, modulation scheme, \textit{the Golden angle modulation (GAM)}. Geometric- and probabilistic-shaping-based GAM schemes are designed that practically overcome the shaping-loss of 1.53 dB. Specifically, we consider mutual information (MI)-optimized geometric-, probabilistic-, and joint geometric-and-probabilistic-GAM, under SNR-equality, and PAPR-inequality, constraints. Out of those, the joint scheme yields the highest MI-performance, and then comes the probabilistic schemes. This study finds that GAM could be an interesting candidate for future communication systems. Transmitter resource limited links, such as space probe-to-earth, satellite, and mobile-to-basestation, are scenarios where capacity achieving GAM could be of particular value.
... Here, PCSI at the legitimate receiver was assumed to benefit these conventional schemes. We also considered the classic differential star-QAM (SQAM) [72] and the conventional nonsquare DUC (N-DUC) [33], both of which worked efficiently without CSI. As a reference, the massive MIMO (M-MIMO) cryptography method of [73] was considered, although it required PCSI at both the transmitter and receiver. ...
... For our simulations, we assumed the ideal Rayleigh fading channel model as described in Section II. [72], and the C-MIMO scheme [10] having T = 1 and 2. ...
In this paper, we propose a differential multiple-input multiple-output (MIMO) scheme based on the novel concept of chaos-based time-varying unitary matrices to demonstrate—for the first time in the literature—the ability of differential encoding in achieving practical physical layer security even without the need for using channel estimation. In the proposed scheme, an erroneous secret key, which is extracted from the wireless nature, is used to initialize a chaos sequence that is responsible for generating artificially time-varying unitary matrices capable of obfuscating the transmitted data symbols from illegitimate eavesdroppers. Contrary to conventional studies, the key agreement ratio in this study is assumed to be imperfect, which is often true and very realistic in high-mobility scenarios. Following this, we conceive a new calibration algorithm for reconciling the chaotic sequence generated at the legitimate parties, thus making this calibration algorithm a unique, novel solution to the key sharing problem of conventional chaos-based communication techniques, which has been overlooked over the past few decades. It is found out that differential encoding obviates additional complexity and insecurity in dealing with channel estimation, whereas an eavesdropper must tackle the complicated differentially encoded patterns, which have an exponentially increasing complexity order. In addition, the obtained simulation results demonstrate that the proposed scheme can outperform conventional chaos-based MIMO schemes that assume perfect channel knowledge.
... In Single-Input Single-Output (SISO) channels, Differential Phase Shift Keying (DPSK) [1], [2], Differential Amplitude Phase Shift Keying (DAPSK) [3]- [5] and Absolute-amplitude Differential Phase Shift Keying (ADPSK) [4]- [6] constitute low-complexity alternatives to coherent PSK/QAM schemes. In Multiple-Input Multiple-Output (MIMO) channels, Differential Space-Time Modulation (DSTM) that dispenses with high-complexity channel estimation has also attracted substantial research interests. ...
... The differential encoding applied to the unitary matrices in (31) is still given by (3) as S n = X n−1 S n−1 . Moreover, the differential encoding applied to the ring-amplitudes in (31) is the same as in classic DAPSK [3]- [5], which is given by Γ n = γ n−1 Γ n−1 . The L A -level transmitted ring-amplitude and data-carrying ringamplitude are given by Γ n = α µn √ β and γ n−1 = αǎ, respectively. ...
We propose a new single-RF Differential Space-Time Block Coding using Index Shift Keying (DSTBC-ISK), which is the first in the family of Differential Space-Time Modulation (DSTM) schemes that can simultaneously achieve the following three imperative objectives of (1) forming a finite-cardinality transmit-signals set under the matrix multiplications of differential encoding; (2) retaining a single-stream ML detection complexity that does not grow with the constellation size; (3) offering a beneficial transmit diversity gain over the recently developed Differential Spatial Modulation (DSM). In order to make a fair comparison, we also conceive a low-complexity single-stream detector for DSM, which does not impose any performance loss in comparison to the existing solutions in open literature. Furthermore, in order to improve the performance of finite-cardinality DSTM schemes at higher throughputs, we propose to generalize both Differential Amplitude Shift Keying (DASK) and Amplitude Shift Keying (ASK), which form the generic multi-level-ring star QAM constellation that subsumes the existing two/four-level-ring DASK solutions as special cases. Although the DASK approach has been popularly used in DSTM schemes, we demonstrate that our generalized ASK technique achieves a higher capacity and a better performance in channel coding assisted systems. As a result of using star QAM signalling, the power of the DSTM's signal matrix becomes variable. Against this background, we further develop bespoke Maximum-Likelihood (ML), Minimum Mean Squared Error (MMSE) and Least Square (LS) detectors for DSTM using DASK/ASK, which exhibit different performance versus complexity tradeoffs. Our simulation results demonstrate that the proposed DSTBC-ISK is capable of achieving substantial diversity gains over DSM without eroding its low transceiver complexity.
... M ODULATION schemes, in great number and variety, have been developed and analyzed in uncountable works. Examples of modulation formats are pulse amplitude modulation (PAM), square/rectangular quadrature amplitude modulation (QAM), phase shift keying (PSK), Star-QAM [1], and amplitude-PSK (APSK) [2]. Square-QAM, (or just QAM), is the de-facto-standard in existing wireless communication systems. ...
... , c K ), x ∈ (0, 1), and let the magnitude for the nth signal point be r n = f P (n/N ). 1 We also want to ensure that f P (x) is positive and growing. This is e.g. ...
Quadrature amplitude modulation (QAM), deployed in billions of communication devises, exhibits a shaping-loss of ( dB) compared to the Shannon-Hartley theorem. With inspiration gained from special (leaf, flower petal, and seed) packing arrangements (so called spiral phyllotaxis) found among plants, we have designed a shape-versatile, circular symmetric, modulation scheme, \textit{the Golden angle modulation (GAM)}. Geometric- and probabilistic-shaping-based GAM schemes are designed that practically overcome the shaping-loss of 1.53 dB. Specifically, we consider mutual information (MI)-optimized geometric-, probabilistic-, and joint geometric-and-probabilistic-GAM, under SNR-equality, and PAPR-inequality, constraints. Out of those, the joint scheme yields the highest MI-performance, and then comes the probabilistic schemes. This study finds that GAM could be an interesting candidate for future communication systems. Transmitter resource limited links, such as space probe-to-earth, satellite, and mobile-to-basestation, are scenarios where capacity achieving GAM could be of particular value.
