Analysis of diversity schemes employing antenna selection in the presence of channel estimation errors and feedback delay

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐m fading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates of M‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of Carrier Frequency Offset and Channel Estimation Errors on the Performance of MIMO-OFDM Systems in Spatially Correlated Channels

As an effective technique for combating multipath fading and for high-bit-rate transmission over wireless channels, orthogonal frequency division multiplexing (OFDM) is extensively used in high-rate wireless communication systems, such as, the wireless local area network (WLAN) and the digital television terrestrial broadcasting (DTTB) systems, to support high performance bandwidth-efficient multimedia services. Multiple antennas and transmit or receive diversity, multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), can be used to improve error performance and capacity of wireless systems. In this paper, we consider the effects of carrier frequency offset and channel estimation errors on the performance of MIMO-OFDM systems in spatially correlated channels. Theoretical calculations and computer simulations are done to analyze the performance degradation of MIMO-OFDM systems in spatially correlated channels due to carrier frequency offset and channel estimation errors, and the theoretical and simulated results match well.     

Analysis of transmit antenna selection/orthogonal space‐time block coding with receive selection and combining in the presence of feedback errors

Examining the effect of imperfect transmit antenna selection (TAS) caused by the feedback link errors on the performance of hybrid TAS/orthogonal space‐time block coding (OSTBC) with single receive antenna selection (i.e., joint transmit and receive antenna selection (JTRAS)/OSTBC) and TAS/OSTBC (with receive maximal‐ratio combining‐like combining structure) over slow and frequency‐flat Nakagami‐m fading channels is the main objective of this paper. Under ideal channel estimation and delay‐free feedback assumptions, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio are derived by defining a unified system model concerning both JTRAS/OSTBC and TAS/OSTBC schemes. Exact analytical expressions for outage probability (OP) and bit/symbol error rates of M‐ary modulations are presented in order to provide a detailed examination on the OP and error performances of the unified system that experiences feedback errors. Also, the asymptotic diversity order analysis, which shows that the diversity order of the investigated schemes is equal to the diversity order provided by OSTBC transmission itself, is included in the paper. Moreover, we have validated the theoretical results via Monte Carlo simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Exploiting Multipath Diversity in Multiple Antenna OFDM Systems With Spatially Correlated Channels

Multiple antennas are useful in orthogonal frequency division multiplexing (OFDM) systems for providing transmit and receive diversity to overcome fading. Typically, these designs require considerable separation between the antennas. Spatial correlation is introduced when antennas are not well separated, and it often leads to performance degradation in a flat fading environment. However, in frequency selective fading channels with rich multipath diversity, OFDM receivers can overcome this performance degradation due to antenna correlation. This is due to transformation of a highly spatially correlated channel impulse response to a less spatially correlated channel frequency response inherently by an OFDM system in the presence of rich multipath diversity. We illustrate this for a simple receive diversity OFDM system and hence introduce the concept of space sampling at the receiver where antennas are placed relatively close to each other. The minimum separation required between the antennas under such circumstances is derived analytically, and it is shown that even with a separation of only$0.44lambda$, the required spatial correlation in the channel frequency response becomes sufficiently low. Simulated performance results with such spacing for various multiple antenna OFDM systems corroborate the analytical results.     

Reduced-Complexity Decision-Directed Channel Estimation in OFDM Systems with Transmit Diversity

Decision-directed channel estimation (DDCE) in orthogonal frequency-division multiplexing (OFDM) systems with transmit diversity suffers from high computation complexity in the simultaneous estimation of channel responses between the receiver and all the transmitters. Exploiting the correlation of the channel frequency response at adjacent subcarriers can help decouple the inter-antenna interference (IAI). This makes it possible to independently estimate each channel response, resulting in the reduction of computational complexity. However, existing IAI decoupling algorithms employ the least squares (LS) method for channel estimation from the IAI decoupled data. This approach is suboptimal because of the unequal variance of noise components in the decoupled data. Residual IAI, which arises from unequal channel gains at two adjacent subcarriers because of the channel frequency selectivity, occurs in the decoupled data, causing biases in the LS channel estimation. To improve the performance of reduced-complexity DDCE in transmit diversity OFDM systems, the proposed algorithm applies the best linear unbiased estimation method to independently estimate each channel response from IAI decoupled data. This approach is optimal regarding the unequal noise variances of the decoupled data. This study also exploits temporal channel correlation to remove residual IAI using the latest channel information of DDCE. Simulation results show that the proposed method can improve the performance of the reduced complexity algorithm, making it close to that of the joint estimation algorithm with significantly higher complexity.     

