Concatenated coded modulation techniques and orthogonal space-time block codes in the presence of fading channel estimation errors

Performance of coding and modulation systems in fading channels is usually analysed under the assumption that the receiver has perfect knowledge of channel condition. However, various shortcomings in practical channel estimation techniques lead to imperfections, resulting in channel estimation errors. The authors analyse a practical coding and modulation scheme for multiple-antenna systems considering channel estimation errors. The novelty of this study resides in providing error probability bounds for concatenated trellis coded modulation (TCM) or bit-interleaved coded modulation (BICM) schemes with orthogonal space--time block codes (OSTBC) under imperfect channel estimation assumption. Moreover, our analytical results quantify the performance degradation associated with various levels of channel estimation error variance. The authors also show that if channel estimation quality does not improve sufficiently with SNR, there would be error floor in performance, such that the coded system could get outperformed by a system with differential signalling that requires no channel estimation. Simulation results are presented, which confirm the validity of the analytical results.     

Concatenated peak-to-average power ratio reduction scheme with threshold limited selection for coded orthogonal frequency-division multiplexing

The authors propose a concatenated scheme to reduce the peak-to-average power ratio (PAPR) in coded orthogonal frequency-division multiplexing (OFDM) systems. First, they employ a label-bits-inserted encoder of a random-like code to achieve selected mapping (SLM). Then they set a threshold at the selector to limit the number of candidate sequences. Both analytical and numerical results show that the complexity of the SLM implemented by the label-bit-inserted encoder can be significantly reduced by threshold limited selection. With the same complexity, the performance of PAPR reduction is improved. The proposed concatenated PAPR reduction scheme enjoys many advantages including low-complexity, small overhead, no side information transmission and no performance loss or additional complexity at the receiver.     

Closed-form symbol error rate expression of decode-and-forward relaying using orthogonal space-time block coding

The authors investigate the symbol error rate (SER) performance of the cooperative decode-andforward (DF) relaying strategy with orthogonal space-time block coding (OSTBC) applied at all links of sourcerelay, source-destination and relay-destination. Only when one relay node is able to correctly decode the OSTBC codeword of the source, it will forward source information to the destination with the same OSTBC codeword. The exact SER expressions of DF relaying with OSTBC are presented for M-PSK and M-QAM modulations, respectively, over dissimilar Rayleigh fading channels. By virtue of the multinomial theorem and the law of total probability, the derived expressions are further deduced in closed form. Simulations demonstrate the proposed closed-form analytical results. It is pointed out that such results have seldom appeared in literatures before.     

Iterative low-complexity multi-user detection for asynchronous multi-sequence signalling based bit-interleaved coded modulation code division multiple access systems

An uplink direct sequence spread spectrum communications systems employing a multi-sequence model over a quasi-static frequency-selective fading channel is considered. In analogy with bit-interleaved coded modulation (BICM) technique, a group of bits at the output of a bit-wise interleaver is mapped uniquely to a complex signalling vector belonging to an orthogonal plane sequence modulation signal space, which is constructed over a set of expanded signature sequences. This transmission system provides not only bandwidth efficiency offered by additional signal planes but also time diversity resulting from the BICM technique. It is observed that at high system traffic load error performance could degrade substantially due to user cross-correlations, multi-access asynchronism as well as channel frequency selectivity. The authors employ a 'turbo principle' receiver, consisting of a soft interference cancellation scheme, soft demappers and maximum a posteriori decoders, to avert this capacity loss by exploiting the serially concatenating structure at the transmitter. After simple mathematical manipulation, a soft space-time linear minimum mean-square error multi-user detector could even be explored on the basis of per signal plane per user. Both analytical performance-bound and computer simulation of the proposed framework in terms of bit-error rate (BER) are revealed. Further, performance comparisons with convolutionally coded and conventional bandwidth-efficient coded direct sequence code division multiple access systems under the same system conditions are illustrated. The authors have also investigated the impact of labelling maps on the BER performance.     

