Conventional and modified TAS/OSTBC schemes in dual‐hop fixed‐gain amplify‐and‐forward relaying systems with imperfect feedback

Modified transmit antenna selection (TAS)/orthogonal space‐time block coding (OSTBC) (M‐TAS/OSTBC) schemes have been shown to achieve superior error performance together with a reduced‐rate feedback channel in the presence of feedback errors (FEs) when compared with the conventional TAS/OSTBC (C‐TAS/OSTBC) schemes. This paper focuses on the bringing of fixed‐gain amplify‐and‐forward (FGAF) relaying schemes that employ M‐TAS/OSTBC schemes at both hops that provides reduced feedback‐rate and robust error performance in the presence of erroneous‐feedback channels. The exact expressions of the outage and error probabilities for both dual‐hop FGAF relaying schemes in Nakagami‐m fading channels have been derived and validated via Monte Carlo simulations. Additionally, with the help of high signal‐to‐noise ratio (SNR) (i.e., asymptotic) approaches and some analytical approximations, the asymptotic diversity order analysis has been carried out. Besides, by providing a simulation‐based examination on the inclusion of power allocation within the modified scheme, the additional advantages on the performance have been exhibited. The extensive investigation and comparisons to the conventional schemes have shown that M‐TAS/OSTBC schemes employed at each transmission link provide full diversity order and considerable error performance as the C‐TAS/OSTBC scheme in ideal feedback cases and also achieve more robust error performance in the presence of FEs. Thus, by using M‐TAS/OSTBC schemes, the overall performances of the dual‐hop FGAF relaying schemes have been enhanced, which would result in reductions on the average SNR requirements to achieve a specified error rate constraint. Copyright © 2015 John Wiley & Sons, Ltd.     

Signature optimization for CDMA with limited feedback

We study the performance of joint signature-receiver optimization for direct-sequence code-division multiple access (DS-CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a random vector quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent and identically distributed (i.i.d.) elements, we evaluate the received signal-to-interference plus noise ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear minimum mean-squared error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver, one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.     

Adaptive precoding and power allocation in distributed antenna systems with limited feedback

This paper introduces the limited feedback precoding into the distributed antenna system and proposes to adapt the predetermined orthogonal space time block codes to the available channel state information at the transmitter. The optimal representation of precoding information, namely the precoder, with least bits therefore becomes the key problem. Inspired by the characteristics of the distributed antenna system, we focus our work on the precoder construction, adaptable in response to the large and small scale fading, such that the symbol error probability is significantly reduced over that of a fixed, non‐adaptive, independent and identically distributed precoder codebook design. Furthermore, a suboptimal power‐loading strategy is presented by minimizing the derived tight upper bound on the average pairwise error probability of the precoded orthogonal space time block codes, which approaches the optimal performance asymptotically without additional channel knowledge other than the available feedback information. We prove that the proposed precoded orthogonal space time transmission scheme can achieve full diversity order. In particular, the robustness of our proposed transmission scheme to channel estimation error and feedback delay is respectively investigated in some detail, and numerical results show that it obviously improves the link reliability and obtains substantial gains even with few bits of feedback in comparison with conventional antenna selection scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive Transmit Diversity with Quadrant Phase Constraining Feedback

An adaptive transmit diversity scheme with quadrant phase constraining feedback is proposed in this paper. With simple linear operations at both transmitter and receiver, the proposed algorithm can achieve better system performances with only 2M−2 bits of feedback information for systems with M transmit antennas. Theoretical performance bounds of the proposed transmit diversity scheme are derived. Simulation examples and theoretical analyses show that the proposed transmit diversity scheme outperforms not only the conventional open-loop transmit diversity techniques, but also some closed-loop transmit diversity techniques with more information transmitted in the feedback channel.     

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.     

Limited feedback-based block diagonalization for the MIMO broadcast channel

Block diagonalization is a linear preceding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multi-user interference is experienced at any of the receivers. This low-complexity scheme operates only a few dB away from capacity but requires very accurate channel knowledge at the transmitter. We consider a limited feedback system where each receiver knows its channel perfectly, but the transmitter is only provided with a finite number of channel feedback bits from each receiver. Using a random quantization argument, we quantify the throughput loss due to imperfect channel knowledge as a function of the feedback level. The quality of channel knowledge must improve proportional to the SNR in order to prevent interference-limitations, and we show that scaling the number of feedback bits linearly with the system SNR is sufficient to maintain a bounded rate loss. Finally, we compare our quantization strategy to an analog feedback scheme and show the superiority of quantized feedback.     

Adaptive Channel‐Matched Extended Alamouti Space‐Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space‐time block code, various quasi‐orthogonal space‐time block codes (QSTBC) for multi‐input multi‐output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2ⁿ (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum‐likelihood receiver or low‐complexity zero‐forcing receiver.     

