Pilot Symbol Assisted Modulation Research Articles

Channel estimation in bit-interleaved coded modulation with iterative decoding

This study improves the fading channel estimation in bit-interleaved coded modulation systems with iterative decoding (BICM-ID) and signal space diversity (SSD) by embedding a training sequence. Existing training schemes work well at high signal-to-noise ratio (SNR) or slowly time-varying channels whereas the applications of BICM-ID are beneficial at low SNR and fast time-varying fading channels. Motivated by the power/bandwidth efficiency of the SSD technique and the fact that superimposed training outperforms pilot symbol-assisted modulation (PSAM) training over relatively fast time-varying channels, a new superimposed training sequence is explored. The proposed training sequence inserts pilot bits into the coded bits prior constellation mapping and signal rotation. This becomes a superimposed training sequence in the rotated symbols and helps the estimator to track fast variation of the channel gains. A soft iterative channel estimator is developed to work with the superimposed training sequence. The performance of the proposed scheme, namely SSD-pilot, is shown to be superior to PSAM scheme. To gauge the performance improvement achieved with the proposed channel estimation, an analytical bound on the asymptotic bit error probability for BICM-ID using SSD over correlated fading channels is provided. The Cramer-Rao bound on the mean-square error of the channel estimator is also derived to evaluate the performance of the iterative channel estimator.

A low-complexity noncoherent iterative space-time demodulator

Turbo coded unitary space-time modulation (USTM) can provide large coding gain as compared to uncoded USTM. Because the noncoherent space-time maximum a posteriori demodulator is very complicated, in this letter, we propose a new low-complexity noncoherent iterative space-time demodulator for the USTM constructed from pilot symbol-assisted modulation. The proposed demodulator utilizes both hard and soft decisions from the turbo decoder to simplify the computational task as well as produce reliable soft outputs. Several examples demonstrate that this demodulator has both low complexity and good error performance.

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbol-assisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in medium-rate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.

On the Power Allocation and System Capacity of OFDM Systems Using Superimposed Training Schemes

Channel estimation in multipath environments is typically performed using the pilot-symbol-assisted modulation (PSAM) scheme. However, the traditional PSAM scheme requires the use of dedicated pilot subcarriers and therefore leads to a reduction in the bandwidth utilization. Accordingly, this paper investigates a channel-estimation approach for orthogonal frequency-division multiplexing (OFDM) systems using a superimposed training (ST) scheme, in which the pilot symbols are superimposed onto the data streams prior to transmission. By using equally spaced pilot symbols of equal power and assuming that the number of pilots is larger than the channel order, it is shown that the channel-estimation performance is independent of the number of pilots used. The optimal ratio of the pilot symbol power to the total transmission power is analyzed to maximize the lower bound of the channel capacity. Overall, the current results show that the ST-based channel estimation schemes have a slightly poorer performance than the PSAM scheme but yield higher system capacity.

Optimized rate-adaptive PSAM for MIMO MRC systems with transmit and receive CSI imperfections

The impact of imperfect channel state information (CSI) on the performance of transmit-beamforming (TB) over multiple-input multiple-output (MIMO) Rayleigh fading channels when using constant-power rate-adaptive pilot symbol assisted modulation (PSAM) is investigated. Specifically, imperfect CSI is accounted for with respect to both estimation and prediction errors, thereby allowing to quantify the performance degradation of the adaptive PSAM-based TB system due to both channel estimation and prediction errors. Such errors entail a mismatch between the optimal transmit/receive beamforming weights and the transmission rate implied by the true CSI on the one hand, and the actual values of these quantities as determined based on the estimated and predicted CSI, on the other hand. The compound effect of both estimation and prediction errors on the overall system performance is assessed in terms of the achievable average spectral efficiency, average bit error probability and outage probability, for which approximate closed-form expressions are derived for arbitrary numbers of transmit and receive antennas. Furthermore, the latter metrics are used to optimize the PSAM parameters, namely the power allocation between data and pilot symbols as well as the pilot spacing in order to maximize the achievable average spectral efficiency while adhering to a fixed target bit error probability.

Pilot design for OFDM with null edge subcarriers

Pilot symbol assisted modulation (PSAM) orthogonal frequency division multiplexing (OFDM) has proven to be a popular technique for high-speed communication through multipath fading channels. In this paper we examine PSAM pilot design optimization in OFDM systems that employ edge null subcarriers for spectral shaping. Specifically, we show that the commonly used even pilot spacing design is suboptimal in terms of symbol estimate mean squared error (MSE) performance when a sufficient number of null subcarriers are present. We pursue a parametric design of the pilot spacings and use convex optimization techniques in order to find a pilot design that results in near-optimal symbol estimate MSE performance. Finally, we present several example PSAM OFDM pilot designs including one example based on the IEEE 802.16 standard to demonstrate performance improvements over the conventional even-spacing pilot design when null edge subcarriers are present.

