Minimum Mean Square Error Detector Research Articles

Asynchronous CDMA Systems With Random Spreading—Part I: Fundamental Limits

Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal to interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by under-sampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g., positive roll-off factors. For example, with the pulse shaping demanded in the UMTS standard, user synchronization reduces spectral efficiency up to 12% at 10 dB normalized signal-to-noise ratio. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if the users are de-synchronized on the chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of the effective interference spectral density arises. This generalizes and refines Tse and Hanly's concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided.

Frequency-Domain Block Signal Detection for Single-Carrier Transmission

One-tap frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can significantly improve the bit error rate (BER) performance of single-carrier (SC) transmission in a frequency-selective fading channel. However, a big performance gap from the theoretical lower bound still exists due to the presence of residual inter-symbol interference (ISI) after MMSE-FDE. In this paper, we point out that the frequency-domain received SC signal can be expressed using the matrix representation similar to the multiple-input multiple-output (MIMO) multiplexing and therefore, signal detection schemes developed for MIMO multiplexing, other than simple one-tap MMSE-FDE, can be applied to SC transmission. Then, for the reception of SC signals, we propose a new signal detection scheme, which combines FDE with MIMO signal detection, such as MMSE detection and Vertical-Bell Laboratories layered space-time architecture (V-BLAST) detection (we call this frequency-domain block signal detection). The achievable average BER performance using the proposed frequency-domain block signal detection is evaluated by computer simulation.

Improved SISO MMSE Detection for Joint Coded-Precoded OFDM under Imperfect Channel Estimation

An improved soft-input soft-output (SISO) minimum mean-squared error (MMSE) detection method is proposed for joint coding and precoding OFDM systems under imperfect channel estimation. Compared with the traditional mismatched detection which uses the channel estimate as its exact value, the signal model of the proposed detector is more accurate and the influence of channel estimation error (CEE) can be effectively mitigated. Simulations indicate that the proposed scheme can improve the bit error rate (BER) performance with fewer pilot symbols.

Comparative Study of Different Space-Time Coding Schemes for MC-CDMA Systems

In this paper, performance of space-time trellis-code (STTC), space-time block code (STBC), and space-time trellis-code concatenated with space-time block code (STTC-STBC) for multi-carrier code-division multiple-access (MC-CDMA) system are studied. These schemes are considered by employing different detection techniques with various multi input multi output (MIMO) antenna diversity for different number of states in multi-path fading channel. The corresponding bit error rate (BER) is obtained using simulation for minimum mean-square error (MMSE), maximum-ratio combining (MRC), and equal-gain combining (EGC) receivers employing Viterbi decoder. The simulation results show that the STTC-STBC MC-CDMA system perform better compared to other schemes considered in this paper using MMSE detection and it is also observed that the performance can also be enhanced by increasing diversity using more transmitter and receiver antennas. However, this improvement in performance comes at the cost of increased computational complexity, which is calculated for different transmitting and receiving antennas.

Frequency-domain adaptive detectors for single-carrier frequency-domain equalisation in multiuser direct-sequence ultra-wideband systems based on structured channel estimation and direct adaptation

Here, the authors propose two adaptive detection schemes based on single-carrier frequency-domain equalisation (SC‐FDE) for multiuser direct-sequence ultra-wideband systems, which are termed structured channel estimation (SCE) and direct adaptation (DA). Both schemes use the minimum mean square error (MMSE) linear detection strategy and employ a cyclic prefix. In the SCE scheme, adaptive channel estimation is performed in the frequency domain and the despreading is implemented in the time domain after the FDE. In this scheme, the MMSE detection requires the knowledge of the number of users and the noise variance. For this purpose, simple algorithms are proposed for estimating these parameters. In the DA scheme, the interference suppression task is fulfilled with only one adaptive filter in the frequency domain and a new signal expression is adopted to simplify the design of such a filter. Least mean squares, recursive least squares and conjugate gradient adaptive algorithms are then developed for both schemes. A complexity analysis compares the computational complexity of the proposed algorithms and schemes, and simulation results for the downlink illustrate their performance.

