Improved error performance of a 3/4‐Sezginer space‐time block codes

The Alamouti space‐time block code (STBC) achieves full diversity gain at a rate of 1/2. However, the Alamouti scheme does not provide multiplexing gain. The Silver code offers both diversity and multiplexing gain. It has a minimum normalization determinant of . The Golden code is another STBC that offers both diversity and multiplexing gain. The Golden code is ranked higher than the Silver code because of its lower minimum normalization determinant of , however, the golden code suffers from a high detection complexity in the modulation order of M⁴. The 3/4‐Sezginer code is another STBC, which compromises between the Alamouti scheme and the Golden code in terms of diversity gain and multiplexing gain. The 3/4‐Sezginer code achieves full diversity and half of multiplexing gain. The uncoded space‐time labeling diversity (USTLD) is a recent scheme that improves the error performance when applied to the STBC in multiple‐input multiple‐output (MIMO) systems and will be applied to the 3/4‐Sezginer STBC to improve the error performance in this paper. The theoretical error probability for both the 3/4‐Sezginer STBC and the improved system is formulated using the union bound in this paper. The theoretical error probabilities of both 16‐QAM and 64‐QAM are validated through Monte Carlo simulation. The simulation and theoretical results show that the proposed system with 4 N_R can achieve an SNR gain of 1 dB for 16‐QAM and 1.2 dB 64‐QAM at a bit error rate (BER) of 10^?6.     

SSD‐enhanced uncoded space‐time labeling diversity

Space‐time labeling diversity (STLD) has been shown to be an efficient technique for improving the bit error rate (BER) performance of an uncoded space‐time coded modulation system. In this paper, signal space diversity (SSD) is incorporated into the uncoded STLD system to further enhance the system BER performance. A tight closed‐form union bound on the BER of the proposed system is derived and is used to optimize the rotation angle of the SSD scheme. Simulation results are used to confirm the theoretical bound derived for the system. The results also show performance gains of approximately 2.0 dB at a BER of 10^?6 and 1.6 dB at a BER 10^?4 from incorporating SSD into the uncoded STLD system using 16QAM and 64QAM, respectively. Furthermore, a low complexity detection scheme based on orthogonal projection is formulated for the proposed scheme and, in comparison with the optimal maximum‐likelihood detector, is shown to result in a 56% and 95% reduction in computation complexity for the 16QAM and 64QAM versions of the proposed system, respectively.     

Performance analysis of M‐APSK generalised spatial modulation with constellation reassignment

Generalised spatial modulation (GSM) is a recently developed multiple‐input multiple‐output (MIMO) technique aimed at improving data rates over conventional spatial modulation (SM) systems. However, for identical antenna array size and configurations (AASC), the bit error rate (BER) of GSM systems in comparison with SM systems is degraded. Recently, a GSM system with constellation reassignment (GSM‐CR) was proposed in order to improve the BER of traditional GSM systems. However, this study focused on M‐ary quadrature amplitude modulation (M‐QAM) schemes. The focus of this paper is the application of a circular constellations scheme, in particular, amplitude phase shift keying (APSK) modulation, to GSM and GSM‐CR systems. An analytical bound for the average BER of the proposed M‐APSK GSM and M‐APSK GSM‐CR systems over fading channels is derived. The accuracy of this bound is verified using Monte Carlo simulation results. A 4 × 4 16‐APSK GSM‐CR system achieves a gain of 2.5 dB at BER of 10^?5 over the traditional 16‐APSK GSM system with similar AASC. Similarly, a 6 × 4 32‐APSK GSM‐CR system achieves a gain of 2 dB at BER of 10^?5 over equivalent 32‐APSK GSM system.     

