BER analysis of QAM on fading channels with transmit diversity

In this letter, we derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) using quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. The approach presented here can be used in the BER analysis of any STBC from COD with linear processing for any value of M in an M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC, and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. In addition to being used in the BER analysis, the LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding as in high speed downlink packet access (HSDPA) in 3G.     

Performance of low density parity check coded continuous phase frequency shift keying (LDPCC‐CPFSK) over fading channels

In this paper, in order to improve bit error performance, bandwidth efficiency and reduction of complexity compared to related schemes such as turbo codes, we combine low density parity check (LDPC) codes and continuous phase frequency shift keying (CPFSK) modulation and introduce a new scheme, called ‘low density parity check coded‐continuous phase frequency shift keying (LDPCC‐CPFSK)’. Since LDPC codes have very large Euclidean distance and use iterative decoding algorithms, they have high error correcting capacity and have very close performances to Shannon limit. In all communication systems, phase discontinuities of modulated signals result extra bandwidth requirements. Continuous phase modulation (CPM) is a powerful solution for this problem. Beside CPM provides good bandwidth efficiency; it also improves bit error performance with its memory unit. In our proposed scheme, LDPC and CPFSK, which is a special type of CPM, are considered together to improve both error performance and bandwidth efficiencies. We also obtain error performance curves of LDPCC‐CPFSK via computer simulations for both regular and irregular LDPC code. Simulation results are drawn for 4‐ary CPFSK, 8‐ary CPFSK and 16‐ary CPFSK over AWGN, Rician and Rayleigh fading channels for maximum 100 iterations, while the frame size is chosen as 504. Copyright © 2006 John Wiley & Sons, Ltd.     

On the performance of BICM with mapping diversity in hybrid ARQ

Hybrid ARQ with packet combining for high‐order modulations (such as 16‐QAM) may be significantly enhanced if the bits‐to‐symbols mappings are appropriately changed throughout the transmissions. In this paper, we analyze the relationship between such mapping diversity and channel coding. We calculate the capacity of the popular bit‐interleaved‐coded modulation (BICM) to draw qualitative and approximate quantitative conclusions that are valid for strong codes approaching the capacity limits. We conclude that the choice/design of the appropriate mapping depends on the targeted spectral efficiency and we demonstrate that certain forms of mapping diversity may be counterproductive. We also show that iterative demapping may be successfully applied to significantly reduce (by more than 1 dB) the gap between the BICM and coded modulations (CM) capacities. The analysis is illustrated with results obtained when the mapping diversity is combined with practical turbo codes. Copyright © 2007 John Wiley & Sons, Ltd.     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.     

Turbo‐coded APSK modulations design for satellite broadband communications

This paper investigates the design of power and spectrally efficient coded modulations based on amplitude phase shift keying (APSK) modulation with application to satellite broadband communications. APSK represents an attractive modulation format for digital transmission over nonlinear satellite channels due to its power and spectral efficiency combined with its inherent robustness against nonlinear distortion. For these reasons APSK has been very recently introduced in the new standard for satellite Digital Video Broadcasting named DVB‐S2. Assuming an ideal rectangular transmission pulse, for which no nonlinear inter‐symbol interference is present and perfect pre‐compensation of the nonlinearity, we optimize the APSK constellation. In addition to the minimum distance criterion, we introduce a new optimization based on the mutual information; this new method generates an optimum constellation for each spectral efficiency. To achieve power efficiency jointly with low bit error rate (BER) floor we adopt a powerful binary serially concatenated turbo‐code coupled with optimal APSK modulations through bit‐interleaved coded modulation. We derive tight approximations on the maximum‐likelihood decoding error probability, and results are compared with computer simulations. The proposed coded modulation scheme is shown to provide a considerable performance advantage compared to current standards for satellite multimedia and broadcasting systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Joint source-coding, channel-coding and modulation schemes for AWGN and Rayleigh fading channels

Joint source-coding, channel-coding and modulation schemes based on variable length codes, inphase-quadrature phase interleaved trellis coded modulation (TCM) and turbo TCM (TTCM) schemes are proposed. A significant coding gain and a lower error floor are achieved without bandwidth expansion.     