Comb type pilot aided channel estimation in OFDM systems with transmit diversity

Transmit diversity can be applied to OFDM systems by adopting space time code. Since the received signal is the overlapped signals transmitted from different transmit antennas, channel estimation is a rather challenging task for space time coded OFDM (ST-OFDM) systems. Pilot structure can help the receiver to effectively separate the overlapped signals and perform accurate channel estimation. In this paper, we propose three different channel estimation algorithms based on specially designed comb type pilots inserted in frequency domain. One of our proposed algorithms is performed in frequency domain and the other two are performed in time domain. Such comb type pilot based algorithms can provide higher bandwidth efficiency than common significant-tap-catching algorithm using training block pilots. Numerical analyzes and computational simulation show that our proposed estimation schemes have the same good performance while the time domain methods have relatively simple structure.     

A Robust Joint Frequency Offset Estimation for the OFDM System Using Cyclic Delay Diversity

Cyclic delay diversity (CDD) is a low-complexity transmit diversity technique for orthogonal frequency division multiplexing (OFDM), which transforms a multiple-input channel into an equivalent single-input channel with a large delay spread. Consequently, high frequency selectivity makes channel and frequency estimation a challenging task. This paper proposes an improved joint estimation of carrier frequency offset and sampling frequency offset for the OFDM system using CDD technique. By finding the amount of a transmit-antenna specific delay which reduces the variance of the frequency estimation scheme, these parameters improve the robustness of the joint frequency estimation scheme against the frequency selectivity of the channel. Computer simulation shows that the joint frequency-offset estimation scheme with properly designed cyclic delay parameters performs robustly, with the performance better than the conventional scheme.     

Data-efficient blind OFDM channel estimation using receiver diversity

We investigate non data-aided channel estimation for cyclically prefixed orthogonal frequency division multiplexing (OFDM) systems. By exploiting channel diversity using only two receive antennas, a blind deterministic algorithm is proposed. Identifiability conditions are derived that guarantee the perfect channel retrieval in the absence of noise. In the presence of noise, the proposed method has the desired property of being data efficient-only a single OFDM block is needed to achieve good estimation performance for a wide range of SNR values. The algorithm is also robust to input symbols as it does not have any restriction on the input symbols with regard to their constellation or their statistical properties. In addition, this diversity-based algorithm is computationally efficient, and its performance compares favorably to most existing blind algorithms.     

A Computationally Efficient QR-Successive Interference Cancellation Scheme for Simplified Receiver Implementation in SFBC-OFDM Systems

In this paper, we propose a computationally efficient square-root and division free recursive QR (SDRQR) decomposition based successive interference cancellation (SIC) receiver for space-frequency block coded orthogonal frequency division multiplexing (SFBC-OFDM) transmit diversity schemes. The performance of the proposed SDRQR-SIC receiver is semi- analytically evaluated taking into account the effects of channel estimation errors and error propagation during SIC. In addition, performance and complexity comparisons are drawn with previously proposed approaches. These comparisons show an excellent performance-complexity tradeoff achieved by SDRQR-SIC over the previous solutions under various channel conditions.     

Space-frequency-time turbo coded modulation

A new bandwidth and power efficient signaling scheme is proposed that achieves high data rates over wideband radio channels exploiting the bandwidth efficient OFDM modulation, multiple transmit and receive antennas and large frequency selectivity offered in typical low mobility indoor environments. Owing to its maximum transmit diversity gain and large coding gain, space-frequency-time turbo coded modulation strongly outperforms other space-frequency-time coding schemes proposed in literature. A simple way of combining space-frequency-time coding with OFDM delay diversity for cost effective exploitation of more than two transmit antennas is also proposed in this paper     