... The fundamental characteristics of the four abovementioned MIMO schemes, the coherent SM scheme [5], [6], and the single-antenna differential scheme modulated by star quadrature amplitude modulation (QAM) [21] are summarized in Table I. 3 III. PROPOSED RECTANGULAR DSM In this section, we introduce the system model of the proposed RDSM scheme, in which the number of symbol intervals per transmission block is T = 1. ...
... We considered both the quasi-static Rayleigh fading channel and the time-varying Rayleigh fading channel obeying the classic Jakes model of Section III-C. The single-antenna differential star-QAM scheme [21], the conventional square DSM scheme [17], the semi-blind CE and DD scheme [16], and the conjugate BF scheme [1] were considered as benchmarks for the proposed G-RDSM scheme. The coherent counterparts of the proposed scheme were equivalent to the SM scheme [5] for T = 1 and the asynchronous STSK scheme [6] for T ≥ 2. The DMs of the conventional DSM scheme and those of the proposed G-RDSM scheme were obtained by the RDC criterion [24]. ...
In the present paper, a novel differential space-time coding scheme is conceived for open-loop noncoherent multipleinput multiple-output (MIMO) downlink scenarios, where the transmission rate increases logarithmically in a scalable manner upon increasing the number of transmit antennas. More specifically, the proposed scheme relies on the projection of a differentially encoded square matrix to its rectangular counterpart and so is capable of reducing the number of symbol intervals needed for block transmission. This is especially beneficial for massive MIMO scenarios, in which the number of transmit antennas is very high. Another advantage exclusive to the presented scheme is that no channel state information (CSI) is required at either the transmitter or the receiver, which eliminates pilot overhead, CSI estimation, CSI feedback, and time-division duplex reciprocity. Furthermore, the rectangular transmission matrix of the proposed scheme contains only a single non-zero element per column, and hence the transmitter may rely on only a single RF chain, similar to the conventional coherent spatial modulation scheme.
... The aim of this paper is to investigate the use of OFDM for high bit rate wireless applications. In order to improve spectral efficiency the use of Differentially Encoded (DE) 16 star Quadrature Amplitude Modulation (QAM) is employed to modulate the parallel carriers [5]. OFDM is a wideband modulation scheme which is specifically designed to cope with the problems of multipath reception. ...
... In general 16 QAM (square) requires coherent detection. However, since the performance of coherent detection is severely affected by multipath fading, (mainly because of carrier recovery issues), the 16 Star QAM constellation shown in fig. 2 combined with differentially coherent detection is preferred [5]. ...
The multicarrier transmission technique known as Orthogonal Frequency Division Multiplexing (OFDM) was devised in the 1960's for voiceband data transmission. Today there are two principle OFDM applications, one is for the high speed digital subscriber loop and the other is for the broadcasting of digital audio and video signals. We will consider the use of OFDM for high-bit rate wireless applications. The Bit Error Rate (BER) performance of OFDM utilising Differentially Encoded (DE) 16 star Quadrature Amplitude Modulation (QAM) and differentially coherent demodulation in frequency flat fading channels is considered via the use of Monte Carlo simulation methods. The BER results are presented for OFDM with 16 QAM (OFMDM/16 QAM), OFDM De-Encoded 16 QAM (OFDM/DE-16 QAM) for frequency flat Rician channel in the presence of Additive White Gaussian Noise (AWGN). The performance of OFDM is also compared with equivalent single carrier systems. (OFDM) , : . (OFDM) . (OFDM) (QAM) 16 . . OFDM/16QAM QAM OFDM/DE-16 Star (AWGN) (OFDM) .
... For the sake of further improving the achievable spectral efficiency, differential amplitude and phase shift keying (DAPSK) [3,4] expanded the single-ring constellation of the traditional DPSK to multiple rings. Essentially, the information bits are mapped to both the amplitude and phase differences between successively transmitted symbols. ...
... The resultant permuted bits b are then fed through the DAPSK modulator. The 2 p -DAPSK, also known as the Star Quadrature Amplitude Modulation (Star-QAM) scheme [3], employs multiple concentric rings by combining the 2 q -DASK and 2 (p−q) -DPSK modulation schemes. ...
Differentially encoded and noncoherently detected transceivers exhibit low complexity since they dispense with a complex channel estimation. In pursuit of high bandwidth efficiency, differential amplitude/phase (A/P)-shift keying (DAPSK) was devised using constellations of multiple concentric rings. To increase resilience against the typical high-Doppler-induced performance degradation of DAPSK and/or to enhance the maximum achievable error-free transmission rate for DAPSK-modulated systems, multiple-symbol differential detection (MSDD) may be invoked. However, the complexity of the maximum a posteriori (MAP) MSDD exponentially increases with the detection window size and hence may become excessive upon increasing the window size, particularly in the context of an iterative detection-aided channel-coded system. To circumvent this excessive complexity, we conceive a decomposed two-stage iterative A/P detection framework, where the challenge of having a nonconstant-modulus constellation is tackled with the aid of a specifically designed information exchange between the independent A/P detection stages, thus allowing the incorporation of reduced-complexity sphere detection (SD). Consequently, a near-MAP-MSDD performance can be achieved at significantly reduced complexity, which may be five orders of magnitude lower than that of the traditional MAP-MSDD in the 16-DAPSK scenario that was considered.
... It consists of multiple concentric PSK circles with equal constellation points in each circle and identical phase angle between them. Amplitude and phase of the constellation points are mutually independent [41], [42]. Hence, differential detection can be applied successfully rather than the coherent detection, which omits the need for accurate phase tracking and channel estimation at the receiver [43], [44]. ...
Communication system’s performance is sensitive to bandwidth, power, cost etc. There have been various solutions to improve the performance, out of them, one of the fundamental solutions over the years is design of optimum modulation schemes. As the research on beyond 5G heats up, we survey and explore power and bandwidth efficient modulation schemes for the next generation communication systems in details. In the existing literature, initially square quadrature amplitude modulation (SQAM) was considered. However, only square constellations are not sufficient for varying channel conditions and rate requirements, thus, efficient odd power of 2 constellations were introduced. For odd power of 2 constellations, rectangular QAM (RQAM) is most commonly used. However, RQAM is not a good choice and modified cross QAM (XQAM) constellation is preferred which provides improved power efficiency over RQAM due to its energy efficient two dimensional (2D) structure. The increasing demand for high data-rates has further encouraged research towards more compact 2D constellations which leads to hexagonal lattice structure based hexagonal QAM (HQAM) constellations. In this work, various QAM constellations are discussed and detailed study of star QAM, XQAM, and HQAM is presented. Generation, peak and average energies, peak-to-average-power ratio, symbol-error-rate, decision boundaries, bit mapping, Gray code penalty, and bit-error-rate of star QAM, XQAM, and HQAM constellations for different constellation orders are presented. Finally, a comparative study of various QAM constellations is presented which justifies the supremacy of HQAM over other QAM constellations for various wireless communication systems and a potential modulation scheme for future standards.
