Space-Time Trellis Codes Over Rapid Rayleigh Fading Channels With Channel Estimation---Part I: Receiver Design and Performance Analysis

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.     

Pilot symbol-assisted detection of CPM schemes operating in fastfading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes     

Pilot-symbol aided coherent M-ary PSK in frequency-selective fastRayleigh fading channels

Pilot-symbol aided coherent M-ary PSK modems in digital cellular mobile radio systems are analyzed theoretically. The error-floors caused by the Doppler spread in a fast fading channel are removed in both flat and selective fading channels. However, the error-floors caused by the delay spread are lower-bounded by those that exist in the ideal coherent detection. The systems are modeled as frequency-selective fast Rayleigh fading channels, corrupted by co-channel interference (CCI) and additive white Gaussian noise (AWGN). In the proposed scheme, pilot symbols are inserted periodically to monitor the channel characteristics. The fading processes experienced by the pilot symbols are used to estimate those suffered by the data symbols using interpolation or filtering. The estimated fade characteristics are used to compensate the random phase variation caused by the Doppler spread, so that the signals can be demodulated coherently. The theoretical performances of the fade compensated coherent modems are evaluated. The results show that the fade compensated coherent demodulation with the least redundancy achieves the same performance as the ideal differential detection in a fading channel. The performance approaches that of the ideal coherent demodulation as more redundancy is allowed. The pilot-symbol-insertion (PSI) scheme is also applicable to M-ary QAM modems and Rician channels. The residual frequency offset can also be compensated by the PSI technique     

Mobile speed estimation based on average fade slope duration

Based on the zero crossing rate of the slope (first derivative) of the underlying fading process, a mobile speed-estimation scheme, constructed by counting the average number of sampling steps in a positive-going (and/or negative-going) fade envelope slope, is proposed. The proposed speed-estimation approach requires neither knowledge of the average fade power nor a variable temporal observation window. The computational complexity and the required memory storage are negligibly small. Simulation results show that the proposed speed estimator yields good estimation accuracy, with relatively small estimation error.     

Performance of cross-layer design for orthogonal space-time block coded MIMO systems with imperfect CSI in Ricean fading channels

A cross-layer design (CLD) scheme for orthogonal space-time block coded MIMO systems with imperfect channel state information is presented by combining adaptive modulation and automatic repeat request, and the corresponding system performance is investigated over Ricean fading channel. The fading gain value is partitioned into a number of regions by which the modulation is adapted in terms of the region the fading gain falls in. The fading gain switching thresholds subject to a target packet error rate (PER) constraint are derived. According to these results, and using the generalized Marcum Q-function, we derive the theoretical formulae of average PER and spectrum efficiency (SE) of the system with CLD for both perfect and imperfect estimation in detail. As a result, closed-form expressions for average PER and SE are obtained. These expressions include some existing expressions in Rayleigh channel as special cases. With these expressions, the system performance in Ricean channel with perfect and imperfect estimation information can be evaluated effectively. Computer simulation for average PER and SE show that the theoretical analysis and simulation are consistent. The results show that the system performance will be effectively improved as Ricean factor increases, but it will be degraded as estimation errors increases.     

Space-time codes for high data rate wireless communication:performance criteria in the presence of channel estimation errors,mobility, and multiple paths

Space-time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas. Specific codes have been constructed using design criteria derived for quasi-static flat Rayleigh or Rician fading, where channel state information is available at the receiver. It is evident that the practicality of space-time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information. It is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the Doppler spread. This paper presents a theoretical study of these issues beginning with the effect of channel estimation error. Here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy, it is proved that in the absence of ideal channel state information the design criteria for space-time codes is still valid. The analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space-time codes provided that the number of transmit antennas is small. We also derive the maximum-likelihood detection metric in the presence of channel estimation errors. Next, the effect of multiple paths on the performance of space-time codes is studied for a slowly changing Rayleigh channel. It is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space-time codes. Similar results hold for rapid fading channels with or without multiple paths. The conclusion is that the diversity order promised by space-time coding is achieved under a variety of mobility conditions and environmental effects     

Modeling End-to-End Wireless Lossy Channels: A Finite-State Markov Approach

In this paper, we present a model for wireless losses in packet transmission data networks. The model provides information about the wireless channel status that can be used in congestion control schemes. A Finite State Markov Channel (FSMC) approach is implemented to model the wireless slow fading for different modulation schemes. The arrival process statistics of the packet traces determine the channel state transition probabilities, where the statistics of both error-free and erroneous bursts are captured. Later, we establish SNR partitioning scheme that uses the transition probabilities as a basis for the state margins. The crossover probability associated with each state is calculated accordingly. We also propose an end-to-end approach to loss discrimination based on the channel state estimation at the receiver. Finally, we present a scheme for finding the channel optimal number of states as a function of the SNR. The presented FSMC approach does not restrict the state transitions to the adjacent states, nor does impose constant state duration as compared to some literature studies. We validate our model by experimental packet traces. Our simulation results show the feasibility of building a fading channel model for better wireless-loss awareness.     

