Multi‐carrier platform for wireless communications. Part 2: OFDM and MC‐CDMA systems with high‐performance,high‐throughput via innovations in spreading

Multi‐carrier technologies in general, and OFDM and MC‐CDMA in particular, are an integral part of the wireless landscape. In this second part of a two‐part survey, the authors present an innovative set of spreading codes known as CI codes, and demonstrate how these significantly increase performance and capacity in OFDM and MC‐CDMA systems, all the while eliminating PAPR concerns. Regarding OFDM: the spreading of each symbol over all N carriers using CI spreading codes (replacing the current one symbol per carrier strategy) are presented. CI codes are ideally suited for spreading OFDM since, when compared to traditional OFDM, CI‐based OFDM systems achieve the performance of coded OFDM (COFDM) while maintaining the throughput of uncoded OFDM, and, at the same time, eliminate PAPR concerns. When applied to MC‐CDMA, CI codes provide a simple means of supporting 2N users on N carriers while maintaining the performance of an N‐user Hadamard Walsh code MC‐CDMA system, i.e., CI codes double MC‐CDMA network capacity without loss in performance. The CI codes used in OFDM and MC‐CDMA systems are directly related to the CI pulse (chip) shapes used to enhance TDMA and DS‐CDMA (see part 1): hence, the CI approach provides a common hardware platform for today's multi‐carrier/multiple‐access technologies, enabling software radio applications. Copyright © 2002 John Wiley & Sons, Ltd.     

Improvement and Analysis of Carrier-Interferometry Orthogonal Frequency Division Multiplexing System

1IntroductionOrthogonal Frequency Division Multiplexing(OFDM) isknown to be with high spectrumefficiency and effectivein coping with such wireless channel i mpairments asmultipath fading and Inter-Symbol Interference(ISI)[1]. Moreover ,OFDMsystems have become prac-tical toi mplement using Fast Fourier Transform(FFT)techniques[2]thanks to advances in digital signal pro-cessing. Up to the present , OFDMhas been employedin several digital transmission systems , such as AD-SL[3], HIP…     

High-performance MC-CDMA via carrier interferometry codes

This paper introduces the principles of interferometry to multicarrier code division multiple access (MC-CDMA). Specifically, we propose the use of MC-CDMA with novel carrier interferometry (CI) complex spreading codes. The CI/MC-CDMA method, applied to mobile wireless communication systems, offers enhanced performance and flexibility relative to MC-CDMA with conventional spreading codes. Specifically, assuming a frequency selective Rayleigh-fading channel, CI/MC-CDMAs performance matches that of orthogonal MC-CDMA using Hadamard-Walsh codes up to the MC-CDMA N user limit; and, CI/MC-CDMA provides the added flexibility of going beyond N users, adding up to N-1 additional users with pseudo orthogonal positioning. When compared to MC-CDMA schemes capable of supporting greater than N users, CI/MC-CDMAs performance exceeds that of MC-CDMA. Additionally, this new system is analyzed in the presence of phase jitters and frequency offsets and is shown to be robust to both cases     

Performance Analysis of COFDM for Broadband Transmission on a Fading Multipath Channel

This paper gives a unified analysis of the effects of multipath dispersion and Doppler spreading due to fast fading in OFDM systems, deriving simple closed-form expressions for intersymbol and interchannel interference in the most important cases. It shows also why sine wave carriers are in general the optimum bearers for the sub-channels. The expressions for interference are used to estimate the BER performance of coded OFDM, showing that the use of forward error correction (FEC) coding and a guard period are both essential for optimum performance. As an example it is shown that a 64 sub- channel OFDM system can achieve a data rate of 6.4 Mbit/s on a typical urban mobile radio channel.     