Optimal antenna subset selection and blind detection approach applied to orthogonal space-time block coding

An approach combining optimal antenna subset selection with blind detection scheme for Orthogonal Space-Time Block Coding （OSTBC） is proposed in this paper. The optimal antenna subset selection is taken into account at transmitter and/or receiver sides, which chooses the optimal antennas to increase the diversity order of OSTBC and improve further its performance. In order to enhance the robustness of the detection used in the conventional OSTBC scheme, a blind detection scheme based on Independent Component Analysis （ICA） is exploited which can directly extract transmitted signals without channel estimation. Performance analysis shows that the proposed approach can achieve the full diversity and the flexibility of system design by using the antenna selection and the ICA based blind detection schemes.     

Design of reduced complexity feedback precoding for MIMO‐OFDM

Beamforming technique is applied to significantly increase the performance of a MIMO system, if the channel information (CI) of the communication system is available at the transmitter. For the transmitter to obtain the entire CI, however, a considerable reverse‐link bandwidth is required. To save the bandwidth, a limited‐rate closed‐loop system, therefore, uses a predetermined codebook which is derived from the CI. The codebook consists of a finite number of precoders out of which the index of the best one is transmitted from the receiver to the transmitter using only a few bits saving substantial bandwidth. However, the amount of bits that need to be fed back can still be significantly large for MIMO‐OFDM systems when the precoding matrix index (PMI) for each subcarrier should be transmitted. Such per‐subcarrier precoding scheme has high feedback overhead and also incurs huge computational cost to determine the best PMI for each subcarrier. We, therefore, propose a per‐band precoding scheme that precodes a band (group) of subcarriers by only one precoder. More importantly, we develop, for the proposed per‐band scheme, reduced‐complexity precoding selection methods that lead to the design of efficient receivers. The effectiveness of the proposed scheme is investigated through computer simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

BER minimization for dual‐polarized wireless systems with polarization‐domain rotation

We consider the problem of bit error rate (BER) degradation because of the power gain imbalance between horizontal (H)‐polarization and vertical (V)‐polarization components in an orthogonal dual‐polarization transmission system. To alleviate the aforementioned BER degradation problem, we propose a non‐orthogonal polarization‐domain rotation scheme where the axes of H‐polarization and V‐polarization components are rotated with different angles at the transmitter and de‐rotated at the receiver. In addition, in order to assess the effectiveness of the polarization‐domain rotation scheme, we derive the closed‐form BER expression under a practical dual‐polarized channel model, which is represented by cross‐polarization ratio and co‐polarization ratio (CPR). We also derive the approximated BER expressions for the two asymptotic values of CPR: balanced CPR and infinite CPR. With the derived BER expressions, we find the optimal rotation angles that jointly minimize the BER. According to the numerical results, it is shown that about 3dB E_b/N₀ gain is obtained at the BER of 10^?4 and the CPR of 10dB by the polarization‐domain rotation scheme with optimal rotation angles compared with the conventional orthogonal dual‐polarization transmission. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal diagonal precoder for multiantenna communication systems

In this paper, we examine a multiantenna single-user wireless communication system fitted with a QR-based successive cancellation receiver (QR receiver). Initially, our consideration is confined to uncoded binary phase shift keying (BPSK) signals transmitted through independent and identically distributed (IID) Rayleigh fading channels and to the design of an optimum precoder for the transmitter. For minimum feeding back of the channel state information (CSI) to the transmitter from the receiver, we stipulate the precoder to be in the form of a power loading square diagonal matrix. We proceed to develop the theory for the design of this diagonal matrix based on the minimization of the lower bound of the average bit error rate (BER) of transmission. The design obtained provides substantially lower error rates than most of other existing schemes under the same environment. The corresponding gain in signal-to-noise ratio (SNR) can be several decibels. To further improve the performance, we extend the design to include an optimal detection order of the received bits using an iterative approach. This iterative process proves to have fast convergence and results in a design providing significant SNR gain. We also propose a subchannel dropping scheme for cases in which SNR is low, and when the minimum BER precoder is equipped with this scheme, its average performance can be substantially superior to the Vertical Bell Laboratories Layered Space-Time (V-BLAST) detection. We extend our design of the optimum precoder to quadrature amplitude modulation (QAM) modulation scheme and similar performance gain has been observed.     

