Performance analysis of coded modulation with generalized selection combining in Rayleigh fading

We consider coded modulation with generalized selection combining (GSC) for bandwidth-efficient-coded modulation over Rayleigh fading channels. Our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance. We provide a number of new results by calculating the cutoff rate, and by deriving analytical upper bounds on symbol-interleaved trellis-coded modulation (TCM) and bit-interleaved-coded modulation (BICM) with GSC. All are verified by simulation. We show that our new bounds on TCM with GSC, which includes maximum ratio combining and selection combining as special cases, are tighter than the previously derived bounds. A new asymptotic analysis on the pairwise error probability, which can be used as a guideline for designing coded modulation over GSC channels, is also given. Finally, we show that BICM with iterative decoding (BICM-ID) can achieve significant coding gain over conventional coded modulation in a multiple-receiving-antenna channel.     

Distribution of max-log metrics for QAM-based BICM in fading channels

In this letter we derive closed-form expressions for the probability density functions (PDFs) of the bits' reliability metrics (L-values) in bit-interleaved coded modulation (BICM) transmission over fully-interleaved fading channels. The expressions are valid for the relevant case of quadrature amplitude modulation (QAM) with Gray mapping when the metrics are calculated via the so-called max-log approximation. Using the developed expressions, the performance of coded BICM transmissions is efficiently evaluated, i.e., without resorting to otherwise required two-dimensional numerical integration. The BICM capacity for different fading channels and constellation sizes is also evaluated.     

Pilot-symbol-assisted LDPC coded BICM over correlated Rayleigh fading channels

Pilot-symbol-assisted low-density parity-check (LDPC)-coded bit-interleaved coded modulation (BICM) is analyzed using the density evolution (DE) and the extrinsic information-transfer (EXIT) chart for correlated Rayleigh fading channels. The key parameter (the power correlation coefficient) is identified, and the threshold degradation is quantified. The optimal tradeoff of energy allocation between pilots and coded symbols is found to be sensitive to the normalized Doppler spread of the channel, the interpolation filter, the modulation scheme, and the pilot selection. In addition, a simple upper bound on the performance of any receiver that performs joint iterative decoding and channel estimation is derived. Extension to irregular code design is also discussed.     

Performance and distance spectrum of space-time codes in fast rayleigh fading channels

In this paper, we analyze the performance of spacetime codes and propose a distance spectrum computation method in fast Rayleigh fading channels. We first derive a new FER upper bound using the union bound and the PEP upper bound in the fast fading environment. The derived FER upper bound is very accurate, requires only the distance spectrum of the spacetime code, and takes a closed-form expression. Then we propose a distance spectrum computation method of space-time codes in fast fading channels, which exploits the symmetric property of the error state diagram in space-time trellis coded MPSK modulation to reduce the computation complexity. Numerical results illustrate that the derived FER bound is tight enough to estimate the performance of space-time codes in fast fading channels with sufficient accuracy.     

Concatenated Trellis Coded Modulation for Quasi-Static Fading Channels

In this paper, we present a novel concatenated trellis coded modulation (CTCM) scheme for limited diversity order fading channels. Examples for such channels include those encountered in indoor wireless networks like IEEE 802.11. It is first shown that when the diversity order afforded by the channel is fixed, bit interleaved coded modulation (BICM) is no longer the best way to encode. We then develop CTCM, which is superior to both BICM and conventional TCM of similar complexities. Unlike conventional TCM where convolutional codes are designed over modulated signal sets, CTCM has TCM concatenated to short length inner codes. Each trellis branch in the TCM now corresponds to a short block-code. We discuss design of good inner codes that allow for simple decoders. CTCM design incorporates useful features of both BICM and conventional TCM. Code design is explained with examples. Simulation results and information theoretic supporting the arguments are shown.     

Adaptive bit-interleaved coded modulation

Adaptive coded modulation is a powerful method for achieving a high spectral efficiency over fading channels. Previously proposed adaptive schemes have employed set-partitioned trellis-coded modulation (TCM) and have adapted the number of uncoded bits on a given symbol based on the corresponding channel estimate. However, these adaptive TCM schemes do not perform well in systems where channel estimates are unreliable, since uncoded bits are not protected from unexpected finding. In this paper, adaptive bit-interleaved coded modulation (BICM) is introduced. Adaptive BICM schemes remove the need for parallel branches in the trellis-even when adapting the constellation size, thus making these schemes robust to errors made in the estimation of the current channel fading value. This motivates the design of adaptive BICM schemes, which will lead to adaptive systems that can support users with higher mobility than those considered in previous work. In such systems, numerical results demonstrate that the proposed schemes achieve a moderate bandwidth efficiency gain over previously proposed adaptive schemes and conventional (nonadaptive) schemes of similar complexity     