A Bayesian Multiuser Detection Algorithm for MIMO-ODFM Systems Affected by Multipath Fading, Carrier Frequency Offset, and Phase Noise

We derive a novel Bayesian algorithm for multiuser detection in the uplink of a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system employing stacked space-time block codes, such as the stacked Alamouti code with two transmit antennas, and a stacked quasi-orthogonal code with four transmit antennas. The proposed technique accomplishes joint estimation of the carrier frequency offset, phase noise, channel impulse response and data of each active user. Its derivation relies on the specific structure of the transmitted signal and on efficient Markov chain Monte Carlo (MCMC) methods. Simulation results evidence the robustness of the proposed algorithm in both uncoded and coded systems.     

A novel CDD-OFDM scheme with pilot-aided channel estimation

Cyclic delay diversity (CDD) is a low-complexity standard-conformable transmit diversity scheme for coded orthogonal frequency division multiplexing (OFDM) systems. However, it makes channel estimation more challenging due to the increased frequency-selectivity of the equivalent single-input single-ouput channel. In this paper, we propose a novel CDD-OFDM scheme with pilot-aided channel estimation for any number of transmit antennas. By alternating and optimizing the cyclic delay parameter over adjacent OFDM symbols, we design a simple yet efficient channel estimation scheme and illustrate its excellent performance for the DVB-T application.     

An Enhanced Embedded-Pilot Channel Estimation Architecture for MIMO MC-CDMA Systems

In this work an enhanced semi-blind channel estimator is presented for multicarrier CDMA systems with multiple transmit and receive antennas. The novel scheme is based on embedded pilots that are characterized as virtual users and their number is determined in a dynamic fashion according to the propagation channel conditions. The superimposed code-multiplexed pilots are used initially for channel estimation before the despreading operation, thus achieving per subcarrier estimation using the known unique multi-layer pattern of the virtual users. Afterwards, the estimation is enhanced by using the despread pilots. Furthermore, an iterative scheme is incorporated in channel estimation process minimizing the effect of multiuser interference and operates either in interference cancellation, or in virtual user mode. The proposed architecture is evaluated for spatial diversity systems (space- frequency block coded) with two transmit and up to four receive antennas operating in realistic propagation channels for various modulation and coding schemes. The results demonstrate a significant performance improvement especially as the channel is dominated by its time variant characteristics. The dynamic assignment of spreading codes in the payload and the pilots offers to the system realistic flexibility and adaptivity in demanding channels achieving concurrently maximization of the real overall system throughput, while maintaining low overhead and complexity burden.     

Single-block differential transmit scheme for broadband wireless MIMO-OFDM systems

In frequency-selective multiple-input multiple-output (MIMO) channel, differential space-time-frequency (DSTF) modulations are known as practical alternatives that are capable of exploiting the available spatial and frequency diversities without the requirement of multichannel estimation at the receiver. However, the encoding nature of the DSTF schemes that expand several OFDM symbol periods makes the DSTF schemes susceptible to fast-changing channel conditions. In this paper, we propose a differential scheme for MIMO-OFDM systems that is able to differentially encode signal within two OFDM symbol periods, and the proposed scheme transmits the differentially encoded signal within one OFDM block. The scheme not only reduces encoding and decoding delay but also relaxes the restriction on channel assumption. The successful differential decoding of the proposed scheme depends on the assumption that the fading channels keep constant over two OFDM symbol periods rather than multiple of them as required in the existing DSTF schemes. We also provide pairwise error probability analysis and quantify the performance criteria in terms of diversity and coding advantages. The design criteria reveal that the existing diagonal cyclic codes can be applied to achieve full diversity. Performance simulations under various channel conditions show that our proposed scheme yields superior performance to previously proposed differential schemes.     

