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We introduce a novel framework for soft-input, soft-output (SISO) equalization in frequency selective multiple-input multiple-output (MIMO) channels based on the well-known belief propagation (BP) algorithm. As in the BP equalizer, we model the multipath channels using factor graphs (FGs) where the transmitted and received signals are represented by the function and variable nodes respectively. The edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively. We incorporate powerful techniques such as groupwise iterative multiuser detection (IMUD), probabilistic data association (PDA) and sphere decoding (SD) in order to reduce the computational complexity of BP equalizer with relatively small degradation in performance. The computational complexity of this new reduced-complexity BP (RCBP) equalizer grows linearly with block size and memory length of the channel. The proposed framework has a flexible structure that allows for parallel as well as serial detection. We will illustrate through simulations that the RCBP equalizer can even handle overloaded scenarios where the channel matrix is rank deficient, and it can achieve excellent performance by applying iterative equalization using the low-density parity check codes (LDPC). Index Terms--MIMO systems, frequency selective channel, equalizers, iterative methods, belief propagation (BP).

Narrowband cellular systems require no bandwidth expansion for spectrum sharing. This attractive property is offset by the need to separate cochannel cells in order to reduce mutual interference. The net effect is a larger cluster size and a smaller system capacity than can be obtained by wideband cellular systems that operate with a cluster size of one. We propose to use a joint maximum-likelihood detection in the uplink of a narrowband system as a method to also allow it to operate with a unit cluster size. Unlike previous research, we jointly perform the detection on the desired and other-cell users. The focus of this multicell multiuser detection is more on cluster-size reduction than additional same-cell users, although the latter is also achieved. We address the problem of computational complexity by including only the strongest interferers in the joint detection. We have shown that, with a small computational cost, a narrowband system can operate with a cluster size of one and, thereby, obtain many times the spatial reuse efficiency of conventional narrowband systems. Index Terms--Bit error rate (BER), cluster size, joint maximum likelihood (JML), multiuser detection (MUD), other-cell user, reuse efficiency, sectorization.

In a general wireless system, cells are loosely defined and user signals appear at multiple antennas with various powers and delays. Despite the enormous performance benefits of system-wide maximum-likelihood multiuser detection (ML MUD), its application to such systems is hampered by the lack of a regular structure. Prior work usually dismisses the possibility on computational grounds as exponential in the total number of users, at least. This paper is the first to address efficient computation of system-wide ML MUD. We present a computational organization that achieves dramatic reduction in complexity through exploitation of the partial overlap of user sets at different antennas. This algorithm, which applies to code-division multiple access or narrowband systems, can be viewed as a spatio-temporal extension of the well-known Viterbi algorithm (VA), and, like the VA, it is derived from dynamic programming principles. Index Terms--Antenna arrays, land mobile radio cellular systems, macrodiversity, maximum-likelihood (ML), multiuser detection (MUD).

In this paper, a simple structure is proposed for accommodating reuse-within-cell in the downlink of a time-division multiple-access system using a transmit antenna array at the base station and joint detection of the cochannel signals at the single-antenna mobile receivers. The transmit array is used solely for system capacity increase; diversity is obtained in the traditional way through standard coding and interleaving. Due to the spatial formatting of the coded symbols prior to transmission, a single multiantenna channel usage spans several trellis transitions--an unconventional situation which is handled through a "merged trellis". Using the merged trellis, a combined joint detector/soft-decision decoder is constructed, and an analytical expression is derived for the coded bit-error rate based on the exact computation of pairwise error probabilities. It is shown that while the system suffers a reduction in diversity order as the number of intracell cochannel users increases, the reduction may be countered by increasing the constraint length of the code. Although this increases complexity, it is shown that multiple users may be supported, all enjoying good performance at iow signal-to-noise ratios, while keeping the complexity in check. Index Terms--Antenna arrays, channel coding, cochannel interference, maximum-likelihood detection, multiuser channels.