A New Verifiable Multi-secret Sharing Scheme Based on Bilinear Maps

In a (t, n)-threshold multi-secret sharing scheme, several secrets are shared among n participants in such a way that any t (or more) of them can reconstruct the secrets while a group of (t − 1) can not obtain any information. Therefore, when such schemes are used to distribute sensitive information over a network, fault tolerance property is achieved since even if n − t of the nodes go out of function, the remaining t nodes suffice to recover the information. In 2009, Wang et al. proposed a verifiable (t, n)-threshold multi-secret sharing scheme (WTS) based on elliptic curves in which the secrets can change periodically [Wireless Pers. Commun., Springer-Verlage, doi:. In this paper, we propose a verifiable (t, n)-threshold multi-secret sharing scheme based on bilinear maps. Our scheme does not require a secure channel and participants can verify the shares pooled in the reconstruction phase. Our proposed scheme is multi-use such that in order to change the secrets, it is sufficient to renew some public information. Furthermore, the proposed scheme is flexible to the threshold value. Therefore, our proposed scheme has all the merits of (WTS), however, we achieve two major improvements. First when the secrets are to be changed, we require to publish fewer public values. This reduction can be very important in certain applications such as steganographic use of secret sharing schemes. The second is that (WTS) is designed with the assumption that the number of secrets (m) is equal to the threshold t so that the case m > t is handled by repeating the scheme é \fracmt ù{\left\lceil \frac{m}{t}\right\rceil} times. However, in designing the scheme we do not assume any restrictions on the number of secrets.     

Two signaling schemes for improving the error performance of frequency division duplex (FDD) transmission systems using transmitter antenna diversity

We propose two signaling schemes that exploit the availability of multiple (N) antennas at the transmitter to provide diversity benefit to the receiver. This is typical of cellular radio systems where a mobile is equipped with only one antenna while the base station is equipped with multiple antennas. We further assume that the mobile-to-base and base-to-mobile channel variations are statistically independent and that the base station has no knowledge of the base-to-mobile channel characteristics. In the first scheme, a channel code of lengthN and minimum Hamming distanced _minN is used to encode a group ofK information bits. Channel code symbolc _i is transmitted with thei th antenna. At the receiver, a maximum likelihood decoder for the channel code provides a diversity ofd _min as long as each transmitted code symbol is subjected to independent fading. This can be achieved by spacing the transmit antennas several wavelengths apart. The second scheme introduces deliberate resolvable multipath distortion by transmitting the data-bearing signal with antenna 1, andN–1 delayed versions of it with antennas 2 throughN. The delays are unique to each antenna and are chosen to be multiples of the symbol interval. At the receiver, a maximum likelihood sequence estimator resolves the multipath in an optimal manner to realize a diversity benefit ofN. Both schemes can suppress co-channel interference. We provide code constructions and simulation results for scheme 1 to demonstrate its merit. We derive the receiver structure and provide a bound on the error probability for scheme 2 which we show to be tight, by means of simulations, for the nontrivial and perhaps the most interesting caseN=2 antennas. The second scheme is backward-compatible with two of the proposed digital cellular system standards, viz., GSM for Europe and IS-54 for North America.     

Outage Minimization With Limited Feedback for the Fading Relay Channel

Outage Minimization With Limited Feedback for the Fading Relay Channel In this paper, we consider practical methods to approach the theoretical performance limits in the fading relay channel under different assumptions of transmitter channel knowledge. Specifically, we consider two degrees of transmitter channel knowledge: 1) perfect feedback is available and power control is employed; and 2) no channel-state knowledge is available at the transmitters, and only spatial power allocation is possible. First, when perfect feedback is available, the optimal power-control policy determines the ultimate limits of performance for constant-rate transmission in the slow fading environment. However, in practice, perfect channel knowledge is not possible at the transmitters due to the finite capacity of the feedback links. We find practical methods to approach this performance limit through the use of power control with finite-rate feedback. The finite-rate feedback results are shown for the low-complexity, full-diversity amplify-and-forward (AF) protocol. Interestingly, we see that only a few feedback bits are needed to achieve most of the gains of the optimal perfect feedback power-control algorithm. Second, we consider the performance limit when the transmitter has no channel-state knowledge, and derive the optimal spatial power allocation between the source and relay for a given sum power constraint for the AF protocol. In the foremost practical cases of interest, equal power allocation between the source and relay is shown to be nearly optimal. Our work suggests that there is minimal power savings from using spatial power allocation at the transmitters. To obtain large performance improvements over constant power transmission, it is imperative to have feedback for each realization of the channel state to allow for temporal power control.     