Analysis of BPSK modulated asynchronous band-limited DS-CDMA systems with diversity receivers over generalised-K fading channels

The authors studied bit-error rate (BER) performance of asynchronous band-limited direct-sequence code-division multiple-access (DS-CDMA) systems with various diversity-combining receivers over Generalised-K fading channels. The effects of band-limited pulse shapes, multitone jamming, multiple-access interference as well as both flat and frequency-selective fading are considered. The Generalised-K model is adopted in order to include the effects of shadowing and fading of a wireless channel. The authors consider binary phase-shift keying as the modulation technique. The analytical expressions are valid for any arbitrary value of Generalised-K distribution parameters. Two types of band-limited pulses, namely spectrum raised cosine and Beaulieu-Tan-Damen (BTD) pulses, are incorporated in the analysis. Numerical results show that the system with BTD pulse outperforms the one with SRC pulse for various diversity-combining receivers under various channel conditions. Furthermore, by incorporating a minimum mean-square error stage in the multipath diversity receiver, the BER performance can be further improved.     

New concatenated coding and space?time modulation scheme for MIMO wireless communications

Zheng and Tse have demonstrated that there exists an optimal trade-off between diversity gain and multiplexing gain. To realise the predicted optimal trade-off, we propose a new multiple-input multiple-output transmission scheme for a concatenated coding and space-time (ST) modulation system aimed at applications that require flexible trade-off between performance and data rate. The proposed scheme is multi-layered with linear ST modulation to allow various multiplexing gain. Through a judicious design of the inner ST modulation, the optimisation of spatial multiplexing is made simple. Moreover, a joint iterative receiver based on MMSE criterion with a priori information is developed to reduce computational complexity. Simulation results are provided to demonstrate the merits of the new design.     

Trellis coded modulation based distributed channel coding

A novel technique is described for distributed channel coding in wireless communication networks. The protocol is based on a block fading model of the multi-user uplink channel and on adapting multidimensional trellis coded modulation techniques to a coding theorem derived for the block fading channel. The coded modulation (CM) protocol is designed to optimise code performance, especially at high spectral efficiencies. The CM protocol is very simple to implement at the cooperating users. Complexity is completely transferred to the destination. The latency of the protocol is only one symbol. The CM protocol achieves full diversity order equal to the number of cooperating users and maximises coding gains by designing the code for the specific modulation used. We derive analytical results and present simulation results showing the benefits of CM protocol over other comparable schemes.     

Average BER performance of FSO SIM-QAM systems in the presence of atmospheric turbulence and pointing errors

This paper presents the exact average bit error rate (BER) analysis of the free-space optical system employing subcarrier intensity modulation (SIM) with Gray-coded quadrature amplitude modulation (QAM). The intensity fluctuations of the received optical signal are caused by the path loss, atmospheric turbulence and pointing errors. The exact closed-form analytical expressions for the average BER are derived assuming the SIM-QAM with arbitrary constellation size in the presence of the Gamma–Gamma scintillation. The simple approximate average BER expressions are also provided, considering only the dominant term in the finite summations of obtained expressions. Derived expressions are reduced to the special case when optical signal transmission is affected only by the atmospheric turbulence. Numerical results are presented in order to illustrate usefulness of the derived expressions and also to give insights into the effects of different modulation, channel and receiver parameters on the average BER performance. The results show that the misalignment between the transmitter laser and receiver detector has the strong effect on the average BER value, especially in the range of the high values of the average electrical signal-to-noise ratio.     

Bandwidth efficient concatenated coding schemes

Concatenated coded modulation is a powerful method for constructing coding schemes with large coding gain and low decoding complexity. For the concatenated scheme, the outer code has redundancy and the overall transmission rate is reduced. The problem of bandwidth expansion can be overcome by two procedures. First, the code rate of inner codes is increased with a special coding design. Second, a two-level concatenated scheme is constructed to compensate the rate loss. This way, the low-complexity concatenated coded modulation schemes can be designed without bandwidth expansion as compared with the uncoded scheme.     