GF(2p)LDPC编码的相位调制OFDM系统在瑞利衰落信道的性能

OFDM是一项能有效对抗高速无线通信中多径衰落的关键技术，为了进一步提高OFDM系统的误码性能，许多信道编码技术已被应用于OFDM系统中，二元域LDPC码以其近香农限的误码性能和较低的译码复杂度成为研究的热点。在AWGN信道下，多元域LDPC码比等效码长的二元域LDPC码有更好的纠错性能。本文提出了一种将多元域LDPC码经过MPSK调制后用于OFDM系统的新方法。仿真结果表明，在多径衰落信道下，通过合理选择多元LDPC码域的阶数和调制的方法，多元域LDPC编码的高阶调制OFDM系统比等效码长的二元域LDPC编码OFDM系统具有更好的性能，并且由于采用了多元域LDPC的快速BP译码，译码复杂度只是稍有增加。     

PAPR Reduction in OFDM Systems with Large Number of Sub-Carriers by Carrier Interferometry Approaches

High Peak-to-Average Power Ratio(PAPR)is one of the major drawbacks of Orthogonal Frequency DivisionMultiplexing(OFDM)systems.This paper presents the structures of the particular bit sequences leading to the maximumPAPR(PAPR_(max))in Carrier-Interferometry OFDM(CI/OFDM)and Pseudo Orthogonal Carrier-Interferometry OFDM(PO-CI/OFDM)systems for Binary Phase Shift Keying(BPSK)modulation.Furthermore,the simulation and analysisof PAPR_(max) and PAPR cumulative distribution in CI/OFDM and PO-CI/OFDM systems with 2048 sub-carriers are pre-sented in this paper.The results show that the PAPR of OFDM system with large number of sub-carriers reduced evidentlyvia CI approaches.     

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.     

ZP-CI/OFDM: A Power Efficient Wireless Transmission Technology

Low power efficiency is a deficiency in traditional Orthogonal Frequency Division Multiplexing (OFDM) systems. To counter this problem, a new wireless transmission technology based on Zero-Padding Carrier Interferometry OFDM (ZP-CI/OFDM) is proposed. In a ZP-CI/OFDM system, transmission symbols are spread to all OFDM subcarriers via carrier interferometry codes. This reduces the Peak-to-Average Power Ratio (PAPR) that traditional OFDM suffers and also exploits frequency diversity gain. By zero-padding at the transmitter, advanced receiver technologies can be adopted for ZP-CI/OFDM so that frequency diversity gain can be further utilized and the power efficiency of the system is improved.     

Performance analysis and design optimization of LDPC-coded MIMO OFDM systems

We consider the performance analysis and design optimization of low-density parity check (LDPC) coded multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems for high data rate wireless transmission. The tools of density evolution with mixture Gaussian approximations are used to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios (SNRs) for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations, which include a different number of antennas, different channel models, and different demodulation schemes; the optimized performance is compared with the corresponding channel capacity. It is shown that along with the optimized irregular LDPC codes, a turbo iterative receiver that consists of a soft maximum a posteriori (MAP) demodulator and a belief-propagation LDPC decoder can perform within 1 dB from the ergodic capacity of the MIMO OFDM systems under consideration. It is also shown that compared with the optimal MAP demodulator-based receivers, the receivers employing a low-complexity linear minimum mean-square-error soft-interference-cancellation (LMMSE-SIC) demodulator have a small performance loss (< 1dB) in spatially uncorrelated MIMO channels but suffer extra performance loss in MIMO channels with spatial correlation. Finally, from the LDPC profiles that already are optimized for ergodic channels, we heuristically construct small block-size irregular LDPC codes for outage MIMO OFDM channels; as shown from simulation results, the irregular LDPC codes constructed here are helpful in expediting the convergence of the iterative receivers.     