... It consists of multiple concentric PSK circles with equal constellation points in each circle and identical phase angle between them. Amplitude and phase of the constellation points are mutually independent [34], [35]. Hence, differential detection can be applied successfully rather than the coherent detection, which omits the need for accurate phase tracking and channel estimation at the receiver [36], [37]. ...
As the research on beyond 5G heats up, we survey and explore power and bandwidth efficient modulation schemes in details. In the existing publications and in various communication standards, initially square quadrature amplitude modulation (SQAM) constellations (even power of 2) were considered. However, only the square constellations are not efficient for varying channel conditions and rate requirements, and hence, odd power of 2 constellations were introduced. For odd power of 2 constellations, rectangular QAM (RQAM) is commonly used. However, RQAM is not a good choice due to its lower power efficiency, and a modified cross QAM (XQAM) constellation is preferred as it provides improved power efficiency over RQAM due to its energy efficient two dimensional (2D) structure. The increasing demand for high data-rates has further encouraged the research towards more compact 2D constellations which lead to hexagonal lattice structure based constellations, referred to as hexagonal QAM (HQAM). In this work, various QAM constellations are discussed and detailed study of star QAM, XQAM, and HQAM constellations is presented. Generation, peak and average energies, peak-to-average-power ratio, symbol-error-rate, decision boundaries, bit mapping, Gray code penalty, and bit-error-rate of star QAM, XQAM, and HQAM constellations with different constellation orders are presented. Finally, a comparative study of various QAM constellations is presented which justifies the supremacy of HQAM over other QAM constellations. With this, it can be claimed that the use of the HQAM in various wireless communication systems and standards can further improve the performance targeted for beyond 5G wireless communication systems.
... The design dilemma between coherent and NC communication has intrigued the community for decades (Webb et al. 1991). NC detection has indeed compelling benefits in terms of dispensing with power-thirsty channel estimation, as also argued in Wang and Hanzo (2012) and Wang et al. (2014). ...
The 5G radio access network (RAN) brings new requirements, with higher spectral efficiency to accommodate the needs of emerging applications. In this context, massive multiple‐input multiple‐output (m‐MIMO) is becoming one of the key enabling technologies for 5G and beyond. However, the current communication technologies are based on coherent transmission techniques, which require the transmission of a huge amount of signaling. Therefore, the differential encoding (DE) and non‐coherent (NC) detection are interesting alternatives. New constellation schemes for NC m‐MIMO have been proposed based mainly on energy detection and phase detection, combined with channel coding schemes to reduce the required number of antennas.
... When the transmitted digital symbols of the coherent photonic transmitter are far greater than the number of the constellations (ie, the transmitted digital symbols are far greater than 16), the signal-noise-ratio (SNR) of the transmission system can be expressed as 31 : ...
We propose and demonstrate an all optical wavelength conversion of Nyquist differential phase 16 quadrature amplitude modulation based on microwave photonics signal processing for flex-grid optical networks. By analyzing the mechanism of the microwave photonics and adjusting the parameters of the components, multi-wavelength tunable laser with smooth and adjustable optical intensity can be obtained. Then, the multi-channel photonic signals with the minimal guard space of 5 GHz can be obtained, which provide more than 20 flex-grids for optical transmission with transparent rate and format. The optical power of converted wavelengths, optical signal-to-noise ratio, error vector magnitude, and bit error rate (BER) are studied under the condition of different flex-grids, the frequencies of which are from 15 GHz to 36 GHz. The channel frequency spacing and amplitude of the converted wavelength can be dynamically adjusted via parameter configuration. Flex-grid spacing strategies and channel selecting strategies are given. The BER performance of all converted channels can fall below the forward error correction threshold of 3.8 × 10 −3 by optimizing the optical power of the receiver end. The results show the tradeoff between the BER and the detected optical power of the receiver end. These research findings could provide solutions for spectrum allocation and routing selection when wavelength conversion is needed in optical links. K E Y W O R D S coherent communication, flex-grid optical networks, microwave photonics, wavelength conversion
... More explicitly, in the face of high Doppler frequency, the training-based Channel State Information (CSI) estimation that assumes a constant CSI may suffer from irreducible error floor [4]. Similar trends are also valid for Conventional Differential Detection (CDD) that detects a single data symbol based on (N w = 2) received samples [5], [6]. Against this background, the pilot-based techniques [7] constitute better choices, where the pilot symbols that are known to the receiver are periodically transmitted, while the FIR filter at the receiver may estimate and interpolate the fading channel based on Least Square (LS), Minimum Mean Square Error (MMSE) and recursive algorithms [1]. ...
In this treatise, first of all, we conceive a generic Multiple-Symbol Differential Sphere Detection (MSDSD) solution for both single- and multiple-antenna based noncoherent schemes in both uncoded and coded scenarios, where the high-mobility aeronautical Ricean fading features are taken into account. The bespoke design is the first MSDSD solution in open literature that is applicable to the generic Differential Space-Time Modulation (DSTM) for transmission over Ricean fading. In the light of this development, the recently developed Differential Spatial Modulation (DSM) and its diversity counterpart of Differential Space-Time Block Coding using Index Shift Keying (DSTBCISK) are specifically recommended for aeronautical applications owing to their low-complexity single-RF and finite-cardinality features. Moreover, we further devise a noncoherent Decision- Feedback Differential Detection (DFDD) and a Channel State Information (CSI) estimation aided coherent detection, which also take into account the same Ricean features. Finally, the advantages of the proposed techniques in different scenarios lead us to propose for the aeronautical systems to adaptively (1) switch between coherent and non-coherent schemes, (2) switch between single- and multiple-antenna based schemes as well as (3) switch between high-diversity and high-throughput DSTM schemes.