一种高效的联合编码调制分集——迭代接收方案

本文研究了加入迭代解调译码的比特交织编码调制方案,并通过联合编码调制分集扩展此方案。BICM-ID通过信号空间分集增加分集数,并选择最优旋转角度使性能上进一步取得了明显增益。     

Performance analysis of convolutionally coded systems over quasi-static fading channels

This paper presents an improved upper bound on the performance of convolutionally coded systems over quasi-static fading channels (QSFC). The bound uses a combination of a classical union bound when the fading channel is in a high signal-to-noise ratio (SNR) state together with a new upper bound for the low SNR state. This new bounding approach is applied to both BPSK convolutional and turbo codes, as well as serially concatenated BPSK convolutional/turbo and space-time block codes. The new analytical technique produces bounds which are usually about 1 dB tighter than existing bounds. Finally, based on the proposed bound, we introduce an improved design criterion for convolutionally coded systems in slow flat fading channels. Simulation results are included to confirm the improved ability of the proposed criterion to search for convolutional codes with good performance over a QSFC.     

基于软判决的BICM-ID在Rayleigh信道下的性能研究

从理论上对不同映射方式下的BICM-ID系统在Rayleigh衰落信道中的性能做了分析和估计,通过3种映射方式(SP,SSP,Gray)下BICM-ID系统的性能仿真,对理论分析进行了验证。仿真结果和理论分析吻合,在Rayleigh衰落信道下,SSP映射性能最佳。与其他编码调制方式(TTCM,BICM)的性能相比,在Rayleigh衰落信道下,随着信噪比的增加,BICM-ID性能要优于其他编码调制方式。     

Performance of BICM-SC and BICM-OFDM systems with diversity reception in non-gaussian noise and interference

In this paper, we present a general mathematical framework for performance analysis of single?carrier (SC) and orthogonal frequency division multiplexing (OFDM) systems employing popular bit?interleaved coded modulation (BICM) and multiple receive antennas. The proposed analysis is applicable to BICM systems impaired by general types of fading (including Rayleigh, Ricean, Nakagami-m, Nakagami-q, and Weibull fading) and general types of noise and interference with finite moments such as additive white Gaussian noise (AWGN), additive correlated Gaussian noise, Gaussian mixture noise, co-channel interference, narrowband interference, and ultra-wideband interference. We present an approximate upper bound for the bit error rate (BER) and an accurate closed-form approximation for the asymptotic BER at high signal-to-noise ratios for Viterbi decoding with the standard Euclidean distance branch metric. For the standard rate-1/2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at BERs of 10-6 and 10-12, respectively. However, if the code is punctured to higher rates (e.g. 2/3 or 3/4), the asymptotic approximation also becomes tight at a BER of 10-6. Exploiting the asymptotic BER approximation we show that the diversity gain of BICM systems only depends on the free distance of the code, the type of fading, and the number of receive antennas but not on the type of noise. In contrast their coding gain strongly depends on the noise moments. Our asymptotic analysis shows that as long as the standard Euclidean distance branch metric is used for Viterbi decoding, BICM systems optimized for AWGN are also optimum for any other type of noise and interference with finite moments.     

Trellis-coded modulation with bit interleaving and iterativedecoding

This paper considers bit-interleaved coded modulation (BICM) for bandwidth-efficient transmission using software radios. A simple iterative decoding (ID) method with hard-decision feedback is suggested to achieve better performance. The paper shows that convolutional codes with good Hamming-distance property can provide both high diversity order and large free Euclidean distance for BICM-ID. The method offers a common framework for coded modulation over channels with a variety of fading statistics. In addition, BICM-ID allows an efficient combination of punctured convolutional codes and multiphase/level modulation, and therefore provides a simple mechanism for variable-rate transmission     

Error probability analysis of bit-interleaved coded modulation

This correspondence presents a simple method to accurately compute the error probability of bit-interleaved coded modulation (BICM). Thanks to the binary-input output-symmetric (BIOS) nature of the channel, the pairwise error probability (PEP) is equal to the tail probability of a sum of random variables with a particular distribution. This probability is in turn computed with a saddlepoint approximation. Its precision is numerically validated for coded transmission over standard Gaussian noise and fully interleaved fading channels for both convolutional and turbo-like codes.     

Benchmarking Iterative Receivers for BICM Multi-Carrier Systems Against Capacity Bounds

In this paper, we analyze iterative receivers for bit-interleaved coded modulation (BICM) multi-carrier systems and compare them against theoretical capacity bounds for the channel, coded modulation, and BICM. We map the theoretical capacity bounds into bit-error rate (BER) versus average signal-to-noise ratio per bit plots to simplify the comparison between the theoretical capacity bounds and simulated BER curves. As BER simulations show, iterative receivers with code doping or spreading reach the turbo-cliff within 1 or 0.3dB of the independent Rayleigh fading channel capacity. While the iterative receiver with spreading is closer to the channel capacity than the one with code doping, the later one can eliminate the residual bit-errors after the turbo-cliff. We further present a combinatorial analysis of the distribution of the spread symbol constellation for Walsh-Hadamard spreading codes used in a BICM multi-carrier system to explain the above results.     