Parameter Optimization for Amplify-and-Forward Relaying Systems with Pilot Symbol Assisted Modulation Scheme

Cooperative diversity is a promising technology for future wireless networks. In this paper, we consider a cooperative communication system operating in an amplify-and-forward (AF) mode with a pilot symbol as-sisted modulation (PSAM) scheme. It is assumed that a linear minimum mean square estimator (LMMSE) is used for the channel estimation at the receiver. A simple and easy-to-evaluate asymptotical upper bound (AUB) of the symbol-error-rate (SER) is derived for uncoded AF cooperative communication systems with quadrature amplitude modulation (QAM) constellations. Based on the AUB, we propose a criterion for the parameter optimization in the PSAM scheme. We discuss how the pilot spacing and the length of the Wiener ?lter should be chosen under the constraint of a tradeoff between pilot overhead, estimation accuracy, and receiver complexity. We also formulate an power allocation problem for the considered system. It is shown that the power allocation problem can optimally be solved by means of a gradient search method. Numerical simulations are presented to verify the correctness of the theoretical results and to demonstrate the benefits of the parameter optimization.

Pilot symbol assisted coding

Proposed is a novel technique, hereby referred to as pilot symbol assisted coding (PSAC), where a predetermined fraction of binary pilot symbols is interspersed with the channel-coded bits at the channel coding stage, instead of multiplexing the pilots with the data symbols at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). It is demonstrated that the PSAC succeeds in gleaning more benefits from the pilot overhead investment, than just simply the capability of channel estimation such as in the PSAM technique.

Power and Rate Adaptation Based on Imperfect Channel Estimation over MIMO Fading Channels

We derive the optimum power and rate adaptation for maximizing the spectral efficiency of Multilevel Quadrature Amplitude Modulation (MQAM) over Multiple-Input Multiple-Output (MIMO) fading channels based on imperfect channel estimation. We use Pilot Symbol Assisted Modulation (PSAM)-based Minimum Mean Square Error (MMSE) channel estimator, and show that the optimum power adaptation on each sub-channel is a generalization of water-filling. We also show that the conventional water-filling (with bias) strategy for power adaptation is a suboptimum solution of the general optimization problem and it tends to the optimal solution as the correlation coefficients between eigenvalues of the true channel matrix and its estimate tend to one.

Optimum Pilot Symbol Assisted Modulation

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.

Effect of Channel Estimation Errors on $M$-QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings

Orthogonal Space–Time Block Code Over Time-Varying Flat-Fading Channels: Channel Estimation, Detection, and Performance Analysis

This paper studies the channel estimation, detection and performance analysis of mobile wireless communication systems employing space-time block codes (STBC), where the channels exhibit flat Rayleigh fading with a significant amount of Doppler spread. Pilot-symbol-assisted modulation (PSAM) is developed to estimate the channels. The performance of the channel estimation is evaluated. Maximum-likelihood (ML) detection is first formulated. A linear detector, called the symmetric linear (SL) detector, is proposed. An interference cancellation (IC) detector is also developed to improve the performance of the SL detector. We derive the closed-form analytical expressions for the bit-error rate (BER) or symbol-error rate (SER) of pilot-sequence-assisted STBC with binary phase-shift keying (PSK), quaternary PSK, 16-quadrature amplitude modulation (QAM) and 64-QAM, when the SL and IC detectors are used. Some important design issues in the pilot-sequence-assisted STBC systems, including the selection of pilot spacing and interpolator size, are discussed. Simulation results are presented that verify our analytical results. The tradeoffs between the performance and complexity for ML, SL, and IC detection are also discussed

Exact BER for M-QAM with MRC and Imperfect Channel Estimation in Rician Fading Channels

In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) and pilot-symbol assisted modulation (PSAM) in generalized Rician fading channels. By expressing the bit error rate (BER) of MRC diversity M-QAM in terms of the distribution of new decision variables, we derive novel, exact, and easy-to-evaluate BER expressions for diversity M-QAM with channel estimation errors. Our results include versatile system and fading channel parameters (e.g., arbitrary spatial and temporal correlation patterns among the diversity branches), and are valid for arbitrary linear channel estimators and square and rectangular M -QAM with different constellation sizes. In addition, we evaluate the performance of minimum mean-squared error (MMSE)- and sinc-interpolator-based channel estimators with PSAM, and provide some new insights into the performance of M-QAM with PSAM in generalized fading channels

On the effects of interpolator window shape and symbol location on the BER of diversity PSAM 16‐QAM

AbstractWe consider pilot symbol assisted modulation (PSAM) implemented with a sinc interpolator. The sensitivity of the error rate performance to different window functions applied to the sinc interpolator is investigated. The bit error rates (BERs) for diversity M‐ary quadrature amplitude modulation (MQAM) with different window functions applied to the sinc interpolator are compared. The Kaiser window is found superior to the other windows considered. A thorough discussion of the dependency of the BER performance on the symbol location is also given. Copyright © 2007 John Wiley & Sons, Ltd.