Channel capacity and error exponents of variable rate adaptivechannel coding for Rayleigh fading channels

We have evaluated the information theoretical performance of variable rate adaptive channel coding for Rayleigh fading channels. The channel states are detected at the receiver and fed back to the transmitter by means of a noiseless feedback link. Based on the channel state informations, the transmitter can adjust the channel coding scheme accordingly. Coherent channel and arbitrary channel symbols with a fixed average transmitted power constraint are assumed. The channel capacity and the error exponent are evaluated and the optimal rate control rules are found for Rayleigh fading channels with feedback of channel states. It is shown that the variable rate scheme can only increase the channel error exponent. The effects of additional practical constraints and finite feedback delays are also considered. Finally, we compare the performance of the variable rate adaptive channel coding in high bandwidth-expansion systems (CDMA) and high bandwidth-efficiency systems (TDMA)     

Space-time coding ambiguities in joint adaptive channel estimation and detection

This paper studies the error propagation effect that is caused by certain ambiguities in joint data detection-channel tracking algorithms for transmission diversity schemes. Here, we use a space-time (ST) receiver based on the maximum a posteriori (MAP) method that takes into account the channel estimation error assuming the unknown channel to have a given complex multivariate Gaussian probability density function (pdf) (i.e., a Ricean channel). The decision criterion that is expressed in quadratic form represents either a linear detector or a noncoherent-nonlinear detector in extreme cases. Then, the channel pdf for the next iteration is updated by estimates of the second-order statistics of the channel coefficients, and a very simple decision-directed adaptive algorithm is derived for adaptive channel estimation. The adaptive algorithm can efficiently track a fast Rayleigh fading channel and, as a result, achieves robust performance. However, the occurrence of two types of ambiguities initiated in deep fades result in error propagation. Some remedies called space-time ambiguity remedies (STARs) are proposed to prevent error propagation. A new time-varying space-time coding (TVST) scheme is suggested as a bandwidth-efficient method to combat the permutation ambiguity impairment. This coding scheme, in conjunction with a differential detector, can resolve the ambiguity problem.     

Diversity combining with imperfect channel estimation

The optimal diversity-combining technique is investigated for a multipath Rayleigh fading channel with imperfect channel state information at the receiver. Applying minimum mean-square error channel estimation, the channel state can be decomposed into the channel estimator spanned by channel observation, and the estimation error orthogonal to channel observation. The optimal combining weight is obtained from the first principle of maximum a posteriori detection, taking into consideration the imperfect channel estimation. The bit-error performance using the optimal diversity combining is derived and compared with that of the suboptimal application of maximal ratio combining. Numerical results are presented for specific channel models and estimation methods to illustrate the combined effect of channel estimation and detection on bit-error rate performance.     

Generalized Quadratic Receivers for Unitary Space–Time Modulation Over Rayleigh Fading Channels

We propose the generalized quadratic receivers (GQRs) for unitary space-time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2-4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space-time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR.     

Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation

In this paper, a general analytical framework is developed for calculating the symbol error rate of two-dimensional (2-D) signaling in Ricean fading with imperfect channel estimation. We show that in the presence of channel estimation errors, the symbol error rate of arbitrary 2-D signaling in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. This new analysis is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. System parameters related to specific channel estimation schemes are optimized and the effect of Doppler frequency shift in the channel line-of-sight component on the error performance is investigated using our analysis.     

Generalized receiver selection combining schemes for alamouti MIMO systems with MPSK

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time sum-of-magnitudes (GSTSoM) selection diversity are proposed. The first provides the same performance as conventional GSC, and the second provides slightly poorer performance, but neither requires channel state information and both have much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.     