... In contrast to both the DPSK [19], [20] and star QAM schemes [21]- [25] routinely used in Single-Input Single-Output (SISO) channels, the matrix multiplication invoked by the DSTM's differential encoding results in arbitrary infinitecardinality of transmit signals for all the aforementioned DSTM schemes. However, in reality, the Transmit Antennas (TAs) can only radiate a limited number of signal transmission patterns [26]- [28]. ...
The matrix-based differential encoding invoked by Differential Space-Time Modulation (DSTM) typically results in an infinite-cardinality of arbitrary signals, despite the fact that the Transmit Antennas (TAs) can only radiate a limited number of patterns. As a remedy, the recently developed Differential Spatial Modulation (DSM) is capable of avoiding this problem by conceiving a beneficial sparse signal matrix design, which also facilitates low-complexity single-RF signal transmission. Inspired by this development, the Differential Space-Time Block Code using Index Shift Keying (DSTBC-ISK) further introduces a beneficial diverstiy gain without compromising the DSM’s appealingly low transceiver complexity. However, the DSTBCISK’s performance advantage tends to diminish as the throughput increases, especially when an increased number of Receive Antennas (RAs) is used. By contrast, the classic Differential Group Code (DGC) that actively maximizes its diversity gain for different Multiple-Input Multiple-Output (MIMO) system setups is capable of achieving a superior performance, but its detection complexity grows exponentially with the throughtput. Against this background, we propose the Differential Space-Time Shift Keying using Diagonal Algebraic Space-Time (DSTSK-DAST) scheme, which is the first DSTM that is capable of achieving the DGC’s superior diversity gain at high throughputs without compromising the DSM’s low transceiver complexity. As a further advance, we also conceive a new Differential Space-Time Shift Keying using Threaded Algebraic Space-Time (DSTSK-TAST) arrangement, which is capable of achieving an even further improved diversity gain at a substantially reduced signal detection complexity compared to the best DGCs. Furthermore, in order to strike a practical tradeoff, we develop a generic multi-element and multi-level-ring Amplitude Phase Shift Keying (APSK) design, and we also arrange for multiple reduced-size DSTM sub-blocks to be transmitted in a permuted manner, which exhibits an improved diversity-throughput tradeoff.
... In contrast to both the DPSK [19], [20] and star QAM schemes [21]- [25] routinely used in Single-Input Single-Output (SISO) channels, the matrix multiplication invoked by the DSTM's differential encoding results in arbitrary infinitecardinality of transmit signals for all the aforementioned DSTM schemes. However, in reality, the Transmit Antennas (TAs) can only radiate a limited number of signal transmission patterns [26]- [28]. ...
The matrix-based differential encoding invoked by Differential Space-Time Modulation (DSTM) typically results in an infinite-cardinality of arbitrary signals, despite the fact that the Transmit Antennas (TAs) can only radiate a limited number of patterns. As a remedy, the recently developed Differential Spatial Modulation (DSM) is capable of avoiding this problem by conceiving a beneficial sparse signal matrix design, which also facilitates low-complexity single-RF signal transmission. Inspired by this development, the Differential Space-Time Block Code using Index Shift Keying (DSTBC-ISK) further introduces a beneficial diverstiy gain without compromising the DSM's appealingly low transceiver complexity. However, the DSTBC-ISK's performance advantage tends to diminish as the throughput increases, especially when an increased number of Receive Antennas (RAs) is used. By contrast, the classic Differential Group Code (DGC) that actively maximizes its diversity gain for different Multiple-Input Multiple-Output (MIMO) system setups is capable of achieving a superior performance, but its detection complexity grows exponentially with the throughtput. Against this background, we propose the Differential Space-Time Shift Keying using Diagonal Algebraic Space-Time (DSTSK-DAST) scheme, which is the first DSTM that is capable of achieving the DGC's superior diversity gain at high throughputs without compromising the DSM's low transceiver complexity. As a further advance, we also conceive a new Differential Space-Time Shift Keying using Threaded Algebraic Space-Time (DSTSK-TAST) arrangement, which is capable of achieving an even further improved diversity gain at a substantially reduced signal detection complexity compared to the best DGCs. Furthermore, in order to strike a practical tradeoff, we develop a generic multi-element and multi-level-ring Amplitude Phase Shift Keying (APSK) design, and we also arrange for multiple reduced-size DSTM sub-blocks to be transmitted in a permuted manner, which exhibits an improved diversity-throughput tradeoff.
... This ideal model does not include CFOs and ICIs, as detailed in Section II. Fig. 7 shows the BER comparisons between the differential star-QAM [56] and the DOSTC schemes. The transmission rate of the original S-DOSTC using a 16-PSK scheme was R = 4.0 [bits/symbol] in Fig. 7(a), while that of its projected counterpart was increased from R = 4.0 to R = 8.0 [bits/symbol] in Fig. 7(b). ...
In this paper, we propose a simple yet powerful mapping scheme that converts any conventional square-matrix-based differential space-time coding (DSTC) into a nonsquare-matrix-based DSTC. This allows DSTC schemes to be used practically in open-loop large-scale multiple-input multiple-output scenarios. Our proposed scheme may be viewed as the differential counterpart of coherent spatial modulation (SM), of the generalized SM, of Bell laboratories layered space-time architecture, and of subcarrier-index modulation. The fundamental impediment of the existing DSTC schemes is the excessive complexity imposed by the unitary constraint. Specifically, the transmission rate of conventional DSTC schemes decays as the number of transmit antennas increases. Our proposed scheme eliminates this impediment and thus achieves a significantly higher transmission rate. We introduce four novel construction methods for the nonsquare codewords, some of which include an arbitrary number of nonzero elements in each codeword column. Our analysis shows
that the proposed encoding technique reduces the complexity of both the inverse Fourier transform and of the detection processes. Our proposed scheme is shown to approach the performance of its coherent counterpart for low-mobility scenarios, where the number of transmit antennas is increased up to 256.<br/
... It is desirable that the average mutual information (MI) vs. the signal-to-noise ratio (SNR), S, of the modulation schemes, is as close to the additive white Gaussian noise (AWGN) (Shannon) capacity, C = log 2 (1 + S) [b/Hz/s] as possible. Well known modulation signal constellations are quadrature amplitude modulation (QAM), phase shift keying (PSK), star-QAM [3], and amplitude PSK (APSK) [4]. QAM, the most studied and deployed of all constellation designs, exhibits an asymptotic 1.53 dB SNR-gap (a shaping-loss) between the MI and the AWGN capacity [5]. ...