Performance bounds for uniformly interleaved serial concatenations with a general inner system

Average performance bounds based on uniform interleaving are considered for a serial concatenation consisting of an outer code, an interleaver and an inner coded modulation system. The exact input-output weight spectrum is derived for the case when only the outer code has the uniform error property. Thereby, an upper bound to the bit error probability under maximum likelihood detection is obtained. However, numerous examples for serially concatenated continuous phase modulation show that neglecting the non-uniform error property of the inner system gives an accurate and less complex approximation. Other inner coded modulations may behave differently.     

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.     

Coding techniques for link adaptation in multicarrier systems

A novel technique for improving coding and diversity gains in orthogonal frequency division multiplexing (OFDM) systems is proposed. Multidimensional symbol design based on complex field codes with interleaving across frequency has been known for some time now. However, such symbols cannot be concatenated to convolutional codes owing to the prohibitive complexity of decoding. A novel way of designing multidimensional symbols that allow to concatenate them to convolutional codes while maintaining a low decoding complexity is shown. The proposed multidimensional symbols are based on tailbiting convolutional codes and the design of codes is discussed with desirable properties. Also the design of bit interleaved coded modulation-type and trellis-coded modulation-type codes over these multidimensional symbols is shown. Simulations show that the proposed coding scheme provides significant performance and/or complexity improvements over existing alternatives and also provides more degrees of freedom for channel-based link adaptation.     

Non-coherent improved-gain diversity reception of binary orthogonal signals in Nakagami-q (Hoyt) mobile channels

A novel non-coherent receiver with diversity reception for binary orthogonal signals in non-identical Nakagami-g (Hoyt) fading channels (channels having arbitrary average fading powers and arbitrary fading parameters) is proposed. A closed-form expression for the average bit error probability of the proposed receiver is derived, which is given in terms of elementary functions, and can be readily evaluated numerically. In addition, the results clarify that the proposed receiver does not incur non-coherent combining loss, and at the same time, lower bounds the performance of the conventional non-coherent equal-gain combining (NC-EGC) receiver. Simulation results are provided to validate the mathematical analysis.     

Closed-form expressions for symbol error probability of orthogonal space?time block codes over Rician?Nakagami channels

The performances of orthogonal space-time block codes (OSTBCs) over Rician- Nakagami channels are investigated. In particular, we derive closed-form symbol error probability (SEP) expressions for OSTBC systems in which M-ary phase-shift-keying modulation and M-ary quadrature-amplitude modulation are used. These SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions, which can be easily evaluated numerically. When the Rician-Nakagami channel degenerates to the Rician-Rayleigh channel, or equivalently the Rayleigh fading channel, the closed-form SEP expressions are rewritten in terms of higher transcendental functions, that is, Gauss hypergeometric function and Appell hypergeometric function.     

Performance of differential pulse-position modulation (DPPM) with concatenated coding over optical wireless communications [optical wireless communications]

The concatenation of marker and Reed-Solomon codes in order to correct insertion/ deletion errors in differential pulse-position modulation (DPPM) over optical wireless communications is presented. The concatenated code decoding algorithms with hard-decision and soft-decision detection are presented. The performance of the hard-decision coded DPPM system is evaluated over both nondispersive and dispersive channels via analysis and simulation. It is shown that the coding gain provided by the concatenated code is approximately 4 dB when the code rate is about 0.7 and the channel is nondispersive. Over a dispersive channel, the coded system performs better than the uncoded system when the ratio of delay spread to bit duration is not high. A soft-decision detector is employed to combat intersymbol interference. The soft- decision decoding algorithm, which has low complexity and can be practically implemented, is described. The performance over nondispersive and dispersive channels is evaluated by analysis and simulation. It is shown that the soft-decision system requires approximately 2 dB less transmit power than the hard-decision system for additive white Gaussian noise and low-dispersive channels. Soft decoding also provides a performance improvement in high-dispersive channels.     