Radio frequency (RF) power amplifiers require linearization to reduce the intermodulation (IM) power if the signal does not have a constant envelope. Digital predistortion (PD) is one of the more successful methods. However, implementations usually employ uniform spacing of the PD lookup table entries, since the question of optimum nonuniform spacing has been unresolved. This paper provides the solution: a way to compute the IM for different spacing methods, a comparison of several table spacing schemes, a derivation of the optimum table spacing method, and a demonstration that the IM of optimum spacing is only a few decibels lower than that of equal spacing by amplitude when variations in operating point are considered. Index Terms - Linearization, power amplifiers, radio transceivers.

Errors and erasures decoding has the capability to improve the performance of a Reed-Solomon decoder if each error location is correctly identified, or "flagged", and is considered as an erasure. However, the erasure flagging must be extremely reliable. In this paper, we present a new way to flag erasures, based on the side information provided by pilot signals. We derive a Bayesian method for optimum character erasure flagging, using both the received data signals and the channel estimates provided by pilot signals, and we present a simpler method which flags erasures on a modulation symbol basis. Our simulation results demonstrate that the method results in significant transmit power savings compared to errors-only decoding. Index Terms - Encoding, fading channels, modulation/demodulation, Reed-Solomon codes.

Joint detection based on exploiting differences among the channels employed by several users allows a receiver to distinguish cochannel signals without reliance on spectrum spreading. This paper makes a number of new contributions to the topic: it provides an analytical expression for the union bound on average symbol-error rate for an arbitrary number of users and diversity antennas in a fading environment, for both perfect and imperfect channel state information (CSI), and it compares the performance of joint detection with diversity antennas against classical minimum-mean-square-error (MMSE) combining. The performance is remarkable. With accurate CSI, several users can experience good performance with only a single antenna; moreover, for perfect CSI, only a 2-dB penalty is incurred for each additional user. With several antennas, many more users than the number of antennas may be supported with a slow degradation in performance for each additional user. Furthermore, high accuracy is not required from the channel estimation process. In all cases. the performance of joint detection exceeds that of MMSE combining by orders of magnitude. Index Terms - Antenna arrays, cochannel interference, fading channels, multidimensional signal detection, multiuser channels.

This letter presents a method for exact calculation of the union bound on error performance of trellis-coded modulation (TCM) in fading channels. Previous analyses have approximated the error expression to allow use of the transfer function, or restricted their attention to the most common error events, or both. In contrast, we combine the transfer function, which counts all error events, with exact calculation of event probabilities, and produce an exact expression for the union bound. Although computationally intensive, the technique produces the tightest bound yet published. In addition, it is very general and is applicable to coherent, differential, and pilot-based detection, and to phase-shift keying (PSK)- and quadrature amplitude modulation (QAM)-types of constellations. Index Terms - Error probability bound, fading channel, trellis-coded modulation.

Imperfections in quadrature modulators and de-modulators - gain and phase imbalance and dc offset - have a crippling effect on amplifier linearization circuits, a fact that has previously been noted experimentally. This paper is the first analysis of these effects on an adaptive predistorter. The primary result is an expression that provides an explicit tradeoff among intermodulation power, accuracy of the quadrature modulator and demodulator, and speed of adaptation. Another useful result is a simple and easily measured error figure for quadrature modulators and demodulators. Index Terms - Amplifiers, linearization, transceivers.

Feedforward linearization has advantages in band-width and generality over other linearization methods. However, it is based on the subtraction of nearly equal quantities, so its major parameters must adapt to changes in environmental or operating conditions. This paper is the first published analysis of adaptation behavior in feedforward amplifier linearizers. As such, it presents an analytical framework and several new results, including convergence time and coefficient jitter, a bias effect that leads to extreme accuracy requirements in one coefficient, the effect of delay mismatch, and the mitigating effects of a filter inserted in one adaptation path.