In this work, targeting, e.g., future generation cellular, microwave-links, or optical fiber systems, we propose a new geometric shaping design for golden angle modulation (GAM) based on a (double) truncated Gaussian input distribution. The design improves the mutual information (MI), and the peak-to-average power ratio, over the full signal-to-noise ratio (SNR) range relative to two key GAM schemes introduced in [1],[2]. Inspired by the proposed geometric shaping, a simpler, SNR-dependent, design is also suggested. The performance is numerically evaluated with respect to MI and compared with classical modulation schemes. With the proposed design, the SNR can be decreased relative to classical quadrature amplitude modulation, even for relatively modest target spectral efficiencies. As the GAM design can approach the Gaussian channel capacity, the power/energy efficiency is expected to improve.
... Webb et al. [44] Hard-decision Star QAM/Differential Amplitude Phase Shift Keying (DAPSK) 1992 ...
Unary error correction (UEC) codes have recently been proposed for the joint source and channel coding of symbol values that are selected from a set having an infinite cardinality. However, the original UEC scheme requires the knowledge of the source probability distribution, in order to achieve near-capacity operation. This limits the applicability of the UEC scheme, since the source probability distribution is typically non-stationary and is unknown in practice. In this paper, we propose a dynamic version of the UEC scheme, which can learn the unknown source statistics and gradually improve its decoding performance during a transient phase, then dynamically adapt to the non-stationary statistics and maintain reliable near-capacity operation during a steady-state phase, at the cost of only a moderate memory requirement at the decoder. Based on the same learning technique, we also propose two separate source and channel coding benchmarkers, namely, a learning-aided Elias gamma-convolutional code (CC) scheme and a learning-aided arithmetic-CC scheme. The simulation results reveal that our proposed learning-aided UEC scheme outperforms the benchmarkers by up to 0.85 dB, without requiring any additional decoding complexity or any additional transmission-energy,-bandwidth, or-duration.
... Suitable signal constellations are «A¬PSK for the symbols Ü, which consist of Å « ¡ ¬ points arranged in « distinct concentric rings with different radii , ¼ ½ « ½, and ¬ uniformly spaced phases ³ Ñ , Ñ ¼ ½ ¬ ½, so-called "star-constellations" cf. [20]. As usual, the differential symbols are taken from the same signal set as the transmitted signal. ...
Power line communications for high data rates using orthogonal frequency division multiplexing are considered. We regard the situations where no channel information is available at the transmitter and where channel information is/is not provided to the receiver. In order to enable a performance evaluation of transmission schemes with different bandwidth efficiencies, a stochastic representation of the channel transfer function is given, which leads to a fading channel model. As an appropriate measure of performance when applying powerful channel coding, the capacity of this special fading channel is calculated. The combination of a large signal constellation and low rate codes in order to obtain a fixed target rate proves to be advantageous both for coherent and bandwidth efficient noncoherent transmission over power line. The theoretic considerations are affirmed by means of simulations.
... Star-QAM was originally proposed as a special case of circular amplitude and phase shift keying (APSK) modulation [7], and due its lower peak-to-average power ratio star-QAM is advantageous to square-shaped QAM in terms of achievable mutual information over peak power limited channels [8]. Further, in contrast to square-QAM, where the phase states are not arranged equidistantly, star-QAM offers equally spaced phases which results in mutual independence between amplitude and phase of each signal point [9]. This property allows the receiver to use differential detection which is computationally simpler than coherent detection. ...
Accurate and analytically tractable symbol-error probability (SEP) expressions have been derived for a free-space optics (FSO) communication system that employs M-ary dualring star-quadrature amplitude modulation (QAM) and operates over atmospheric turbulent channels. The turbulence-induced fluctuations of the optical signal intensity are modelled, for weak and strong turbulence conditions, through log-normal and gamma-gamma probability density functions (pdfs), respectively. Resultant end expressions are in the form of summation of single integrals which can be easily computed through numerical integration methods. The accuracy of the theoretical framework is validated through extensive Monte Carlo simulations. It was found that although star-QAM may be used for FSO links extending several kms under weak turbulence, its error performance under strong turbulence is unsatisfactory beyond 1 km.
... More recently, Wang et al. have determined the variance of the more general Viterbi & Viterbi type phase estimator, again for M-QAM in [3] and for M-PSK in [4], both of which treat the power-law estimator as a special case. However, to date, no expression has been provided for the variance of the P th power estimator for more general constellations such as Star 16-QAM [5]- [6], multi-ring DPSK (MR-DPSK) [7], or those in [8]. Moeneclaey and de Jonghe [1] have found an expression for general 2π/P-rotationally symmetric constellations that is the linear approximation to the exact variance and is valid for medium to large SNR. ...
An expression for the true variance of the P th power-law phase estimator, as the number of samples approaches infin-ity, is given. This expression is an extension to the linear ap-proximation of Moeneclaey and de Jonghe [1] which is known to be inadequate in some practical systems. Our new expression covers general 2π/P-rotationally symmetric constellations that include those of PAM, QAM, PSK, Star M-QAM, MR-DPSK, and others. This expression also generalizes the known expres-sions for QAM and PSK. Additionally, our expression reduces to the Cramer-Rao bound given by Steendam and Moeneclaey [9], as SNR goes to zero. Monte Carlo simulations provide experi-mental verification of the theoretical expression for various con-stellations.
... 16 QAM transmission in a wireless channel has been implemented using pilot tones [26]. [60], using star 16 QAM constellations [76] and using training sequences with W iener-filtering interpolation [35]. This chapter discusses a simple one-pole adap tive estim ate of each tone, using short interm ediate training sequences with diversity. ...
... However, this technique suffers from a varying bandwidth, making it unsuitable when fixed bandwidth is required. A promising method is to vary the constellation size Webb, Hanzo, and Steele, 1991) and the coding scheme (Goldsmith and Chua, 1998) according to the quality of the channel. Combinations of these methods with the other adaptive techniques have also been proposed (Goldsmith and Chua, 1997). ...
... However, even near the cell site, an efficient 16QAM modulation scheme is necessary, which achieves a low received Es/N0 value taking into account the transmission back-off for the limited peak transmission power at a UE. In the paper, we investigate the achievable throughput performance for square 16QAM [4] and star 16QAM modulation schemes [6], [7]. Figure 1(a) shows the constellation for the square 16QAM modulation scheme, which is a current working assumption as the uplink data modulation scheme in the Evolved UTRA. Let d(t) be the narrowband modulated signal waveform of the transmitted signal represented as where T is the symbol duration and u(t) is the unit function such that u(t) = 1 for 1 0 t and otherwise, u(t) = 0. Furthermore, g(i) and (i) are the amplitude and phase components of the narrowband data modulation represented in the following equations for the square 16QAM modulation scheme. ...