Adaptive modulation for limited diversity fading channels

In this study, the authors propose a novel technique for adaptive modulation over limited diversity fading channels with channel state information at the transmitter. Limited diversity channels such as those encountered in indoor orthogonal frequency division multiplexing systems are characterised by the fact that achievable diversity orders are limited by the channel and not by code-free distances. The authors first propose a novel analysis technique for the performance of coded modulation on limited diversity block fading channels with different modulation sets on each block. The authors then propose adaptive modulation techniques for maximising the throughput at a fixed bit error probability and also for minimising the bit error probability at a fixed rate. Lastly, the authors show simulation results that support the arguments presented in the paper.     

Peak-to-average power ratio reduction in space-time block coded multi-input multi-output orthogonal frequency division multiplexing systems using a small overhead selective mapping scheme

The selective mapping (SLM) scheme is one of the most popular peak-to-average power ratio (PAPR) reduction techniques proposed for multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. One of the major disadvantages of this scheme is the need for the transmission of side information (SI) bits to enable the receiver to recover the transmitted data. The authors present a small overhead SLM (s-SLM) scheme for space-time block coded (STBC) MIMO-OFDM systems. This proposed scheme improves the system bandwidth efficiency and achieves a significantly lower bit error rate (BER) than the individual SLM (i-SLM) and direct SLM (d-SLM) schemes. In addition, approximate expressions for the complementary cumulative distribution function (CCDF) of the PAPR and the average BER of the proposed s-SLM scheme are derived. The simulation results show that the proposed s-SLM scheme improves the detection probability of the SI bits and hence gives a better performance than the i-SLM and the d-SLM schemes.     

Simultaneous optimisation of filter bandwidths and interferometer free spectral range for DPSK and DQPSK modulation

The authors investigate the optimal bandwidths for transmitter and receiver filters for differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) optical modulation in dense wavelength-division multiplexing (WDM) scenarios. Single-channel setups were investigated as reference. Simultaneously, the optimal free spectral range (FSR) of the delay interferometer (DI) needed at the receiver for both modulation formats was searched. Transmitter (Tx) and receiver (Rx) optimal setups were focused and the propagation effects were not considered. It is demonstrated that the optimal FSR, in general, is larger than the symbol rate for both DPSK and DQPSK modulation formats.     

Internally coded time-hopping coherent ultra-short light pulse code division multiple access scheme with optical amplifier and its performance analysis using additive noise model

The internally coded time-hopping coherent ultra-short light pulse code division multiple access (CULP CDMA) scheme (recently introduced) with an optical amplifier is described and its performance in fibreoptic communication systems is analysed. In accordance with the important role of optical amplifiers in optical communication systems, a preamplifier at the input of the receiver is used in order to compensate the losses because of the spectral encoder, spectral decoder and optical fibre path. The authors evaluate the bit error rate of the system considering the effects of the multiple access interference, noise because of the optical amplifier and thermal noise using saddle point approximation, and compare the results with those of the conventional CULP CDMA system with and without an amplifier. The numerical results indicate a substantial improvement in the performance of the coded system in comparison with the uncoded one. In addition, the negative effect of amplifier noise in the proposed scheme is much less than that of the conventional CULP CDMA system.     

Performance of W-CDMA systems with rectangular signalling in OSTBC MIMO generalised nakagami-m fading channels

The performance of combined temporal multipath diversity with statistically independent branches and spatial antenna diversity with arbitrarily correlated branches is investigated. A downlink wide-band code-division multiple access system employing orthogonal space-time block coding multiple-input-multiple-output communications is considered. The performance is quantified in terms of the average symbol error probability (SEP) of coherent arbitrary rectangular quadrature amplitude modulation in Nakagami-m fading with arbitrary statistics. Through the analysis, new expressions for the average SEP are derived under the generalised system model described above. Specifically, the considerations of the combined path and space diversity model, the arbitrary correlation profile among spatial diversity branches, and the arbitrary statistics of Nakagami-m fading processes are the main aspects that make the system model herein generalised as compared to previous ones. Furthermore, for this generalised system model, the consideration of distinct in-phase and quadrature decision distances as well as modulation orders in the rectangular signalling constellation through the analysis provide additional enhancements on some existing results. Numerical and simulation results are presented to demonstrate the enhanced validity of the analytical development.