Fast Computation of Partial DFT for Comb Spectrum Evaluation

A comb spectrum evaluation problem arises in the channel estimation of pilot symbol-assisted modulation (PSAM) systems and also in the (de)modulation of multichannel communication system based on orthogonal frequency division multiplexing (OFDM). In this letter, we decompose an M-component comb spectrum evaluation with transform length N into 1) a fast Fourier transform evaluation of transform length M of a length M vector, 2) which in turn is obtained from the lengthN input vector (by folding and scaling). This decomposition allows for the application of split-radix and radix-4 algorithms for evaluation of M length transform and efficient computation of the length M vector from the length N input vector, which is classically termed as pruning. When N=2p, the comb spectrum computation requires only N/8+M/3log2 M nontrivial complex multiplications, if N/Mges8. In addition, conditions under which comb spectrum evaluation can be done in O(MlogM) complex multiplies are identified

On the design of sinc interpolator for pilot symbol assisted modulation systems

This paper investigates the design of practical sine interpolation filters in pilot symbol assisted modulation (PSAM) systems. By closely examining the error mechanism in PSAM channel estimation, we show that the error floor phenomenon is caused by the non-ideal characteristic of the interpolation filter. Based on the use of adjustable window functions, we present a set of design guidelines to determine the shape of window functions, the window/filter length and the pilot insertion rate. The design choices essentially reflect the trade-offs between error performance, implementation complexity and transmission rate

Analysis and Optimization of Pilot Symbol-Assisted Rake Receivers for DS-CDMA Systems

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency

A pseudorandom postfix OFDM modulator - semi-blind channel estimation and equalization

This paper details a new orthogonal-frequency-division-multiplexing (OFDM) modulator based on the use of a pseudorandom postfix (PRP)-OFDM and discusses low-complexity equalization and channel estimation/tracking architectures. The main property of this new modulation scheme is the ability to estimate and track the channel variations semi-blindly using order-one statistics of the received signal. Compared with known cyclic prefix OFDM (CP-OFDM) pilot-symbol-assisted modulation (PSAM) schemes, the pilot overhead is avoided: The channel estimation is performed based on the exploitation of pseudorandomly weighted postfix sequences replacing the guard interval contents of CP-OFDM. PRP-OFDM is shown to be of advantage if the target application requires 1) a minimum pilot overhead, 2) low-complexity channel tracking (e.g., high mobility context), and 3) adjustable receiver complexity/performance trade-offs (available due to the similarities of PRP-OFDM to the zero-padded OFDM (ZP-OFDM) modulation scheme) without requiring any feedback loop to the transmitter.

Closed‐form expression for the BER of m‐QAM‐OFDM systems over time‐ and frequency‐selective wireless channels

AbstractThe broadcast DVB‐T system is an m‐QAM‐OFDM communication system that includes pilot‐symbol‐assisted modulation (PSAM) in order to enhance channel estimation at the receiver. This characteristic makes DVB‐T suitable for a mobile reception, over time‐ and frequency‐selective wireless channels. In this work, a closed‐form expression for the BER as a function of the transmission system, channel model and the channel estimation strategy employed at the receiver is derived. In addition, adjacent channel interference due to Doppler effects is also considered. The results are focused on the DVB‐T system under different scenarios. The channel estimation at the receiver has been shown to be very critical, and the impact of channel estimation errors on the BER is analysed in detail. Copyright © 2005 John Wiley & Sons, Ltd.

Peak power reduction for OFDM systems with orthogonal pilot sequences

In this paper, a novel peak-to-average power reduction approach for orthogonal frequency division multiplexing (OFDM) has been addressed. Two-dimensional pilot-symbol assisted modulation (2D-PSAM) is employed in coherent OFDM for channel estimation, and it is based on inserting known symbols spread throughout the 2D time-frequency grid. These pilot symbols are employed to simultaneously perform distortionless peak power reduction with a suboptimum technique named orthogonal pilot sequences (OPS), which reduces additional system complexity and side information compared to optimum pilot values. This proposal attains a further step over other previous works, since this set of sequences allows blind detection at the receiver without prior knowledge of any side information.