This paper compares the achievable packet error rate and throughput performance levels of 16QAM modulation schemes considering the peak-to-average power ratio for single-carrier frequency division multiple access (SC-FDMA) in the evolved UTRA uplink. Simulation results show that the effective required average received signal energy per symbol-to-noise power spectrum density ratio (Es/N0) including the cubic metric (CM) of the (8, 8) star 16QAM modulation scheme is decreased by approximately 0.8 dB compared to that of the square 16QAM modulation scheme using turbo coding with the coding rate of R=1/3 in the six-ray Typical Urban channel model, when the amplitude ratio between the inner and outer ring, Rradius, is equal to 1.2. The results also show that although the star 16QAM modulation scheme reduces the effective required average received Es/N0 including the CM compared to the square 16QAM modulation scheme, this merit is concealed by the application of low modulation schemes such as QPSK and 8PSK when adaptive modulation and coding is applied. Therefore, we conclude that the square 16QAM modulation scheme is an appropriate candidate for SC-FDMA radio access in the evolved UTRA uplink
Passband signals are baseband signals elevated to a higher frequency in order to fit into particular slots in the spectrum. This chapter introduces different analog and digital modulation schemes as well as several approaches to multiplexing. Frequency multiplexing fits all the stations into the spectrum assigned to amplitude modulation (AM) broadcasting. The chapter also provides a discussion on frequency‐modulated signals, phase‐modulated signals, and amplitude‐modulated signals. Digital AM or amplitude shift keying (ASK) represents binary symbols by discrete amplitude steps. Quadrature amplitude modulation combines ASK and phase shift keying (PSK) in order to generate more distinguishable and longer symbols than either ASK or PSK alone. The chapter also introduces frequency division multiplexing (FDM) and time division multiplexing (TDM) before explaining the more versatile multiple access schemes. FDM divides the spectrum into bands and assigns signals to the bands. TDM divides time into slots then assigns signals to time slots.
In this letter, motivated by the recent differential faster-than-Nyquist (DFTN) signaling concept, we propose an improved 16-point double-ring star quadrature amplitude modulation (QAM)-aided DFTN signaling transmission, which allows us to attain a higher bandwidth efficiency as well as a simple receiver based on noncoherent detection. We derive an analytical error-rate bound for the proposed star-QAM DFTN signaling in an uncoded scenario. The derived bound is used for optimizing the star-QAM constellation for our DFTN signaling in terms of error-rate performance in an uncoded scenario. Our simulation results demonstrate that the proposed star-QAM DFTN scheme outperforms its conventional phase-shift-keying-based DFTN counterpart.
Coherent optical systems have relatively high laser phase noise, which affects the performance of forward error correction (FEC) codes. In this paper, we propose a method for selecting Bose–Chaudhuri–Hocquenghem (BCH) codes for coherent systems with star-shaped constellations and M-ary differential quadrature amplitude modulation (DQAM). Our method supports constellations of any order M which is a power of 2, and includes differential M-ary phase shift keying as a special case. Our approach is straightforward, requiring only short pre-FEC simulations to parameterize a statistical model, based on which we select codes analytically. It is applicable to pre-FEC bit error rates (BERs) of around 10−3. We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of 10−5, codes selected with our method yield BERs within 2× target. Lastly, we extend our method to systems with interleaving, which enables us to use codes with lower overhead.
Multiple-Symbol Differential Sphere Detection (MSDSD) relies on the knowledge of channel correlation. More explicitly, for Differential PSK (DPSK), the transmitted symbols' phases form a unitary matrix, which can be separated from the channel's correlation matrix by the classic Multiple-Symbol Differential Detection (MSDD), so that a lower triangular matrix extracted from the inverted channel correlation matrix is utilized for the MSDSD's sphere decoding. However, for Differential QAM (DQAM), the transmitted symbols' amplitudes cannot form a unitary matrix, which implies that the MSDD's channel correlation matrix becomes amplitude-dependent and remains unknown, unless all the data-carrying symbol amplitudes are detected. In order to tackle this open problem, in this paper, we propose to determine the MSDD's non-constant amplitudedependent channel correlation matrix with the aid of a sphere decoder, so that the classic MSDSD algorithms that were originally conceived for DPSK may also be invoked for DQAM detection. As a result, our simulation results demonstrate that the MSDSD aided DQAM schemes substantially outperform their DPSK counterparts. However, the price paid is that the detection complexity of MSDSD is also significantly increased. In order to mitigate this, we then propose a reduced-complexity MSDSD search strategy specifically conceived for DQAM constellations, which separately map bits to their ring-amplitude index and phase index. Furthermore, the classic Decision-Feedback Differential Detection (DFDD) conceived for DQAM relies on a constant channel correlation matrix, which implies that these DFDD solutions are sub-optimal and they are not equivalent to the optimum MSDD operating in decision-feedback mode. With the advent for solving the open problem of MSDSD aided DQAM, we further propose to improve the conventional DFDD aided DQAM solutions in this paper.
This paper presents the average block error rate (BLER) performance of the star 16QAM scheme using iterative decision-directed channel estimation (DDCE) for discrete Fourier transform (DFT)-precoded orthogonal frequency division multiple access (OFDMA). The star 16QAM scheme achieves more efficient modulation compared to square 16QAM in that it decreases the actual required average received signal-to-noise power ratio (SNR) satisfying the target average BLER considering the peak-to-average power ratio (PAPR) of the transmitted signal for a low channel coding rate. Hence, the feature of the paper is that we apply iterative DDCE using soft-decision symbol estimation based on the log-likelihood ratio (LLR) of an extrinsic probability at the Max-Log-MAP (maximum a posteriori probability) decoder output to achieve an efficient modulation scheme with a low required average received SNR. Computer simulation results show that for the star 16QAM scheme, the average BLER using the iterative DDCE is very close to that with ideal channel estimation for a low channel coding rate such as an R = 1/3 turbo code. We also show that when iterative DDCE is employed, the (8, 8) star 16QAM scheme decreases the required average received SNR considering the cubic metric at the average BLER of 10-2 by approximately 0.7 dB compared to the square 16QAM scheme.