Analysis of the effects of time delay spread on TCM performance

We investigate the effect of time delay spread on trellis coded modulation (TCM) in a wireless radio environment where equalization is not employed to mitigate the effects of frequency selective fading when the time delay spread is small. Using a random variable decomposition technique and a Gaussian approximation of the intersymbol interference terms, we obtain explicit bounds for the pairwise error probability of TCM over multipath Rayleigh fading channels characterized by various power delay profiles. A method to calculate an upper bound of the bit error rate (BER) based on Jamali and LeNgoc (1995) bound is also presented. These bounds are used to evaluate TCM performance as well as investigate the delay spread tolerance limit of TCM, including I-Q TCM, over frequency selective fading channels     

Chernoff bound of trellis-coded modulation over correlated fadingchannels

We derive a Chernoff upper bound for the pairwise error probability in the presence of an additive white Gaussian noise and a Rayleigh or Rice correlated fading. The bound is useful for situations where perfect interleaving cannot be achieved. We use it to determine some indications in the design of optimum trellis coded modulation for correlated fading channels     

采用预判决信息的LDPC码编码调制方案性能研究

低密度奇偶校验(LDPC)码是Turbo码以外另一种性能接近香农限的好码.本文将LDPC码与比特交织编码调制(BICM)相结合,首先给出了在不使用传统解调器与译码器之间迭代的情况下8PSK调制方案在AWGN信道和Rayleigh衰落信道中的性能(简称为无迭代方案).然后提出了一种新的接收端解决方案:首先对接收符号进行预判决,判决信息被用来调整解调器,从而在一定程度上弥补了不使用解调器与译码器之间迭代所造成的性能损失,并且相对于无迭代方案接收端复杂度几乎没有变化,但性能却有所提高.这说明原有比特度量产生方法并不是最佳的,该文使用预判决信息的方案给出了一个改善的思路.通过仿真结果可以得到结论:使用本文所提出的方案在AWGN信道和Rayleigh衰落信道中都可以在不增加复杂度的情况下提高性能.     

Multilevel coding for multiple-antenna transmission

The application of powerful coding for transmission over multiple-input/multiple-output channels is discussed. The authors emphasize that as an immediate consequence of the mutual information chain rule, multilevel coding (MLC) constitutes the optimum coded modulation scheme. On the other hand, simple bit-interleaved coded modulation (BICM) is only a convenient alternative for the case of two transmit and one receive antennas when combined with orthogonal space-time block codes. Starting from MLC, the authors further propose a hybrid coded modulation scheme, which favorably combines the advantages of MLC and BICM.     

Bit-interleaved coded modulation with iterative decoding

A simple iterative decoding technique using hard-decision feedback is presented for bit-interleaved coded modulation (BICM). With an 8-state, rate-2/3 convolutional code, and 8-PSK modulation, the improvement over the conventional BICM scheme exceeds 1 dB for a fully-interleaved Rayleigh flat-fading channel and exceeds 1.5 dB for a channel with additive white Gaussian noise. This robust performance makes BICM with iterative decoding suitable for both types of channels     

Multidimensional Subcarrier Mapping for Bit-Interleaved Coded OFDM With Iterative Decoding

A power and bandwidth-efficient bit-interleaved coded modulation (BICM) with orthogonal frequency-division multiplexing (OFDM) and iterative decoding (BI-COFDM-ID) using combined multidimensional mapping and subcarrier grouping is proposed for broadband transmission in a frequency-selective fading environment. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence, they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multidimensional mapping for bit-interleaved coded modulation with iterative decoding (BICM-ID) in frequency-flat Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with linear constellation preceding (LCP). Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using LCP and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth, and receiver complexity.     

Iterative demodulation and decoding of turbo-coded M-ary noncoherent orthogonal modulation

This paper considers bit-interleaved coded modulation (BICM) with a turbo channel code and M-ary orthogonal modulation. The BICM signal is iteratively demodulated and decoded in a noncoherent fashion. A soft demodulator suitable for noncoherent orthogonal modulation is presented, and the convergence of the iterative receiver is analyzed through extrinsic information transfer charts. The demodulator can work either with or without fading amplitude estimates. Extensive simulation results are presented for the well-known cdma-2000 turbo code, and the results are compared with the corresponding channel capacities, which are computed using a Monte Carlo technique. The results indicate gains of up to 1 dB relative to noniterative BICM can be achieved with the iterative receiver.