An efficient space-frequency coded OFDM system for broadband wireless communications

We propose an efficient space-frequency coded orthogonal frequency-division multiplexing (OFDM) system for high-speed transmission over wireless links. The analytical expression for the pairwise probability of the proposed space-frequency coded OFDM system is derived in slow, space- and frequency-selective fading channels. The design criteria of trellis codes used in the proposed system are then developed and discussed. It is shown that the proposed space-frequency coded OFDM can efficiently achieve the full diversity provided by the fading channel with low trellis complexity, while for traditional space-frequency coded OFDM systems, we need to design space-time trellis codes with high trellis complexity to exploit the maximum achievable diversity order. The capacity properties of space-frequency coded OFDM over multipath fading channels are also studied. Numerical results are provided to demonstrate the significant performance improvement obtained by the proposed space-frequency coded OFDM scheme, as well as the excellent outage capacity properties.     

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.     

Impact of time-selective fading on the performance of quasi-orthogonal space-time-coded OFDM systems

In this paper, we study the impact of time-selective fading on quasi-orthogonal space-time (ST) coded orthogonal frequency-division multiplexing (OFDM) systems over frequency-selective Rayleigh fading channels. OFDM is robust against frequency-selective fading, but it is more vulnerable to time-selective fading than single-carrier systems. In ST-OFDM, channel time variations cause not only intercarrier interference among different subcarriers in one OFDM symbol, but also intertransmit-antenna interference. We quantify the impact of time-selective fading on the performance of quasi-orthogonal ST-OFDM systems by deriving, via an analytical approach, the expressions of carrier-to-interference and signal-to-interference-plus-noise ratios. We observe that system error performance is insensitive to changes in vehicle speeds and the channel power-delay profile, but very sensitive to changes in the number of subcarriers. We also evaluate the performance of five different detection schemes in the presence of time-selective fading. We show that although there exist differences in their relative performances, all these detection schemes suffer from an irreducible error floor.     

Cooperative Coding for OFDM Systems

In this paper, we study Orthogonal Frequency Division Multiplexing (OFDM) systems with cooperative coding over frequency selective Rayleigh fading channels. We derive the pairwise error probability (PEP) for the block-fading OFDM channel model. We use the derived PEP to get an upper bound on the frame error probability for the coded cooperative OFDM system. This bound is then utilized in the study of the diversity and coding gains achievable through cooperative coding in OFDM systems for various inter-user channel qualities. We consider the design of cooperative convolutional codes based on the principle of overlays and provide simulation results for different cooperation scenarios. We observe significant gains over conventional non-cooperative OFDM systems. Finally, based on some simple approximations, we provide guidelines for the choice of partners in coded cooperative OFDM systems.     

Bit Interleaved Coded Multiple Beamforming

In this paper, we investigate the performance of bit-interleaved coded multiple beamforming (BICMB). We provide interleaver design criteria such that BICMB achieves full spatial multiplexing of min( N, M) and full spatial diversity of NM with N transmit and M receive antennas over quasi-static Rayleigh flat fading channels. If the channel is frequency selective, then BICMB is combined with orthogonal frequency division multiplexing (OFDM) (BICMB-OFDM) in order to combat ISI caused by the frequency-selective channels. BICMB-OFDM achieves full spatial multiplexing of min(N, M), while maintaining full spatial and frequency diversity of NML for an NtimesM system over L-tap frequency-selective channels when an appropriate convolutional code is used. Both systems analyzed in this paper assume perfect channel state information both at the transmitter and the receiver. Simulation results show that, when the perfect channel state information assumption is satisfied, BICMB and BICMB-OFDM provide substantial performance or complexity gains when compared to other spatial multiplexing and diversity systems.     