Recently we proposed a novel differential encoder by a look-up table. In this paper, we present further research results on this subject. We first propose a bit-assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance. Then differential encoding for multiple-symbol differential detection is proposed. After that, we indicate that differential encoding by a table is equivalent to differential encoding by a trellis, so we propose a novel differential detector which uses the Viterbi algorithm on the trellis. A theorem about the sufficient number of states for various modulations is proposed. In addition, we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding. For this noncoherent trellis coding scheme, we propose augmented-state Viterbi decoding. Finally, we extend the proposed differential encoding and detection to differential space-time modulation (DSTM). We propose a new definition of DSTM by which the set of transmitted blocks is determined first. The differential encoding is implemented by a look-up table which can be optimized. The proposed DSTM has satisfactory error performance without constellation expansion.
Multilevel Differential Amplitude and Phase-Shift Keying (DAPSK) schemes do not require any channel estimation, which results in low complexity. In this treatise we derive the soft-output probability formulas required for a soft-decision based demodulation of high-order DAPSK, in order to facilitate iterative detection by exchanging extrinsic information with an outer Turbo Code (TC). Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. Compared to the identical-throughput TC assisted 64-ary Differential Phase-Shift Keying (64-DPSK) scheme, the 4-ring based TC assisted 64-ary DAPSK arrangement has a power-efficiency improvement of 2.3 dB at a bit error rate (BER) of 10-5. Furthermore, when the TC block size is increased, the system operates closer to the channel capacity. More specifically, when using a TC block length of 400 modulated symbols, the 64 DAPSK (4, 16) scheme is 7.56 dB away from its capacity curve, while it had a reduced gap as low as 2.25 dB, when using a longer TC block length of 40 000 modulated symbols. Finally, as a novel application example, the soft-decision M-DAPSK scheme was incorporated into an Amplify-and-Forward (AF) based cooperative communication system, which attains another 4.5 dB SNR improvement for a TC block length of 40 000 modulated symbols.
This paper studies the differentially amplitude- and phase-encoded quadrature amplitude modulation (DAPE QAM) transmission for the amplify-and-forward multiple-relay system using the fixed-relay-gain mechanism over independent Rician and Nakagami-m fading links. In the multiple-relay system, the destination collects signals from the source and multiple relays in distinct phases. Operating over two successively received symbols, an equal-gain combining (EGC) receiver and a weighted-gain combining (WGC) receiver are developed to noncoherently combine received signals from direct and multiple-relay links and thereby achieve cooperative diversity. The EGC receiver operates without any link-side information, whereas the knowledge of average signal-to-noise ratios (SNRs) on source–relay and relay–destination links is required for realizing the WGC receiver. Based on Beaulieu's convergent series approach, efficient computation formulas of the bit error probability (BEP) upper bounds are derived for both receivers. Numerical and simulation results on 16- and 64-point signal constellations show that the WGC receiver exhibits better BEP performance than the EGC receiver when link SNR estimates are not significantly large in error. The WGC receiver for DAPE QAM is also shown to outperform, in terms of BEP, the conventional receiver for differentially detecting the differential phase-shift keying modulation signal with the same constellation size.
This paper presents comparisons of the achievable throughput between the star 32/64QAM and square 32/64QAM schemes based on mutual information (MI) considering the peak-to-average power ratio (PAPR) of the modulated signal. As a PAPR criterion, we use a cubic metric (CM) that directly corresponds to the transmission back-off of a power amplifier. In the analysis, we present the best ring ratio for the star 32 or 64QAM scheme from the viewpoint of minimizing the required received signal-to-noise power ratio (SNR) considering the CM that achieves the peak throughput, i.e., maximum error-free transmission rate. We show that the required received SNR considering the CM at the peak throughput is minimized with the number of rings of M = 3 and 4 for star 32QAM and star 64QAM, respectively. Then, we show with the best ring ratios, that the (4, 12, 16) star 32QAM scheme with M = 3 achieves a lower required received SNR considering the CM compared to that for the square 32QAM scheme. Similarly, we show that the (4, 12, 20, 28) star 64QAM scheme with M = 4 achieves almost the same required received SNR considering the CM as that for the square 64QAM scheme.
This paper presents the transmission performances, by simulation, of optical communication systems over 10 spans of dispersion
compensated and optically amplified fiber distance with a bit rate of 100 Gb/s, by employing modulation formats of two amplitude
levels and 8 phase states per amplitude level, the 2R-16-Star QAM constellation under direct and coherent detection with and
without phase estimation. Different ring ratios of the amplitude levels are examined and associate transmission performances
are reported. Optical signal to noise ratio is achieved with 18 dB and 23 dB for back to back and long haul transmission cases
with a dispersion tolerance of ±67 ps/nm at 2 dB power penalty of the eye opening at 100 Gb/s. Monte–Carlo simulation is
also performed and a receiver sensitivity of − 15 dBm is achieved for a BER of 10−5under direct detection after 1100 km of dispersion-compensated and optically amplified transmission. Transmission performances,
bit error rate versus receiver sensitivity, are also confirmed with the use of the eye diagram and associate multiple-peaks
statistical spectral density distribution. For 100 Gb/s 2R-16-Star QAM coherent transmission, an improvement of the receiver
sensitivity of 2.5 dB and 3.5 dB is obtained for coherent detection without phase estimation and respectively. Under coherent
detection with phase estimation, the chromatic dispersion tolerance reaches ±100 ps/nm for a 2 dB eye opening penalty at
100 Gb/s bit rate. Comparative studies of the transmission performances of the Star and Square QAM modulation formats are
also conducted under the fiber linear and nonlinear effects and detection with and without phase estimation.