Capacity-aware linear MMSE detector for OFDM-SDMA systems

This paper presents a capacity-aware linear minimum mean square error (MMSE) detector for orthogonal frequency-division multiplexing/space-division multiple access (OFDM-SDMA) applications. We derive closed-form expressions for the signal-to-interference plus noise ratio (SINR) performance of OFDM-SDMA systems with linear MMSE detection method, where capacity enhancements have been introduced in the transmit/receive weight computations. Using the derived expressions, we compare the performance of the proposed scheme with the regular multiple-input multiple-output (MIMO)-MMSE system in OFDM-SDMA applications. It is shown that in enhancing the system capacity, the capacity-aware MIMO-MMSE scheme also enhances the SINR, resulting in lower symbol error rate (SER) compared to the conventional MIMO-MMSE beamforming schemes.

A simplified MMSE-based iterative receiver for MIMO systems

A simplified minimum mean square error (MMSE) detector is proposed for joint detection and decoding of multiple-input multiple-output (MIMO) systems. The matrix inversion lemma and the singular value decomposition (SVD) of the channel matrix are used to simplify the computation of the coefficient of the MMSE filter. Compared to the original MMSE detector, the proposed detector has a much lower computational complexity with only a marginal performance loss. The proposed detector can also be applied to MIMO systems with high order modulations.

LMSE-based parameter acquisition for multicarrier CDMA systems

An acquisition scheme, based on the least mean-squared error (LMSE), for the symbol timing, carrier phases, and multipath gains for multicarrier code-division multiple-access (MC-CDMA) systems is proposed. A new coefficient called the quasi-mean-squared accuracy coefficient (QMSAC) is introduced. This allows the search for multiple optimal parameters to be split into simpler single-parameter estimates. The symbol timing is acquired with a comparison of the QMSACs followed by a linear interpolation scheme or a search of a minimizing variable. Carrier phases and multipath gain coefficients are then estimated via some algebraic computations based only on the estimated symbol timing and the QMSACs. The spreading sequence of the desired user is the only prior knowledge required for the proposed approach. Simulation results demonstrate the near-far resistance of the approach and show that the error performance of minimum mean-squared error (MMSE) detection with acquired parameters is only a few decibels worse for the considered channel than the performance obtained with perfect knowledge about the channel impulse response.

Gaussian process regressors for multiuser detection in DS-CDMA systems

In this paper we present Gaussian processes for Regression (GPR) as a novel detector for CDMA digital communications. Particularly, we propose GPR for constructing analytical nonlinear multiuser detectors in CDMA communication systems. GPR can easily compute the parameters that describe its nonlinearities by maximum likelihood. Thereby, no cross-validation is needed, as it is typically used in nonlinear estimation procedures. The GPR solution is analytical, given its parameters, and it does not need to solve an optimization problem for building the nonlinear estimator. These properties provide fast and accurate learning, two major issues in digital communications. The GPR with a linear decision function can be understood as a regularized MMSE detector, in which the regularization parameter is optimally set. We also show the GPR receiver to be a straightforward nonlinear extension of the linear minimum mean square error (MMSE) criterion, widely used in the design of these receivers. We argue the benefits of this new approach in short codes CDMA systems where little information on the users' codes, users' amplitudes or the channel is available. The paper includes some experiments to show that GPR outperforms linear (MMSE) and nonlinear (SVM) state-ofthe- art solutions.

Bit error performance of convolutional coded MIMO system with linear MMSE receiver

In this letter, we introduce an analytical expression to the coded bit error rate (BER) of a MIMO system with a linear minimum mean square error (MMSE) receiver. We derive the moment generating function (MGF) of the SINR for arbitrary antenna configurations from the cumulative density function of SINR.We show that the moment generating function of the SINR at the MMSE detector output can be used to estimate the BER performance of a coded MIMO system. The analysis is simple and gives an accurate BER estimation at a high SNR. Based on the analytical and simulated results, the diversity order is dependent on the antenna configuration and the free distance of the convolutional code. Finally, we compare the analytical expression with simulated results for validation.