Multiuser OFDM with adaptive subcarrier, bit, and power allocation

Multiuser orthogonal frequency division multiplexing (OFDM) with adaptive multiuser subcarrier allocation and adaptive modulation is considered. Assuming knowledge of the instantaneous channel gains for all users, we propose a multiuser OFDM subcarrier, bit, and power allocation algorithm to minimize the total transmit power. This is done by assigning each user a set of subcarriers and by determining the number of bits and the transmit power level for each subcarrier. We obtain the performance of our proposed algorithm in a multiuser frequency selective fading environment for various time delay spread values and various numbers of users. The results show that our proposed algorithm outperforms multiuser OFDM systems with static time-division multiple access (TDMA) or frequency-division multiple access (FDMA) techniques which employ fixed and predetermined time-slot or subcarrier allocation schemes. We have also quantified the improvement in terms of the overall required transmit power, the bit-error rate (BER), or the area of coverage for a given outage probability     

Blind Channel Identification for Cyclic-Prefixed MIMO-OFDM Systems with Virtual Carriers

This paper applies the repetition index scheme(RIS)to the channel identification of cyclic prefixed(CP)multiple-input multiple-output orthogonal frequency division multiplexing(MIMO-OFDM)systems with virtual carriers(VCs)in the environment of the number of receive antennas being no less than that of transmit antennas.The VCs will cause a rank deficiency problem in computing the subspace information.With the subcarrier mapping matrix,the received signal is simplified to remove the rank deficiency.We use the RIS scheme to generate many times of equivalent symbols so the channel identification can converge with few received OFDM blocks.The RIS scheme will convert the white noise into non-white noise.With the Cholesky factorization,a noise whitening technique is developed to turn the non-white noise back to white noise.We further analyze the necessary conditions of identifiability of channel estimation.Simulations are performed to show the superiority of the proposed method.     

CD3-OFDM: a novel demodulation scheme for fixed and mobilereceivers

This paper describes a novel channel estimation scheme identified as coded decision directed demodulation (CD3) for coherent demodulation of orthogonal frequency division multiplex (OFDM) signals making use of any constellation format [e.g., quaternary phase shift keying (QPSK), 16-quadrature amplitude modulation (QAM), 64-QAM]. The structure of the CD3-OFDM demodulator is described, based on a new channel estimation loop exploiting the error correction capability of a forward error correction (FEC) decoder and frequency and time domain filtering to mitigate the effects of noise and residual errors. In contrast to the conventional coherent OFDM demodulation schemes, CD3-OFDM does not require the transmission of a comb of pilot tones for channel estimation and equalization, therefore yielding a significant improvement in spectrum efficiency (typically between 5-15%). The performance of the system with QPSK modulation is analyzed by computer simulations, on additive white Gaussian noise (AWGN) and frequency selective channels, under static and mobile reception conditions. For convolutional coding rate 1/2, the results indicate that CD3-OFDM allows one to achieve a very fast adaptation to the channel characteristics in a mobile environment (maximum tolerable Doppler shift of about 80 Hz for an OFDM symbol duration of 1 ms, as differential demodulation) and an E_b /N₀ performance similar to coherent demodulation (e.g., E_b/N₀=4.3 dB at bit-error rate (BER)=2·10 ^-4 on the AWGN channel). Therefore, CD3-OFDM can be suitable for digital sound and television broadcasting services over selective radio channels, addressed to fixed and vehicular receivers     

Robust power allocation algorithms for MIMO OFDM systems with imperfect CSI

This paper presents a Bayesian approach to the design of transmit prefiltering matrices in closed-loop schemes robust to channel estimation errors. The algorithms are derived for a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. Two different optimization criteria are analyzed: the minimization of the mean square error and the minimization of the bit error rate. In both cases, the transmitter design is based on the singular value decomposition (SVD) of the conditional mean of the channel response, given the channel estimate. The performance of the proposed algorithms is analyzed, and their relationship with existing algorithms is indicated. As with other previously proposed solutions, the minimum bit error rate algorithm converges to the open-loop transmission scheme for very poor CSI estimates.     

Double differential space-time block coding for time-selectivefading channels

Most existing space-time coding schemes assume time-invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver. Other single differential space-time block coding schemes forego channel estimation but are less effective in rapidly fading environments. Based on a diagonal unitary matrix group, a novel double differential space-time block coding approach is derived in this paper for time-selective fading channels. Without estimating the channels at the receiver, information symbols are recovered with antenna diversity gains regardless of frequency offsets. The resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas. Approximately optimal space-time codes are also designed to minimize bit error rate. System performance is evaluated both analytically and with simulations     

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