一种结合频率扩展编码的空时码MIMO OFDM系统性能及实现

该文利用MIMOOFDM系统中宽带信道的频率选择性衰落对不同窄带子载波上传输信号的不同影响,提出了一种结合频率扩展编码(FSC)的空时码设计．仿真结果表明,与其它的MIMOOFDM系统比较,该方法不仅可以有效地利用选择性信道内在的频率分集及保证系统频谱利用率,而且结构简单,容易实现．     

Performance comparison of FFH and MCFH spread-spectrum systems withoptimum diversity combining in frequency-selective Rayleigh fadingchannels

The performance of frequency-hopping spread-spectrum systems employing noncoherent reception and transmission diversity is analyzed for frequency-selective Rayleigh fading channels. Two different types of transmission diversity systems, a fast frequency-hopping (FFH) system and a multicarrier frequency-hopping (MCFH) system, are investigated. In order to combine received signals from transmit diversity channels, the optimum diversity combining rule based on the maximum-likelihood criterion is developed. Probability of error equations are derived, and utilized to evaluate the performance of the two systems. The MCFH systems are found to outperform FFH systems when the channel delay spread is severe, while FFH systems are superior to MCFH systems when a channel varies rapidly. Furthermore, it is found that performance enhancement due to an increase of diversity order is more significant for MCFH systems than for FFH systems in frequency-selective fading channels. The effect of frequency-selective fading is also investigated in determining optimum frequency deviations of binary frequency-shift keying signals     

A union bound on the error probability of binary codes over block-fading channels

Block-fading is a popular channel model that approximates the behavior of different wireless communication systems. In this paper, a union bound on the error probability of binary-coded systems over block-fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. The distribution of error bits over the fading blocks is computed. For a specific distribution pattern, the pairwise error probability is derived. Block-fading channels modeled as Rician and Nakagami distributions are studied. We consider coherent receivers with perfect and imperfect channel side information (SI) as well as noncoherent receivers employing square-law combining. Throughout the paper, imperfect SI is obtained using pilot-aided estimation. A lower bound on the performance of iterative receivers that perform joint decoding and channel estimation is obtained assuming the receiver knows the correct data and uses them as pilots. From this, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Furthermore, the optimal energy allocation for pilot signals is found for different channel memory lengths.     

Diversity analysis for frequency-selective MIMO-OFDM systems with general spatial and temporal correlation model

In this paper, the effect of a general spatial and temporal fading correlation structure on the performance of coded multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems is studied. The analysis handles an arbitrary joint transmit-receive spatial correlation model, including the non-Kronecker model. An upper bound on the maximum achievable diversity order for frequency-selective MIMO-OFDM systems with general temporal and spatial correlation is derived. Furthermore, a space-time-frequency code design that can achieve the upper bound for any arbitrarily correlated channel scenario is provided. The general framework of the analysis includes space-frequency (SF)-coded systems as a special case. For the SF-coded MIMO-OFDM system, it is shown that any SF code designed to achieve full diversity in the independent fading channel can achieve full diversity in an arbitrary spatially correlated channel. The derived analytical results are consistent with those in the existing literature for special correlation structures. Extensive simulation results are provided to confirm the theoretical analysis.     

Gallager Bounds for Noncoherent Decoders in Fading Channels

Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound.      

Coded modulation for noncoherent reception with application to OFDM

Power- and bandwidth-efficient differentially encoded transmission over slowly time-varying fading channels with noncoherent reception and without channel state information is considered. For high bandwidth efficiencies, combined phase and amplitude modulation is used. For increased power efficiency, channel coding and multiple-symbol differential detection are applied, i.e., interleaving and detection are based on blocks of N>2 consecutive symbols. The presented concepts are directly applicable to transmission over flat fading channels. However, concentrating on the situation of frequency-selective channels, we consider their application to multicarrier transmission using orthogonal frequency-division multiplexing (OFDM). When coding across subcarriers, OFDM transforms the actual frequency-selective channel into a slowly time-varying frequency-nonselective fading channel. This paper presents a design for multilevel coding schemes to approach theoretical limits for power- and bandwidth-efficient noncoherent transmission over the equivalent fading channel. It is shown that bit-interleaved coded modulation, which relies on Gray labeling, is competitive only in the case of conventional differential detection with N=2. The theoretic considerations are well approved by simulation results, where turbo codes are applied as component codes     

Performance bounds for space-time trellis codes

We derive the union bound for space-time trellis codes over quasi-static fading channels. We first observe that the standard approach for evaluating the union bound yields very loose, in fact divergent, bounds over the quasi-static fading channel. We then develop a method for obtaining a tight bound on the error probability. We derive the union bound by performing expurgation of the standard union bound. In addition, we limit the conditional union bound before averaging over the fading process. We demonstrate that this approach provides a tight bound on the error probability of space-time codes. The bounds can be used for the case when the fading coefficients among different transmit/receive antenna pairs are correlated as well. We present several examples of the bounds to illustrate their usefulness.     