BER analysis of arbitrary QAM for MRC diversity with imperfect channel estimation in generalized ricean fading channels

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented.     

Low rate code designs for multilevel signaling

In this letter we present a new approach to designing codes with spectral efficiencies between 0.5 and 1 bit/dimension using multilevel signaling. Traditionally, code design techniques for these rates use high rate codes with binary signaling. However, from constrained channel capacity results, we know that for spectral efficiencies between 0.5 and 1 bit/dimension, the use of low rate codes with multilevel signaling can result in significant gains compared to the conventional approach. We present several examples of bit interleaved coded modulation using low rate turbo codes and a 16QAM signal set that demonstrate this advantage.     

On turbo encodedBicm

The superior performance of the binary turbo codes has stimulated vigorous efforts in generating bandwidth efficient modulation schemes adhering to these codes. Several approaches for the integration of turbo-coding and modulation have emerged in recent years but none seem to dominate. In the bit interleaved coded modulation (Bicm) scheme is used to achieve high bandwidth and power efficiency, while separating coding and modulation. As is now well known, theBicm scheme achieves capacity remarkably close to the constellation channel capacity. The turbo-Bicm scheme enjoys high coding diversity (well suited for fading channels), high flexibility as well as design and implementation simplicity, while maintaining good power efficiency. The system comprises one standard turbo code, an interleaver, a mapper and a modulator at the transmitter, corresponding to a demodulator, a de-interleaver and a turbo decoder at the receiver. A modified system, which improves on performance by incorporating the demodulation in the iterative decoding procedure, is investigated, and some performance gain is demonstrated, especially for low rate codes. Information theoretic arguments for the somewhat minor potential improvement in performance are detailed. The preferred mapper and interleaver for this system are considered. Extending previous works, for higher level modulations, we analyze a system including a convolutional code, an interleaver, a differential encoder (De), a mapper and a modulator at the transmitter. As for theBpsk modulation, the serial concatenation of a convolutional code withDe outperforms the single convolutional code. The serial concatenation withDe approach is analyzed also for a turbo code, where it is found to fail in achieving performance improvement. Several structures for the serial concatenation withDe are examined. These results are substantiated through the ‘spectral thinning’ phenomena of the weight distribution of the convolutional and turbocodes.     

I-Q TCM: reliable communication over the Rayleigh fading channelclose to the cutoff rate

This paper presents some trellis codes that provide high coding gain to channels with slow, non frequency-selective Rayleigh fading. It is shown that the use of two encoders in parallel-used to specify the in-phase and quadrature components of the transmitted signal-results in greater minimum time diversity than the conventional design in which a single encoder is used. Using this approach-which we label “I-Q TCM”-codes with bandwidth efficiencies of 1, 2, and 3 bits/s/Hz are described for various constraint lengths. The performance of these codes is bounded analytically and approximated via simulation; the results show a large improvement in the bit error rate (BER) when compared with conventional trellis-coded modulation (TCM) schemes when perfect channel state information (CSI) is available to the receiver. Indeed, when this approach is applied to channels with independent Rayleigh fading, the resulting coding gain is close to that implied by the cutoff rate limit, even for only moderately complex systems. The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1-bit/s/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4ν yields performance close to what is achieved with ideal interleaving     

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.     

A Tight BER Upper Bound for Bit-Interleaved Coded Modulation with Square QAM and Gray Labeling

Bit-interleaved coded modulation (BICM) is a bandwidth-efficient coded system with diversity order higher than that of Ungerboeck's trellis-coded modulation on fading channels. In this paper, we investigate the BER (bit error rate) performance of BICM in the additive white Gaussian and Rayleigh fading channels. A new upper bound is given for the square QAM constellation with gray labeling, which constitutes a large portion of practical applications of BICM systems. The new upper bound is tighter than the well-known BICM union bound proposed in G. Caire et al. (1998)     