Random coding error exponents for flat fading channels withrealistic channel estimation

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied     

时变信道中自适应VR-HARQ研究

为了更好地解决时变信道中可靠性与吞吐率这一对矛盾,本文提出一种基于线性预测的自适应冗余可变混合ARQ(VR-HARQ)方案.在该方案中,由于时变信道的慢衰落特性,时变信道被等效为有限状态的Markov过程,每个Markov状态对应信道的不同信噪比,同时,文章详细地描述了信道吞吐率与误码率之间的数学关系,推导了每个Markov状态的最佳编码方案,然后系统采用自适应线性预测算法,根据当前个时段的信道状态,估计下一个时段信道的信噪比以及其所对应的Markov状态,最后根据吞吐率最大原则选择合适的纠错编码方案.仿真结果表明:自适应线性预测VR-HARQ方案的性能明显优于传统VR-HARQ方案.     

Iterative vector channel estimation/MAP/PIC for CDMA systems in time-selective correlated multipath fading channels

Recently, Gao et al. proposed the expectation-maximization (EM) vector channel estimation for single-user direct-sequence code-division multiple-access (DS-CDMA) systems to estimate the correlated fading channel coefficients of the paths of a user. They also used one D-lag decision-feedback maximum a posteriori (MAP) detector to detect the information bits. A straightforward extension (noniterative) to multiuser synchronous CDMA cases, i.e., adding the parallel interference cancellation (PIC) multiuser detector into their scheme, results in poor performance. Therefore, we propose an iterative scheme which combines vector channel estimation, decision-feedback MAP detection, and PIC. The partial PIC is applied in the sequence hypothesis stage of MAP in each iteration before the final MAP decision. The proposed scheme has twice the decision delay of the previous scheme for single-user cases. The performance of the proposed system in the time-selective, correlated multipath fading channel environment is investigated. Simulation results show that the proposed scheme significantly outperforms the noniterative scheme. Simulation results also show that the proposed scheme performs better than its scalar channel-estimation version.     

Channel estimation based on distributed compressed sensing in amplify-and-forward relay networks

In orthogonal frequency-division multiplexing(OFDM)amplify-and-forward(AF)relay networks,in order to exploit diversity gains over frequency-selective fading channels,the receiver needs to acquire the knowledge of channel state information(CSI).In this article,based on the recent methodology of distributed compressed sensing(DCS),a novel channel estimation scheme is proposed.The joint sparsity model 2(JSM-2)in DCS theory and simultaneous orthogonal matching pursuit(SOMP)are both introduced to improve the estimation performance and increase the spectral efficiency.Simulation results show that compared with current compressed sensing(CS)methods,the estimation error of our scheme is reduced dramatically in high SNR region while the pilot number is still kept small.     

WCDMA下行链路一种加权的信道估计方法

本文针对第三代移动通信标准WCDMA(FDD)下行链路的结构，提出了一种新的利用公共导频信道和专用数据信道中的导频符号进行加权的信道估计方法。仿真表明本方案有效地提高了信道参数估计的准确度，使Rake接收机的性能比传统的只利用公共导频信道进行信道估计的方案有了一定的改善，特别是在公共导频信道受到明显衰落时。     

On the Fading-Paper Achievable Region of the Fading MIMO Broadcast Channel

We consider transmission over the ergodic fading multiple-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent non-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the "dirty paper" channel. We focus on a similar "fading paper" model. The evaluation of the fading paper capacity is difficult to obtain. We confine ourselves to the linear-assignment capacity, which we define, and use convex analysis methods to prove that its maximizing distribution is Gaussian. We compare our fading-paper transmission to an application of dirty paper coding that ignores the partial state information and assumes the channel is fixed at the average fade. We show that a gain is easily achieved by appropriately exploiting the information. We also consider a cooperative upper bound on the sum-rate capacity as suggested by Sato. We present a numeric example that indicates that our scheme is capable of realizing much of this upper bound.     

Interleaved TC 8DPSK/OFDM with decision-directed channel estimationon frequency-selective Rayleigh fading channels

Trellis-coded modulation (TCM) is a power and bandwidth efficient signaling scheme. In this letter, we propose interleaved trellis-coded (TC) 8DPSK/OFDM combined with decision-directed (DD) channel estimation on frequency-selective Rayleigh fading channels. We use a subchannel block interleaver in an OFDM symbol interval to randomize the burst errors due to the correlated dispersive fading channel. We also use DD channel estimation using the previous detected 8DPSK symbols in the temporal direction to improve the performance at fast fading. Computer simulations show that the proposed technique has good performance at fast fading