ZP-CI/OFDM：一种高功率效率的无线传输技术

针对传统正交频分复用（OFDM）系统的功率效率问题,文章给出一种新的基于添零方式的载波干涉正交频分复用（ZP-CI/OFDM）无线传输技术。ZP-CI/OFDM通过载波干涉码将发射符号扩展到所有OFDM子载波上,在有效消除传统OFDM面临的峰值平均功率比问题的同时,充分利用多载波的频率分集增益;同时,ZP-CI/OFDM通过在发射端添零,采用先进的接收机技术进一步利用频率分集增益,提高系统的功率效率。     

Double-orthogonal coded space-time-frequency spreading CDMA scheme

In this paper, we propose double-orthogonal coded space-time-frequency spreading code-division multiple-access (DOC-STFS-CDMA) scheme for the downlink orthogonal frequency-division multiplexing (OFDM) systems employing multiple transmit and receive antennas. First, we introduce the so-called STFS-CDMA and the corresponding minimum mean-square error (MMSE) detection algorithms for three scenarios with different user information. Then, we propose a new class of spreading codes, called double-orthogonal code (DOC), to match the MMSE detection algorithms for STFS-CDMA system. With the special double orthogonality, DOC can effectively exploit space, time, and frequency diversity to enhance the performance of MMSE detectors, and provide the well-balanced signal-to-interference-and-noise ratio to different users. Finally, the performance gain of the proposed scheme over conventional schemes is shown by computer simulation.     

Performance analysis of channel estimation for LDPC-coded OFDM system in multipath fading channel

In this paper, the channel estimation techniques for Orthogonal Frequency Division Multiplexing （OFDM） systems based on pilot arrangement are studied and we apply Low Density Parity Check （LDPC） codes to the system of IEEE 802.16a with OFDM modulation. First investigated is the influence of channel cstimation schemes on LDPC-code based OFDM system in static and multipath fading channels. According to the different propagation environments in 802.16a system, a dynamic channel estimation scheme is proposed. A good irregular LDPC code is designed with code rate of 1/2 and code length of 1200. Simulation results show that the performance of LDPC coded OFDM system proposed in this paper is better than that of the convolution Turbo coded OFDM system proposed in IEEE standard 802.16a.     

Inter‐carrier Interference Reduction Scheme for SFBC‐OFDM Systems

In this paper, we first analyze carrier‐to‐interference ratio performance of the space–frequency block coded orthogonal frequency‐division multiplexing (SFBC‐OFDM) system in the presence of phase noise (PHN) and residual carrier frequency offset (RCFO). From the analysis, we observe that conventional SFBC‐OFDM systems suffer severely in the presence of PHN and RCFO. Therefore, we propose a new inter‐carrier interference (ICI) self‐cancellation method — namely, ISC — for SFBC‐OFDM systems to reduce the ICI caused by PHN and RCFO. Through the simulation results, we show that the proposed scheme compensates the ICI caused by PHN and RCFO in Alamouti SFBC‐OFDM systems and has a better performance than conventional schemes.     

Reduction of PAPR in coded OFDM using fast Reed-Solomon codes over prime Galois fields

In this work, two new techniques using Reed–Solomon (RS) codes over GF(257) and GF(65,537) are proposed for peak-to-average power ratio (PAPR) reduction in coded orthogonal frequency division multiplexing (OFDM) systems. The lengths of these codes are well-matched to the length of OFDM frames. Over these fields, the block lengths of codes are powers of two and we fully exploit the radix-2 fast Fourier transform algorithms. Multiplications and additions are simple modulus operations. These codes provide desirable randomness with a small perturbation in information symbols that is essential for generation of different statistically independent candidates. Our simulations show that the PAPR reduction ability of RS codes is the same as that of conventional selected mapping (SLM), but contrary to SLM, we can get error correction capability. Also for the second proposed technique, the transmission of side information is not needed. To the best of our knowledge, this is the first work using RS codes for PAPR reduction in single-input single-output systems.     

Reed–Solomon and Simplex Codes for Peak-to-Average Power Ratio Reduction in OFDM

New schemes for peak-to-average power ratio reduction in orthogonal frequency-division multiplexing (OFDM) systems are proposed. Reed–Solomon (RS) and simplex codes are employed to create a number of candidates, from which the best are selected. Thereby, in contrast to existing approaches, the codes are arranged over a number of OFDM frames rather than over the carriers, hence a combination of the principles of multiple signal representation with selection (as done in selected mapping) and the use of channel coding is present. In particular, in multiple-antenna transmission, the proposed schemes do not cause any additional delay, but due to the utilization of the dimension space, additional gains can be achieved. Moreover, the schemes are very flexible; due to the selection step, any criterion of optimality can be taken into account. Besides multiple-antenna transmission, packet transmission is briefly considered, which, moreover, covers the appealing similarities with incremental redundancy check schemes in automatic repeat request (ARQ) applications and with decoding of codes transmitted over the erasure channel. The performance of the schemes is (using some approximations) derived analytically and is covered by numerical results that are in very good agreement with the theory. Significant gains can be achieved with these very flexible and versatile methods.      