Information Theoretic Foundations of Adaptive Coded Modulation

In wireless/mobile communications, terminals adapt their rate and transmit power or, more in general, their coding and modulation scheme, depending on the time-varying channel conditions. This paper presents, in a tutorial form, the information theoretic framework underlying such ldquoadaptive modulationrdquo techniques. First, we review fading channel models, channel state information assumptions, and related capacity results. Then, we treat the case of input power constraint, where the optimal input distribution is Gaussian. Finally, we address the case of discrete modulations. In order to treat the latter, we make use of the recently developed method of ldquomercury-waterfillingrdquo, based on the relationship between mutual information and minimum mean-square error (MMSE) estimation of the channel input from the channel output. While the traditional design of adaptive modulation schemes based on uncoded bit-error rate (BER) involves the optimization over a discrete set of signal constellations, when powerful (i.e., capacity approaching) coding schemes are used the corresponding adaptive coded modulation design becomes surprisingly simple. The regime of very powerful coding is justified by the use of modern coding schemes, such as turbo codes and low-density parity-check codes, able to perform close to channel capacity at very small BER.     

高阶调制系统下LDPC码优化设计

为了提高编码调制系统的整体编码增益,提出一种高阶调制系统下LDPC码的度分布优化方法.根据高阶调制符号中不同比特的误比特特性,将调制符号所经历信道建模为一组对称二进制输入加性高斯信道.在此基础上,推导了高阶调制系统下LDPC码高斯近似密度进化分析方法,并得到译码收敛条件.结合度分布约束关系及译码收敛条件,提出高阶调制系统下LDPC码的度分布优化问题及差分进化实现方法.仿真结果表明,设计的LDPC码在高阶调制系统中的渐进性能和误码性能优于基于比特优化映射的编码调制方案.     

Combining PSA fading estimation techniques for TCM and diversity reception in Rician fading channels

In this paper, a novel pilot‐symbol‐aided (PSA) technique is proposed for fading estimation in the land mobile satellite fading channels. The proposed technique combines the fading estimates obtained from a bandwidth‐efficient technique and a conventional technique according to the signal‐to‐noise ratios (SNRs) of the fading estimates. To enhance the transmission quality, trellis‐coded modulation (TCM) and diversity reception are employed in the system, and the combined estimates are subsequently used to correct the channel fading effects, to weight the signals from different diversity branches, and to provide channel state information to the Viterbi decoder. Monte Carlo computer simulation has been used to study the bit‐error‐rate (BER) performance of the proposed technique on trellis‐coded 16‐ary quadrature amplitude modulation in the frequency non‐selective Rician fading channels. Results have shown that the proposed PSA technique requires a very low bandwidth redundancy to provide satisfactory BER performance at low SNRs, and thus is suitable for use with TCM and diversity reception to achieve both bandwidth and power‐efficient transmission. Copyright © 2002 John Wiley & Sons, Ltd.     

A Parallel Concatenated Convolutional-Based Distributed Coded Cooperation Scheme for Relay Channels

In this paper, we investigate a coded cooperation diversity scheme suitable for L-relay channels operating in the soft-decode-and-forward (soft-DF) mode. The proposed scheme is based on parallel concatenated convolutional codes (PCCC). To improve the overall performance through diversity, the coded cooperation operates by sending the systematic and the first parity outputs via L?+?1 independent fading paths. Instead of using only a centralized turbo code system at the source node, we have proposed a DCC scheme, where the first recursive systematic coding is done at both source and relay nodes. At the destination, the received replicas are combined using the maximal ratio combining (MRC). The entire codeword, comprising the MRC sequence and the second parity part, is decoded via the maximum a-posteriori (MAP) algorithm and turbo decoding principle. We analyze the proposed scheme in terms of bit error rate (BER). In fact, we define the explicit upper bounds for error rate assuming Binary phase shift keying (BPSK) transmission for fully interleaved channels with channel state information (CSI). We use the Rayleigh fading channels with independent fading. Our study shows that the full diversity order is achieved when the source-relay link is more reliable than the other links. Otherwise, the diversity decreases. However, in both cases, it is shown that significant performance improvements are possible to achieve over non-cooperative coded systems. Theorical and simulation results are presented to demonstrate the efficacy of the proposed scheme.     