Golden codeword–based modulation schemes for single‐input multiple‐output systems

The Golden code has full rate and full diversity. The Golden codeword matrix contains two pairs of super symbols. Based on one pair of super symbols, two modulation schemes, Golden codeword–based M‐ary quadrature amplitude modulation (GC‐MQAM) and component‐interleaved GC‐MQAM (CI‐GC‐MQAM), are proposed for single‐input multiple‐output (SIMO) systems. Since the complexities of the maximum likelihood detection for the proposed GC‐MQAM and CI‐GC‐MQAM are proportional to O(M²) and O(M⁴), respectively, low complexity detection schemes for the proposed GC‐MQAM and CI‐GC‐MQAM are further proposed. In addition, the theoretical average bit error probabilities (ABEPs) for the proposed GC‐MQAM and CI‐GC‐MQAM are derived. The derived ABEPs are validated through Monte Carlo simulations. Simulation and theoretical results show that the proposed GC‐MQAM can achieve the error performance of signal space diversity. Simulation and theoretical results further show that the proposed CI‐GC‐16QAM, ‐64QAM, and ‐256QAM with three receive antennas can achieve approximately 2.2, 2.0, and 2.1 dB gain at a bit error rate of 4 × 10^?6 compared with GC‐16QAM, ‐64QAM, and ‐256QAM, respectively.     

Error performance of Uncoded Space Time Labelling Diversity in spatially correlated Nakagami‐q channels

Greater spectral efficiency has recently been achieved for Uncoded Space Time Labelling Diversity (USTLD) systems by increasing the number of antennas in the transmit antenna array. However, due to constrained physical space in hardware, the use of more antennas can lead to degradation in error performance due to correlation. Thus, this paper studies the effects of spatial correlation on the error performance of USTLD systems. The union bound approach, along with the Kronecker correlation model, is used to derive an analytical expression for the average bit error probability (ABEP) in the presence of Nakagami‐q fading. This expression is validated by the results of Monte Carlo simulations, which shows a tight fit in the high signal‐to‐noise ratio (SNR) region. The degradation in error performance due to transmit and receive antenna correlation is investigated independently. Results indicate that transmit antenna correlation in the USTLD systems investigated (3 × 3 8PSK, 2 × 4 16PSK, 2 × 4 16QAM, and 2 × 4 64QAM) causes a greater degradation in error performance than receive antenna correlation. It is also shown that 2 × 4 USTLD systems are more susceptible to correlation than comparable space‐time block coded systems for 8PSK, 16PSK, 16QAM, and 64QAM.     

Spectral efficiency improvement with SISO and SIMO in M‐QAM over millimeter‐wave links

This paper proposes a spectral efficiency improvement technique for millimeter wave (mmWave) links. The proposed technique provides an efficient utilization of the mmWave link capacity. This technique is applied in three cases the single‐input single‐output (SISO), single‐input multiple‐output (SIMO) with the maximal ratio combining and with the equal gain combining. The M‐ary quadrature amplitude modulation scheme is used in our work. The power series expansion is used for deriving closed‐form expressions for bit error rate (BER) performances in all studied cases. The BER closed‐form expressions are confirmed by the numerical solution of the integral equations. The simulation results show that a high spectral efficiency can be accomplished by the proposed technique. As well as the derived expressions closely match with the numerical solution of integration expressions at different values of modulations order the Rician factor. For instance, the spectral efficiency gain achievement is 8 at signal‐to‐noise ratio (SNR) equals 34 dB in the case of SISO system whereas in the case of SIMO system, the same gain is achieved at SNR equals 24 dB. As well as the BER performance is enhanced from 1.188 × 10^?4, 7.112 × 10^?4, 4.164 × 10^?3, and 3.286 × 10^?2 to 8.717 × 10^?16, 1.119 × 10^?12, 1.308 × 10^?9, and 4.905 × 10^?6 for M = 4, 16, 64, and 256, respectively, at SNR equals 30 dB.     