Receiver design for multicarrier CDMA using frequency-domain oversampling

Based on the frequency-domain oversampling and minimum mean-square error (MMSE) principles, we propose three linear single-user detectors for downlink multicarrier codedivision multiple-access (MC-CDMA) systems. We begin with an optimal linear MMSE detector, which is computationally demanding. To reduce the complexity, a two-stage MMSE detector and a diagonal one-stage MMSE detector are developed subsequently. Simulation results show that the proposed detectors can efficiently suppress the multiple access interference (MAI) caused by frequency-selective fading, near-far effect, frequency offset, and nonlinear power amplification.

Performance Analysis of MIMO System with Linear MMSE Receiver

This paper considers the uncoded multiple-input multiple-output (MIMO) system with linear minimum mean square error (MMSE) detection under ideal fast fading. The distribution of SINR at the output of the MMSE detection is derived for a small number of transmit and receive antennas. We present new approximation for the Gaussian Q-function driven by numerical simulation. Based on the SINR distribution and new approximation for Q-function, we analyze the performance of linear MMSE detection under ideal fast fading environment. By comparing the analytical results and Monte Carlo simulated results, we validate the analytical results.

Suboptimal resource allocation with MMSE detector for grouped MC-CDMA systems

This article puts forward two novel user-grouping algorithms for grouped multi-carrier (MC)-code division multiple access (CDMA) systems. As is well known, the adaptive assignment for user-grouping plays an important role for link quality of multi-access transmissions. In the study, the capacity-maximizing problem of user-grouping is formulated. By using the Kuhn-Tucker condition, the optimal criterion is deduced and found to have a similar form with signal to noise plus interference (SINR). However SINR includes the signal power that can only be determined after user-grouping. Therefore the optimal criterion will lead to an impractical application. To deal with it, the user's equivalent SINR for minimum mean square error (MMSE) detector is proposed and served as a suboptimal assignment criterion, based on which two kinds of user-grouping algorithms are proposed. In the algorithms, only partial channel information is needed at the base station, which saves a large part of the bandwidth occupied by feedback information. Computer simulations have evaluated an excellent performance of the proposed algorithms at both link quality and data rate. Meanwhile, the proposed algorithms have lower implementation complexity for practical reality.

Performance of an SIMO FM-DCSK Communication System

A single-input multiple-output (SIMO) architecture of the frequency-modulated (FM) differential code-shift keying (DCSK) modulation technique is proposed. The new scheme employs orthogonal Walsh functions at the transmitter, with parallel substreams transmitted with a single antenna to help achieve a significant increase of the data rate. Multiple antennas are used at the receiver end to form an SIMO structure so as to obtain a diversity gain. Simulation results demonstrate that at a higher signal-to-noise ratio, the proposed SIMO FM-DCSK architecture has an outstanding bit error rate performance, in contrast to the direct-sequence (DS) vertical Bell Labs layered space-time (VBLAST) scheme that uses a complicated Rake receiver and minimum mean-square error detection, at the same data rate over multipath fading channels. In particular, the new scheme does not require any prior knowledge of the channel states, exact synchronization, and the complex Rake receiver, making the proposed algorithm simpler and yet more efficient than the DS-VBLAST scheme.

LDC in MIMO Ricean Channels: Optimal Transmit Strategy With MMSE Detection

In this paper, we study a MIMO system with a transmitter using a linear dispersion code (LDC) and a linear minimum mean square-error (MMSE) detector at the receiver in a Ricean flat-fading environment. We assume that the receiver has perfect channel state information and the transmitter knows only the mean channel matrix either by feedback or channel estimation. The focus of our work is the analysis of the optimal transmit strategy using different types of LDC. On the one hand, we consider spatial multiplexing schemes that achieve high data rates, but sacrifice diversity. On the other hand, we have schemes that achieve full diversity like quasi-orthogonal space-time block codes or orthogonal space-time block code. Depending on the LDC in use, the optimization problem is either convex or nonconvex. For both of these classes of LDC, we first derive the properties of the average normalized MSE and then analyze the impact of the mean component on the MSE, the optimal transmit strategy and the optimal power allocation. Finally, we derive some bounds on the error rate performance for different scenarios with the MMSE receiver.