On the randomization of transmitter power levels to increase throughput in multiple access radio systems

To enhance the throughput of a slotted random access protocol in a radio communication system, we describe the use of a scheme in which multiple power levels are used at the transmitters. We first consider a situation in which n transmitters are simultaneously trying to send a packet to a central receiving station using a time‐slotted access protocol, like slotted ALOHA. Each of these transmitters randomly chooses one of m discrete power levels during each attempt to send a packet. One of the simultaneously sent packets can often be successfully received due to the power capture effect. We consider two types of capture models: (1) one in which the transmitter with the largest received power captures the channel, and (2) one in which the transmitter captures the channel only if its signal‐to‐interference ratio is above some threshold when received at the central station. In this paper, we determine the optimal transmit probabilities for the power levels as well as the optimal values of the power levels themselves, when their range is constrained and for cases both with and without Rayleigh fading. After determining the precise optimal power levels and probabilities for maximizing the capture probabilities (i.e., for a given n), we propose a less complex, but nearly optimal, approximate approach based on using logarithmically equi‐spaced levels. After demonstrating the closeness of our suboptimal results to the optimal results, we apply our approach to the problem of optimizing the throughput of the slotted ALOHA protocol for a case in which the input traffic is generated according to a Poisson process. Several numerical examples are presented along with a demonstration of how the optimal choice of power levels and probabilities can enhance throughput relative to previous ad hoc methodologies. This revised version was published online in July 2006 with corrections to the Cover Date.     

SLNR-Based Transmit Beamforming for MIMO Wiretap Channel

In this paper, a novel closed-form transmit beamforming scheme is proposed for multiple-input multiple-output (MIMO) wiretap channel. The proposed method follows the idea of maximizing signal-to-leakage-plus-noise ratio and does not need additional power allocation. An efficient approach is further developed to implement the generalized eigenvalue decomposition required by our method when n _r  < n _t (n _t , n _r and n _e denote the antenna numbers at the transmitter, the intended receiver and the eavesdropper, respectively), which has lower complexity than the existing approaches. Moreover, we identify some shortcomings of the generalized singular value decomposition (GSVD) based beamforming method, a common beamforming scheme for MIMO wiretap channel. Finally, simulation results show that the proposed method significantly outperforms GSVD-based method when n _e  < n _t and has almost the same performance as GSVD-based method when n _e  ≥ n _t .     

High-Speed Array Multipliers Based on On-the-Fly Conversion

A new on-the-fly conversion algorithm is proposed, and high-speed array multipliers with the on-the-fly conversion are presented. The new on-the-fly conversion logic is used to speed up carry-propagate addition at the last stage of multiplication, and provides constant delay independent of the number of input bits. In this paper, the multiplication architecture and the on-the-fly conversion algorithm are presented and discussed in detail. The proposed architecture has multiplication time of (n + 1)t_FA, where n is the number of input bits and t_FA is the delay of a full adder. According to our comparative performance evaluation, the proposed architecture has shorter delay and requires less area than the conventional array multiplier with on-the-fly conversion.     

基于有限反馈的MIMO系统鲁棒性均匀信道分解

 在MIMO系统中,当假设发送端和接收端已知完美信道状态信息的情况下,均匀信道分解(UCD)被证明在误码率性能上是最优的且是容量无损的.然而在实际系统中,接收端或发送端获得的信道信息通常存在着一定的估计误差.本文提出一种基于有限反馈的鲁棒性均匀信道分解方案,在设计方案中充分考虑了信道估计误差的影响,并利用香农率失真定理和广义Lloyd矢量量化算法(GLA)得到了信道估计误差的近似值,使得本文提出的方案有很好的实用性.仿真结果表明与传统均匀信道分解方案相比,本文提出的鲁棒性均匀信道分解方案有效地降低了系统的误码平层,提高了系统容量.     

Inferring sequences produced by a linear congruential generator missing low-order bits

An efficient algorithm is given for inferring sequences produced by linear congruential pseudorandom number generators when some of the low-order bits of the numbers produced are unavailable. These generators have the formX _n=aX _n–1+b (modm). We assume that the constantsa,b, andm are unknown, and thatt=O(log logm) of the low-order bits are not used.This work was supported by an Educational Opportunity Fellowship and by DARPA Grant No. N00039-82-C-0235.     

Transmitter optimization and performance gain for multiple-input single-output systems with finite-rate direction feedback

Consider finite-rate channel-direction feedback in a system with multiple transmit but single receive antennas. We investigate how the transmitter should be optimized for symbol error rate with finite-rate feedback, and how the symbol error rate and outage probability improve as a function of the number of feedback bits. It is found that when the number of feedback directions is equal to or larger than the number of transmit antennas, transmit beamforming is optimal. Otherwise, the antennas should be divided into two groups, where antenna selection is used in the first group to choose the strongest channel, and equal power allocation is used in the second group. At high signal to noise ratio (SNR), the optimal power allocation between these two antenna groups is proportional to the number of antennas in each group. Based on high SNR analysis, we quantify the power gain of each feedback bit. It is shown that the incremental gain increases initially and diminishes when the number of feedback bits surpasses the logarithm (base 2) of the number of transmit antennas.