LDPC-COFDM系统在多径衰落信道下的性能分析

将正交频分复用(OFDM)技术应用于多径衰落信道下的高速数据传输是一个极富吸引力的方案,包括卷积码、RS码、Turbo码在内的多种纠错编码都曾被应用在OFDM系统中.最近,一种新的编码方案--低密度奇偶校验码(LDPC)引起了人们的注意.LDPC具有低的解码复杂度和逼近香农限的性能.文中仿真分析了LDPC-COFDM(编码正交频分复用)系统的性能,并与Turbo码系统进行了对比,结果表明该系统在多径衰落信道下显示出更为优越的性能.     

Multiple LDPC-Encoder Layered Space-Time-Frequency Architectures for OFDM MIMO Multiplexing

This paper is focused on the study of layered space-time-frequency (LSTF) architectures with channel coding for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) multiplexing systems for high speed wireless communications over a frequency-selective fading channel. In order to achieve the available spatial, temporal and frequency diversities, and also make the system implementation feasible for high speed OFDM MIMO multiplexing, a novel LSTF architecture with multiple channel encoders is proposed with each independently coded layer being threaded in the three-dimensional space-time-frequency transmission resource array. Non-iterative receiver is adopted which consists of list sphere detector and irregular low-density parity-check codes as the constituent codes. Simulation results show that the performance of the proposed multiple-encoder LSTF architecture is very close to that of the conventional single-encoder LSTF where coding is applied across the whole information stream. However, due to the use of multiple parallel encoders/decoders with a shorter codeword length, the proposed LSTF architecture has much lower hardware processing speed and complexity than the conventional LSTF.     

Reed-Solomon Codes Implementing a Coded Single-Carrier with Cyclic Prefix Scheme

This paper presents a novel Reed-Solomon codes based transmission scheme called RS-SC-CP. While RS-SC-CP is essentially a Reed-Solomon (RS) coded single carrier with cyclic prefix (SC-CP) system, a filter bank representation of the RS code is used. This filter bank representation unveils a DFT synthesis bank, just as in a traditional Orthogonal Frequency Division Multiplexing (OFDM) system (allbeit in a finite field). Therefore, RS-SC-CP is topologically equivalent with OFDM. As such, the RS-SC-CP system inherits the advantages of an SC-CP system over a traditional OFDM system like a low Peak to Average Power Ratio (PAPR). But, more importantly, it allows us to use a novel equalization technique that resembles a traditional OFDM equalizer. The equalizer of an RS-SC-CP receiver is split into two stages: the first stage encompasses a partial equalization in the complex field, which ensures that the residual channel response has integer coefficients. It is calculated using a Minimum Mean Square Error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-SC-CP system is further evaluated by simulations showing the performance gain of the RS-SC-CP system compared to a traditional coded OFDM or single carrier with cyclic prefix (SC-CP) scheme.     

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.     

衰落信道下的OFDM系统Lattice编码设计

正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)是应用于高速率无线传输的一项有效技术。标准的OFDM系统的时频格是方形的,因此当信道在格点频率附近存在深度衰落时,未编码的OFDM系统面临着严重的符号恢复问题。为克服上述问题,在符号复用之前,可采用频谱利用率较高的Lattice编码。本文推导了针对衰落信道的编码优化性能指标、相应的编码设计标准,并提供了代数设计方法和实例。数值仿真结果验证了Lattice编码的OFDM系统相对于未编码系统有着更好的抗频率选择性衰落性能。