An eight-dimensional 64-state trellis code for transmitting 4 bitsper 2-D symbol

An eight-dimensional, 64-state, 90° rotationally invariant trellis code for transmitting 4 bits/baud over a bandlimited channel is described. The 2-D constellation contains 20 points. The code achieves a 5.23-dB coding gain over the uncoded 4×4 QAM (quadrature amplitude modulation) constellation and a 1.23-dB gain over the standard CCITT V32 trellis code. Simulation results are presented that verify these coding gains. Simulation results showing symbol error probability versus signal/noise ratio and trellis depth are also presented     

Performance of multilevel‐turbo codes with blind/non‐blind equalization over WSSUS multipath channels

In this paper, in order to improve error performance, we introduce a new type of turbo codes, called ‘multilevel‐turbo codes (ML‐TC)’ and we evaluate their performance over wide‐sense stationary uncorrelated scattering (WSSUS) multipath channels. The basic idea of ML‐TC scheme is to partition a signal set into several levels and to encode each level separately by a proper component of the turbo encoder. In the considered structure, the parallel input data sequences are encoded by our multilevel scheme and mapped to any modulation type such as MPSK, MQAM, etc. Since WSSUS channels are very severe fading environments, it is needed to pass the received noisy signals through non‐blind or blind equalizers before turbo decoders. In ML‐TC schemes, noisy WSSUS corrupted signal sequence is first processed in equalizer block, then fed into the first level of turbo decoder and the first sequence is estimated from this first Turbo decoder. Subsequently, the other following input sequences of the frame are computed by using the estimated input bit streams of previous levels. Here, as a ML‐TC example, 4PSK 2 level‐turbo codes (2L‐TC) is chosen and its error performance is evaluated in WSSUS channel modelled by COST 207 (Cooperation in the field of Science & Technology, Project #207). It is shown that 2L‐TC signals with equalizer blocks exhibit considerable performance gains even at lower SNR values compared to 8PSK‐turbo trellis coded modulation (TTCM). The simulation results of the proposed scheme have up to 5.5 dB coding gain compared to 8PSK‐TTCM for all cases. It is interesting that after a constant SNR value, 2L‐TC with blind equalizer has better error performance than non‐blind filtered schemes. We conclude that our proposed scheme has promising results compared to classical schemes for all SNR values in WSSUS channels. Copyright © 2005 John Wiley & Sons, Ltd.     

Diversity‐multiplexing tradeoff over correlated Rayleigh fading channels: a non‐asymptotic analysis

In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.     

Channel capacity and bit error rate optimization of the ultra‐wide bandwidth transmitted‐reference receiver

The channel capacity and the bit error rate of ultra‐wide bandwidth transmitted‐reference systems are optimized with respect to time delay between the reference and the adjacent data pulses. Approximate and theoretical expressions for the signal‐to‐interference‐plus‐noise ratio are derived. Numerical results show that optimizing the receiver can provide a significant capacity improvement of up to 2.2 bits/s/GHz and a bit error rate performance gain of up to 2 dB in effective signal‐to‐noise ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Space‐time block coded spatial modulation with labeling diversity

Space‐time block coded spatial modulation (STBC‐SM) exploits the advantages of both spatial modulation and the Alamouti space‐time block code. Meanwhile, space‐time labeling diversity has demonstrated an improved bit error rate (BER) performance in comparison to the latter. Hence, in this paper, we extend the application of labeling diversity to STBC‐SM, which is termed STBC‐SM‐LD. Under identical channel assumptions, STBC‐SM‐LD exhibits superior BER performance compared to STBC‐SM. For example, with 4 × 4, 64‐quadrature amplitude modulation (64‐QAM), STBC‐SM‐LD has a BER performance gain of approximately 2.6 dB over STBC‐SM. Moreover, an asymptotic bound is presented to quantify the average BER performance of M‐ary QAM STBC‐SM‐LD over independent and identically distributed Rayleigh frequency‐flat fading channels. Monte Carlo simulations for STBC‐SM‐LD agree well with the analytical framework. In addition to the above, low‐complexity (LC) near‐maximum‐likelihood detectors for space‐time labeling diversity and STBC‐SM‐LD are presented. Complexity analysis of the proposed LC detectors shows a substantial reduction in computational complexity compared to their ML detector counterparts. For example, the proposed detector for STBC‐SM‐LD achieves a 91.9% drop in computational complexity for a 4 × 4, 64‐QAM system. The simulations further validate the near‐maximum‐likelihood performance of the LC detectors.     