Iterative Multiuser Minimum Symbol Error Rate Beamforming Aided QAM Receiver

A novel iterative soft interference cancellation (SIC) aided beamforming receiver is developed for high-throughput quadrature amplitude modulation systems. The proposed SIC-based minimum symbol error rate (MSER) multiuser detection scheme guarantees the direct and explicit minimization of the symbol error rate at the output of the detector. Adopting the extrinsic information transfer (EXIT) chart technique, we compare the EXIT characteristics of an iterative MSER multiuser detector (MUD) with those of the conventional minimum mean-squared error (MMSE) detector. As expected, the proposed SIC-MSER MUD outperforms the SIC-MMSE MUD.

Low-Complexity Iterative Receiver for Coded MIMO-OFDM Systems Based on PIC-MRC

A novel low-complexity iterative receiver for coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is proposed in this letter. The iterative receiver uses the parallel interference cancellation (PIC)-maximum ratio combining (MRC) detector for MIMO-OFDM detection, which is a popular alternative to the minimum mean square error (MMSE) detector due to its lower computational complexity. However, we have found that the conventional PIC-MRC detector tends to underestimate the magnitude of its output log likelihood ratios (LLRs). Based on this discovery, we propose to multiply these LLRs by a constant factor, which is optimized according to the extrinsic information transfer (EXIT) chart of the soft-in soft-out (SISO) detector. Simulation results show that the proposed scheme significantly improves the performance of the PIC-MRC-based receiver with little additional cost in computational complexity, allowing it to closely approach the performance of receiver using the much more complex MMSE detector.

Analysis and Performance Evaluation of Linear Multiuser Detectors in the Downlink of DS-CDMA Systems Applying Spectral Decomposition

This paper studies the performance of linear multiuser detectors for direct-sequence code division multiple access systems at different loading levels and users' powers, using singular value decomposition (SVD) techniques in the downlink of Rayleigh flat-fading and additive white Gaussian channels. The performance of the matched filter (MF), decorrelator (zero-forcing), and minimum mean-squared error (MMSE) detectors are studied and compared. Analytical and simulation results are also presented in terms of the bit error rate. From this analysis, a simple linear multiuser detector is developed that exploits the structure of the system's spreading codes matrix from the SVD viewpoint. Also, the numerical performance of this proposed detector is compared to that of the conventional detector (MF) as a function of the signal-to-noise ratio. Finally, the performance limits are established in terms of the singular values of the spreading codes matrix. Extensive simulation results validate the analysis presented in the paper for equal or unequal users' powers.

Performance Analysis of Multiuser Detectors for Uplink Quasi-synchronous MC-CDMA Systems

This paper analyses and compares the average bit error rate (BER) of different multiuser detectors (MUD) in the uplink of a multicarrier code- division multiple access (MC-CDMA) system. In particular, maximum likelihood, zero-forcing, minimum mean-square error and interference cancellation-based multiuser detectors have been analysed for the special case of uncorrelated subcarriers. The derived BER expressions are based upon previous results on diversity combining and also on recent findings on multiple input multiple output (MIMO) architectures. The subcarrier correlation is considered in the context of physical parameters currently under discussion for future wireless systems to give an indication up to what extent the assumption of uncorrelated subcarrier fading is plausible.

BER-Optimal Linear Parallel Interference Cancellation for Multicarrier DS-CDMA in Rayleigh Fading

In this paper, we consider the design and bit-error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) systems. We propose an LPIC scheme where we estimate and cancel the multiple access interference (MAI) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit-error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. In addition, using an alternate approach involving the characteristic function of the decision variable, we derive BER expressions for the weighted LPIC scheme, matched filter (MF) detector, decorrelating detector, and minimum mean square error (MMSE) detector for the considered multicarrier DS-CDMA system. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating and MMSE detectors.