An adaptive direct conversion transmitter is presented, in which adjacent channel power measurements are used to simultaneously compensate for both power amplifier (PA) nonlinearity and quadrature modulator (QM) errors. Three main contributions are given. First, analysis is presented which shows that adjacent channel power is a quadratic function of power amplifier nonlinearity as well as quadrature modulator errors. Quadrature modulator errors are gain imbalance, phase splitter error, and dc offset errors. Second, a new optimization method is given which uses the predicted adjacent channel power surface to obtain fast convergence. Third, simulation and measured results are given for an adaptive system using offset QPSK modulation. The measured results confirm the analysis and show that a 20-dB reduction in adjacent channel power is achievable. In general, the adaptive direct conversion transmitter has applications in any system where power efficiency and spectral efficiency are important, and allows the use of smaller more efficient power amplifiers in a direct conversion architecture.

The current interest in linear modulation and multi-level signals has resulted in an emphasis on DSP implementations to achieve precision signal manipulation. However, most transceivers, and direct conversion designs in particular, rely on analog implementations of the quadrature modulator and demodulator, thereby sacrificing much of the precision gained through DSP. This paper focuses on the three principal impairments of analog quadrature modulators and demodulators: gain imbalance, phase imbalance, and DC offset. The paper contains three main contributions. First is an analysis and quantitative assessment of the losses - primarily a degraded BER and out-of-band power in the transmitted signal - due to imbalances and offsets. The second contribution is an adaptive compensation technique for the quadrature modulator at the transmitter, and the third is a compensation technique for the quadrature demodulator at the receiver. Both compensation methods converge quickly and present only a modest computational load.

Pilot symbol assisted modulation (PSAM) has been shown to give good performance in Rayleigh fading and additive noise. In cellular systems, though, it is cochannel interference, more than noise, that limits the system. This paper is the first analytical investigation of the performance of PSAM in fading, interference, and noise. The investigation yields both an exact solution and an accurate but much more computationally efficient approximation.

Dense constellations such as 16QAM have not seen much use in mobile communication because of their greater peak-to-average power ratio and their seemingly greater sensitivity to noise and channel interference. In this paper, though, we demonstrate that dense constellations can actually improve performance. Using a completely analytical method, we compare three constellations with the same net throughput of 2 bits/symbol: uncoded QPSK, rate 2/3 TCM 8PSK, and rate 1/2 TCM 16QAM. Comparison on the basis of average power puts TCM 16QAM 5 dB ahead of TCM 8PSK. Even comparison on the basis of peak power gives TCM 16QAM a 2.44-dB advantage over TCM 8PSK. QPSK is much poorer than either. Our results are particularly relevant now, while the new cellular and PCN systems are being designed.

An adaptive predistorter for linearizing a power amplifier in a mobile transmitter is studied and the analytical, simulation, and measured results are presented. Unlike most other predistorters found in the literature, this predistorter does not have the problems of loop delay or phase shifting in its feedback path. The feedback is used only periodically to update the predistorter parameters so that it adapts to changes in the amplifier characteristics due to device aging, temperature changes, channel switching, power supply variations, and component drift. An adaptation method for predistorters of the polynomial type is described. Its complexity is significantly lower than that of the previously described methods and its convergence speed, though low, is more than sufficient to track amplifier drift. There are three main contributions. The first is analytical verification that the measurement of out-of-band power is sufficient to drive the adaptation. The second is a complex convolution method for measuring the out-of-band power that requires no additional local oscillator or phase reference. The third is a demonstration of the system performance utilizing a 16-QAM signal in a 25-kHz bandwidth, centered at 850 MHz.

Spectrum shaping codes introduce redundancy and correlation into a transmitted data stream in order to alter the transmitted spectrum without affecting the pulse shape or peak-to-average power ratio. Most are based on algebraic properties, or on a 'running digital sum.' This paper introduces a new and very general approach to spectral shaping, in which we employ the Viterbi Algorithm at the transmitter to minimize the transmitted power in specified bands. The principal advantage is greatly increased flexibility of width, depth and placement of spectral notches. The computational load at the transmitter is greater than that of earlier algorithms, although the receiver is unaffected.