Combined turbo coding and unitary space-time modulation

Space-time coding is well understood for high data rate communications over wireless channels with perfect channel state information. On the other hand, channel coding for multiple transmit antennas when channel state information is unknown has only received limited attention. A new signaling scheme, named unitary space-time modulation, has been proposed for the latter case. In this paper, we consider the use of turbo coding together with unitary space-time modulation. We demonstrate that turbo coded space-time modulation systems are well suited to wireless communication systems when there is no channel state information, in the sense that the turbo coding improves the bit error rate (BER) performance of the system considerably. In particular, we observe that the turbo-coded system provides 10-15 dB coding gain at a BER of 10/sup -5/ compared to the unitary space-time modulation for various transmit and receive antenna diversity cases.     

On the general BER expression of one- and two-dimensional amplitude modulations

Quadrature amplitude modulation (QAM) is an attractive technique to achieve high rate transmission without increasing the bandwidth. A great deal of attention has been devoted to the study of bit error rate (BER) performance of QAM, and approximate expressions for the bit error probability of QAM have been developed in many places in the literature. However, the exact and general BER expression of QAM with an arbitrary constellation size has not been derived yet. We provide an exact and general closed-form expression of the BER for one-dimensional and two-dimensional amplitude modulations, i.e., PAM and QAM, under an additive white Gaussian noise (AWGN) channel when Gray code bit mapping is employed. The provided BER expressions offer a convenient way to evaluate the performance of PAM and QAM systems for various cases of practical interest. Moreover, simple approximations can be found from our expressions, which are the same as the well-known approximations, if only the dominant terms are considered.     

Coded modulation in the block-fading channel: coding theorems and code construction

We consider coded modulation schemes for the block-fading channel. In the setting where a codeword spans a finite number N of fading degrees of freedom, we show that coded modulations of rate R bit per complex dimension, over a finite signal set /spl chi//spl sube//spl Copf/ of size 2/sup M/, achieve the optimal rate-diversity tradeoff given by the Singleton bound /spl delta/(N,M,R)=1+/spl lfloor/N(1-R/M)/spl rfloor/, for R/spl isin/(0,M/spl rfloor/. Furthermore, we show also that the popular bit-interleaved coded modulation achieves the same optimal rate-diversity tradeoff. We present a novel coded modulation construction based on blockwise concatenation that systematically yields Singleton-bound achieving turbo-like codes defined over an arbitrary signal set /spl chi//spl sub//spl Copf/. The proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block-fading channel. We analyze the ensemble average performance under maximum-likelihood (ML) decoding of the proposed codes by means of upper bounds and tight approximations. We show that, differently from the additive white Gaussian noise (AWGN) and fully interleaved fading cases, belief-propagation iterative decoding performs very close to ML on the block-fading channel for any signal-to-noise ratio (SNR) and even for relatively short block lengths. We also show that, at constant decoding complexity per information bit, the proposed codes perform close to the information outage probability for any block length, while standard block codes (e.g., obtained by trellis termination of convolutional codes) have a gap from outage that increases with the block length: this is a different and more subtle manifestation of the so-called "interleaving gain" of turbo codes.     

Performance of MMSE Receiver Based CDMA System with Higher Order Modulation Formats in a Fading Channel

This paper studies the effect of using higher order modulation formats on the performance of minimum mean-squared error (MMSE) receiver based direct-sequence (DS) code-division multiple access (CDMA) systems at different loading levels in additive white Gaussian noise (AWGN) and slow fading channels. The performance of BPSK, QPSK, and 16QAM modulation formats are compared and analytical and simulation results are presented in terms of the bit error rates (BER) for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. The main contribution of this paper is in showing that user capacity may be increased by using higher order modulation schemes to cause the MMSE receiver to operate away from the interference limiting region. In particular it is shown that under high loading levels, 16QAM outperforms QPSK and BPSK for identical bandwidth and information rate, while at moderate loading levels, QPSK represents the best option. A combination of pilot symbol assisted modulation (PSAM) and linear prediction are used to estimate the fading process. A general structure of the MMSE receiver capable of demodulating a wide range of digital modulation formats in this type of environment is presented.