High‐rate uncoded space‐time labelling diversity with low‐complexity detection

Uncoded space‐time labelling diversity (USTLD) is a recent scheme that improved the error performance compared to conventional multiple‐input, multiple‐output systems. Thus far, USTLD has suffered from limited achievable data rates, as the original model uses only two transmit antennas. This motivates for the work in this paper, where the USTLD model is extended to allow for any desired number of transmit antennas. An analytical bound for the average bit error probability of this high‐rate USTLD (HR‐USTLD) system is derived. This expression is verified using the results of Monte Carlo simulations, which show a tight fit in the high signal‐to‐noise ratio region. The increased data rates associated with larger transmit antenna arrays in HR‐USTLD systems come at the cost of increased detection complexity. Therefore, this paper studies the application of low‐complexity detection algorithms based on the popular QR decomposition technique and proposes a new algorithm specifically designed for HR‐USTLD systems. Analysis of this algorithm in terms of accuracy and computational complexity is also provided and benchmarked against maximum‐likelihood detection (MLD). It is shown that the proposed algorithm achieves near‐MLD accuracy, while reducing complexity by 79.75% and 92.53% for the respective 4 × 4 16QAM and 4 × 5 16PSK HR‐USTLD systems investigated.     

Fractional Multi‐bit Differential Detection Technique for Continuous Phase Modulation

A new low‐complexity differential detection technique, fractional multi‐bit differential detection (FMDD), is proposed in order to improve the performance of continuous phase modulation (CPM) signals such as Gaussian minimum shift keying (GMSK) and Gaussian frequency shift keying (GFSK). In comparison to conventional one‐bit differential detected (1DD) GFSK, the FMDD‐employed GFSK provides a signal‐to‐noise ratio advantage of up to 1.8 dB in an AWGN channel. Thus, the bit‐error rate performance of the proposed FMDD is brought close to that of an ideal coherent detection while avoiding the implementation complexity associated with the carrier recovery. In the adjacent channel interference environment, FMDD achieves an even larger SNR advantage compared to 1DD.     

Optimum Weighted PCM for Speech Signals

Weighted digital modulation schemes which provide bit error probabilities matched to the PCM bits with respect to their sensitivity to digital errors are analyzed. The channel is additive, white Gaussian. The PCM system has arbitrary code, companding law and input signal density function. Especially optimum weighted PSK/PCM and QAM/PCM are given for speech signals. The average channel signal to noise ratio is kept constant when schemes are compared. We obtain a channel signal to noise ratio gain in threshold extension of 2 dB for standard 8 bit PCM. The performance of suboptimum schemes, where the number of different bit error probability levels are smaller than the number of PCM bits are also studied. Two levels per 8 bit PCM word yield more than half of the achievable gain (in dB) and 4 levels is almost equal to optimum.     

Bit error rate for rectangular QAM with arbitrary constellation mapping in Nakagami‐m channels

We present closed‐form expressions for the bit error rate (BER) of rectangular quadrature amplitude modulation (QAM) in Nakagami‐m fading channels. The presented formulas, which are valid for arbitrary bits‐to‐symbols mapping, thus may be used when non‐Gray mapping is employed, are particularly useful in the low signal‐to‐noise ratio (SNR) range and/or for small values of the parameter m. The advantage of the proposed expressions over the known bounding techniques is illustrated through numerical simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Bandwidth‐efficient turbo coding over Rayleigh fading channels

Introduced in 1993, turbo codes can achieve high coding gains close to the Shannon limit. In order to design power and bandwidth‐efficient coding schemes, several approaches have been introduced to combine high coding rate turbo codes with multilevel modulations. The coding systems thus obtained have been shown to display near‐capacity performance over additive white Gaussian noise (AWGN) channels. For communications over fading channels requiring large coding gain and high bandwidth efficiency, it is also interesting to study bit error rate (BER) performance of turbo codes combined with high order rectangular QAM modulations. To this end, we investigate, in this paper, error performance of several bandwidth‐efficient schemes designed using the bit‐interleaved coded modulation approach that has proven potentially very attractive when powerful codes, such as turbo codes, are employed. The structure of these coding schemes, termed ‘bit‐interleaved turbo‐coded modulations’ (BITCMs), is presented in a detailed manner and their BER performance is investigated for spectral efficiencies ranging from 2 to 7 bit/s/Hz. Computer simulation results indicate that BITCMs can achieve near‐capacity performance over Rayleigh fading channels, for all spectral efficiencies considered throughout the paper. It is also shown that the combination of turbo coding and rectangular QAM modulation with Gray mapping constitutes inherently a very powerful association, since coding and modulation functions are both optimized for operation in the same signal‐to‐noise ratio region. This means that no BER improvement is obtainable by employing any other signal constellation in place of the rectangular ones. Finally, the actual influence of the interleaving and mapping functions on error performance of BITCM schemes is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