On the performance of error control coding with diversity formobile channels

Upper bounds on the bit error probability are applied to evaluate the error performance of coded systems over non-interleaved and partially interleaved Rician fading mobile channels. The correlation between successive received symbols is exploited to bound the error performance. The bound allows useful evaluation of coding gains on realistic communication systems without going into lengthy computer simulations. By further defining the maximum energy degradation factors, compact upper bounds are expressed in a similar way as on the fully interleaved or memoryless channels. The maximum energy degradation factors are computed for a wide variety of mobile channel conditions. These factors give an interesting evaluation of the fading conditions and may be used to design coded communication systems on mobile channels. Furthermore, independent space or frequency diversity may be taken into account in these bounds and it is shown that the energy degradation due to correlation is independent of this added independent diversity     

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)     

Union Bounds on the Bit Error Probability of Coded MRC in Nakagami-m Fading

In this letter new union bounds are derived for coded maximal ratio combining (MRC) over Nakagami-m fading channels. The union bounds are expressed in the product form, which makes them easily, evaluated using the transfer function of the code. The bounds are general to any diversity order and coding scheme with a known transfer function. Results show that the new bounds are tight to simulation results for wide ranges of diversity orders and Nakagami parameters     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Achieving Full Frequency and Space Diversity in Wireless Systems via BICM, OFDM, STBC, and Viterbi Decoding

Orthogonal frequency-division multiplexing (OFDM) is known as an efficient technique to combat frequency-selective channels. In this paper, we show that the combination of bit-interleaved coded modulation (BICM) and OFDM achieves the full frequency diversity offered by a frequency-selective channel with any kind of power delay profile (PDP), conditioned on the minimum Hamming distance dfree of the convolutional code. This system has a simple Viterbi decoder with a modified metric. We then show that by combining such a system with space-time block coding (STBC), one can achieve the full space and frequency diversity of a frequency-selective channel with N transmit and M receive antennas. BICM-STBC-OFDM achieves the maximum diversity order of NML over L-tap frequency-selective channels regardless of the PDP of the channel. This latter system also has a simple Viterbi decoder with a properly modified metric. We verify our analytical results via simulations, including channels employed in the IEEE 802.11 standards     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

OFDM or single-carrier block transmissions?

We compare two block transmission systems over frequency-selective fading channels: orthogonal frequency-division multiplexing (OFDM) versus single-carrier modulated blocks with zero padding (ZP). We first compare their peak-to-average power ratio (PAR) and the corresponding power amplifier backoff for phase-shift keying or quadrature amplitude modulation. Then, we study the effects of carrier frequency offset on their performance and throughput. We further compare the performance and complexity of uncoded and coded transmissions over random dispersive channels, including Rayleigh fading channels, as well as practical HIPERLAN/2 indoor and outdoor channels. We establish that unlike OFDM, uncoded block transmissions with ZP enjoy maximum diversity and coding gains within the class of linearly precoded block transmissions. Analysis and computer simulations confirm the considerable edge of ZP-only in terms of PAR, robustness to carrier frequency offset, and uncoded performance, at the price of slightly increased complexity. In the coded case, ZP is preferable when the code rate is high (e.g., 3/4), while coded OFDM is to be preferred in terms of both performance and complexity when the code rate is low (e.g., 1/2) and the error-correcting capability is enhanced. As ZP block transmissions can approximate serial single-carrier systems as well, the scope of the present comparison is broader.     

在频率选择性信道中的差分空频编码

本文提出了频率选择性衰变信道中采用了差分空频编码的正交频分复用(OFDM)传输方法。根据信道长度,我们将每个天线OFDM帧中的输入数据分组,同一组中各天线上的数据编码组成为一个对角信号星座,沿频域方向独立的对每组信号实施差分编码。通过分析成对错误概率,我们证明了这种码潜在能提供的分集是发射天线数,接收天线数和信道长度的乘积,比差分空时码具有更大分集增益,因而具有更好的性能,这一分析结果也为我们的仿真实验证实了。