The (4,12) circular- signal-set constellation [or (4,12) QAM] has been proposed for 16APSK in view of both the minimum Euclidean distance between mapped signal points and the realization of differential phase detection. Usually, the optimum value of the ring ratio, which is the ratio of the inner and outer ring level of signal constellation, is decided as one of the parameters of 16APSK by using the geometrical approach when the channel SNR is assumed to be quite large. However, the optimum value should be calculated by its symbol error rate to realize the best performance over all channel SNRs. From this point of view, symbol error rates of (4,12) QAM for three detection schemes are analyzed theoretically, and the optimum ring ratios for these detections are indicated in this paper. The performance of the envelope amplitude detection is expressed as the sum of PSK's performance and the effect of amplitude detection, which causes degradation of its performance. The optimum ring ratio for envelope detection is smaller when the channel SNR is lower, although the optimum value for ideal coherent detection becomes larger. The procedure used to analyze (4,12) QAM can also be adapted for star QAM, which is a conventional signal constellation of 16APSK. © 2000 Scripta Technica, Electron Comm Jpn Pt 1, 83(10): 19–28, 2000
On the way towards third generation personal communication networks (PCN) the deployment of 16-level quadrature amplitude modulation (QAM) schemes is investigated via flat microcellular Rayleigh-fading mobile radio channels having mild co-channel interference with and without diversity. Our proposed differentially coded non-coherent 16-QAM scheme requires no pilot symbol assistance, no automatic gain control (AGO and no carrier recovery. High speech quality associated with a mean opinion score of about four (MOS = 4.0) is ensured at a signalling rate of 6.2 kBd for channel signal to noise ratios (SNR) above 20 - 25 dB and signal to interference ratios (SIR) above 25 - 30 dB by the 13.4 kbit/s medium complexity regular pulse excited (RPE) speech codec, when carefully matched twin-class low complexity binary Bose-Chaudhuri-Hocquenghem (BCH) error correction coding and 16-QAM combined with second order diversity are deployed. The overall speech delay is about 40 ms and the user bandwidth is 9.3 kHz, which allows us to accommodate 21 users in a 200 kHz channel slot.
A method of coherent detection and channel estimation for punctured convolutional coded binary Quadrature Amplitude Modulation
(QAM) signals transmitted over a frequency-flat Rayleigh fading channels used for a digital radio broadcasting transmission
is presented. Some known symbols are inserted in the encoded data stream to enhance the channel estimation process. The pilot
symbols are used to replace the existing parity symbols so no bandwidth expansion is required. An iterative algorithm that
uses decoding information as well as the information contained in the known symbols is used to improve the channel parameter
estimate. The scheme complexity grows exponentially with the channel estimation filter length. The performance of the system
is compared for a normalized fading rate with both perfect coherent detection (corresponding to a perfect knowledge of the
fading process and noise variance) and differential detection of Differential Amplitude Phase Shift Keying (DAPSK). The tradeoff
between simplicity of implementation and bit-error-rate performance of different techniques is also compared.
We introduce a method for tracking a Rayleigh-fading channel with
Orthogonal Frequency Division multiplexing (OFDM) so that
multi-amplitude bit rate schemes such as 16 QAM may be used in a
wireless channel. In addition, we derive a distribution to predict the
symbol error rate of the modulation scheme. The modulation scheme is
applied to an indoor wireless system operating at a rate of 25 Mb/s. The
probability of error derived from simulation shows good agreement with
the theoretically predicted probability of error. We keep a fairly large
bit rate by using few training symbols; in simulation, the error
propagation accounts for a slight increase in symbol error rate, but is
not catastrophic due to the use of rotationally-invariant 16 QAM
constellations
Squared M-ary quadrature amplitude modulation (QAM) constellations have been widely adopted for modern high-data-rate digital communications. Nevertheless, carrier recovery required by demodulation of 128-QAM signals is almost a formidable task for practical receiver design. In this paper, two types of modified 128-QAM constellations are proposed allowing utilization of a low-complexity carrier recovery mechanism in the receiver. With the proposed constellations, perfect recovery of a frequency offset up to plusmn2.5% of baud rate is guaranteed using a conventional carrier recovery method at the expense of slight Es/N0 and PAPR increment compared with the conventional 128-QAM constellations
Differentially detected noncoherent Star Quadrature Amplitude Modulation (Star-QAM) is ideal for low-complexity wireless communications, since it dispenses with high-complexity channel estimation. We conceive soft-decision based demodulation for 16-level Star-QAM (16-StQAM), which is then invoked for iterative detection aided Iteratively-Detected Bit-Interleaved Coded Modulation (BICM-ID). It is shown that the proposed 16-StQAM based BICM-ID scheme achieves a coding gain of approximately 14 dBs in comparison to the 16-level identical-throughput Differential Phase-Shift Keying (16DPSK) assisted BICM scheme at a bit error ratio of 10-6.
This paper addresses a multiple-symbol differential detection scheme for star 16QAM. At the outset, we analytically scrutinized conventional differential detection of star 16QAM. As a result, it emerged that the energy penalty of differential amplitude detection as compared with ideal coherent detection is larger than that of phase detection. Then to improve the overall performance of star 16QAM, we propose an MLSE algorithm for a large C/N as well as a suboptimum algorithm. Both of them allow multiple-symbol differential amplitude and phase detection. Their performances are also evaluated through computer simulation.
Star Quadrature Amplitude Modulation (Star-QAM) is a non-coherent detection aided scheme ideal for low-complexity wireless transceivers. In this contribution, we first derive soft-decision aided StQAM symbol-to-bit demapping combined with iterative detection aided Turbo Coding (TC). Then we combine this physical layer design with network coding (NC) and quantify the attainable coding gain. It is shown that the proposed 16-level Star-QAM (16-StQAM) based TC scheme is capable of achieving a coding gain of about 1.5~dB over the TC aided 16-level Differential Phase-Shift Keying (16DPSK) benchmark scheme at a BER of . The 16-StQAM based TC assisted scheme is capable of offering another 1.2~dB coding gain, when it is employed in a 'butterfly' topology network arrangement. When the source and relay nodes are allowed to transmit at different power levels, the two-hop 16-StQAM based TC aided NC scheme outperforms the single-hop 16-StQAM based TC scheme by approximately 2.2~dB.
Recently, we proposed a novel differential encoder for non-constant energy signals, by a look-up table instead of a rule. In this paper, we present further research results on this subject. We first propose a new bit-assigning algorithm and some constellations maximizing minimum noncoherent distance. Then we show that differential encoding by a table is equivalent to differential encoding by a trellis, so we use the Viterbi algorithm at the differential detector to improve the error performance. A theorem about the sufficient number of states for various modulations is proposed. Finally, we extend the proposed differential encoding and detection to differential space- time modulation (DSTM). We propose a new definition of DSTM, by which the transmitted block is determined according to the previously transmitted block and current data bits. The encoding table that determines the transmitted block can be optimized. We also propose a theorem to reduce the number of states of the decoding trellis. The proposed DSTM has satisfactory error performance without constellation expansion. Index Terms—Differential encoding, noncoherent detection, quadrature-amplitude modulation
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