In this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.     

Variable‐rate adaptive modulation with optimum switching thresholds for cooperative systems with relay selection

In this paper, the performance of variable‐rate adaptive modulation schemes in the amplify‐and‐forward cooperative systems with relay selection is analyzed over Rayleigh fading channels. We consider constant power and discrete‐rate adaptive multi‐level modulation techniques. The switching levels required for discrete‐rate adaptive modulation have been determined for two schemes, namely fixed switching levels and optimum switching levels, both respecting a target bit error rate requirements, where in the later scheme, the switching levels are optimally determined in a way that the average spectral efficiency of the system is maximized. Two M‐ary modulation schemes, namely quadrature amplitude modulation and phase shift keying, are considered. Closed‐form expressions are derived for three performance metrics, namely average spectral efficiency, outage probability, and average bit error rate, for two cases: independent and identically distributed fading relay links and independent and non‐identically distributed links. It is shown that, compared with using fixed switching levels, employing optimum switching levels provides a slight improvement in the spectral efficiency and moderate improvements in the signal‐to‐noise ratio gain and in the outage probability of the system. It is also shown that compared with the independent and identically distributed links, independent and non‐identically distributed relay links yield a slight increase in the signal‐to‐noise ratio gain and a slight decrease in the diversity order of the system. Copyright © 2011 John Wiley & Sons, Ltd.     

Differential space time block codes using nonconstant modulus constellations

We propose differential space time block codes (STBC) using nonconstant modulus constellations, e.g., quadrature amplitude modulation (QAM), which cannot be utilized in the conventional differential STBC. Since QAM constellations have a larger minimum distance compared with the phase shift keying (PSK), the proposed method has the advantage of signal-to-noise ratio (SNR) gain compared with conventional differential STBC. The QAM signals are encoded in a manner similar to that of the conventional differential STBC. To decode nonconstant modulus signals, the received signals are normalized by the channel power estimated forgoing training symbols and then decoded with a conventional QAM decoder. Assuming the knowledge of the channel power at the receiver, the symbol error rate (SER) bound of the proposed method under independent Rayleigh fading assumption is derived, which shows better SER performance than the conventional differential STBC. When the transmission rate is more than 3 bits/channel use in time-varying channels, the simulation results demonstrate that the proposed method with the channel power estimation outperforms the conventional differential STBC. Specifically, the posed method using the channel power estimation obtains a 7.3 dB SNR gain at a transmission rate of 6 bits/channel use in slow fading channels. Although the performance gap between the proposed method and the conventional one decreases as the Doppler frequency increases, the proposed method still exhibits lower SER than the conventional one, provided the estimation interval L is chosen carefully.     

Performance analysis of selective cooperation in amplify‐and‐forward relay networks over identical Nakagami‐m channels

In cooperative communications, multiple relays between a source and a destination can increase the diversity gain. Because all the nodes must use orthogonal channels, multiple‐relay cooperation becomes spectrally inefficient. Therefore, a bestrelay selection scheme was recently proposed. In this paper, we analyzed the performance of this scheme for a system with the relays operating in amplify‐and‐forward mode over identical Nakagami‐m channels using an exact source–relay–destination signal‐to‐noise ratio (SNR).We derived accurate closed‐form expressions for various system parameters including the probability density function of end‐to‐end SNR, the average output SNR, the bit error probability, and the channel capacity. The analytical results were verified through Monte Carlo simulations. Copyright © 2011 John Wiley & Sons, Ltd.