This letter presents a new computational tool for use in general fading channel analyses when the detection scheme can be expressed as a quadratic form in zero-mean complex Gaussian random variables. We develop a simple numerical algorithm which is capable of inverting a characteristic function consisting of both simple and multiple poles. The approach benefits from the inherent symmetry in the residue calculations and uses the we!l-known Vandermonde matrix in order to take advantage of this symmetry. It is numerically stable, eliminates singularities, and circumvents the need for differentiation. Index Terms--Cauchy's residue theorem, inverse Laplace transform (ILT), Vandermonde matrix.

In maximal ratio transmission, the base station adjusts the complex weights of its transmit antennas to compensate for downlink channel gains in order to produce signal reinforcement--diversity--at a desired mobile that may have only a single antenna. To make the method adaptive, the complex weights are obtained from the instantaneous complex gains in the uplink; however, delay and frequency offset between uplink measurements and downlink transmission reduce the correlation between the gains in the two directions. This paper provides an analysis of the effects of gain decorrelation and of the number of antennas, and an assessment of the effect of fading when the method supports multiple users. It demonstrates that large reductions in downlink transmit power are achievable, and it examines simple transmission models to see how well they support the technique. Index Terms--Adaptive arrays, antenna arrays, diversity systems, fading channels, land mobile radio, multi-user channels.

We derive a fully analytical expression for the union bound on symbol-error rate for the joint detection of several cochannel fading signals using a diversity antenna array, putting numerical results previously published on a firm analytical base. We prove that with pilot-based multiuser channel estimation, any number of users can enjoy diversity order equal to the number of antennas, and we quantify the performance penalty relative to single-user binary phase-shift keying as a function of number of users, constellation density, and number of antennas. We also demonstrate the interdependence of all users participating in the detection process. Index Terms--Antenna arrays, cochannel interference, fading channels, multidimensional signal detection, multiuser channels.

Estimation of the channel impulse responses of multiple cochannel users is a key requirement of all multiuser detection and interference cancellation techniques, though little attention has been paid to the subject in the context of time-divison multiple-access (TDMA) systems. This paper addresses a pilot-based MMSE technique for multiuser channel estimation in a TDMA system, and makes two key contributions. Firstly, it allows for time variation of the channels within and between training sequences, an essential feature in a multiuser environment even at moderate fading rates. Secondly, it addresses the design of training sequences for the multiple cochannel users. Index Terms--Dispersive channels, estimation, fading channels, interference suppression, multidimensional signal detection, multiuser channels, sequences, time division multiaccess.

We consider downlink MIMO beamforming from several coordinated basestations (BSs), and the associated problem of in dependent carrier frequency offsets (CFOs) at the BSs which cause accumulated phase errors to compromise beamforming accuracy. Correction of the CFOs requires estimation of their values, so our topic is multiple CFO estimation, a little-explored area. We present a robust and easily generalized estimator that accounts for the training sequence (TS) correlations caused by the CFOs, and show that it meets the Cramer-Rao lower bound (CRLB) at moderate signal-to-noise ratios (SNRs). The performance of the estimator is contingent upon TSs short enough to ensure convexity of the log-likelihood over the allowable CFO ranges. For combinations of TS length and CFO range that violate this constraint, we present two suboptimal estimators based on segmentation of the TS, both of which also meet the CRLB at moderate to high SNRs. [ABSTRACT FROM AUTHOR]

System-wide multiuser detection (MUD), in which all base stations (BSs) of a cellular system cooperate to detect the data of all mobile stations (MSs), has much promise. However, little is known at present about practical techniques or their performance. An attractive method is belief propagation (BP), with message exchange between nearby cooperating BSs over a backbone landline network, but its performance is known only for a greatly simplified network model and its computation load grows exponentially with the number of interfering MS symbols at each BS. In this paper, we present a reduced complexity variation of BP (RCBP) and show that its performance is close to or identical to that of BP in the simplified network. We also observe excellent performance by iterative multiuser detection and decoding of low-density parity check codes (LDPC). Furthermore, we examine RCBP performance in a realistic wireless network model, with path loss, shadowing, fading and power control. These results, though poorer than those of the simplified network, show that system-wide MUD with cooperating BSs provides great improvement compared with conventional systems. [ABSTRACT FROM AUTHOR]