Jochem Egle

Diversity comparison of spreading transforms for multicarrier spread spectrum transmission

Multicarrier spread spectrum transmission methods based on orthogonal frequency division multiplexing employ a linear transform to spread energy of transmitted symbols over statistically independent Rayleigh fading subcarriers, in order to enable a diversity gain at the receiver. We jointly treat the mapping from bits into transmit symbols and the spreading transform as a code in Euclidean space. We describe criteria to identify good and bad spreading transforms, in terms of the asymptotic bit-error probability (BEP) at high signal-to-noise ratio. Upper and lower bounds on the BEP are derived. It is shown that the BEP performance of the commonly used Hadamard transform is asymptotically bad. Alternative orthogonal transforms with better asymptotic performance are proposed. Simulation results are given for the example of 2-phase-shift keying, block length 8.

Equalization and coding for extended MC-CDMA over time and frequency selective channels

In this work Multi Carrier Code Division Multiple Access (MCCDMA) — based on Orthogonal Frequency Division Multiplex (OFDM) combined with Hadamard spreading sequences — is extended by an additional spreading in time direction. Introducing the Kronecker Product the two transformations in time and frequency direction can be merged, resulting in one larger transformation.

Iterative Joint Equalization and Decoding Based on Soft Cholesky Equalization for General Complex Valued Modulation Symbols

A new iterative equalizer based on the classical block decision feedback equalizer is introduced. The performance of this iterative version benefits from the usage of a soft decision function, which is based on noise whitening and consecutive matched filtering. The derivation of the decision function is very general and, therefore, applicable to arbitrary complex valued modulation symbols. After adding the possibility of processing extrinsic information to this decision function, the equalizer is embedded in an iterative equalization/decoding scheme. To demonstrate the performance of the scheme simulation results are presented for frequency selective channels using BPSK and 16 QAM.

Iterative detection algorithms for extended MC-CDMA

Multicarrier code division multiple access (MC-CDMA) combines the advantages of CDMA and orthogonal frequency division multiplexing techniques. For time-varying channels, it can be further improved by introducing an additional spreading in the time direction (extended MC-CDMA). Two low complexity iterative detection algorithms with soft feedback are described: the iterative soft block decision feedback equalizer and a recurrent neural network based detector. Performance results are given for a typical mobile radio channel and compared to the optimum maximum likelihood detector. Introducing pilot symbol assisted channel estimation, the optimum number of pilot symbols is determined and the bit error rate performance is compared to the case of ideal channel estimation.

On pilot-assisted MAP detection in frequency-flat Rayleigh fading channels

Pilot symbol assisted modulation (PSAM) eases the task of estimating the channel gain and phase in frequency-flat Rayleigh fading. Inaccurate channel estimates may lead to an increased error probability in a subsequent data detection stage. For PSAM and flat Rayleigh fading, the effects of channel estimation errors on the error probability have been analyzed in A. Aghamohammadi and H. Meyr [Nov. 1990]. We pursue the analysis given in A. Aghamohammadi and H. Meyr [Nov. 1990] and derive the maximum a-posteriori (MAP) detector which minimizes the symbol error probability by processing the data and pilot receive symbol(s) simultaneously. This detector is compared to the conventional 2 step receiver which performs channel estimation followed by data detection. Moreover, a basic approach to calculate the symbol error probability is given and we study and illustrate the decision regions of the two detectors.

Iterative soft Cholesky block decision feedback equalizer-a promising approach to combat interference

A novel iterative soft block decision feedback scheme, capable to cope with general complex valued modulation symbols and to combat both inter-symbol and inter-user interference, is introduced. It is shown that this new scheme has the capability to achieve optimum maximum likelihood performance and does not suffer from the unavoidable loss of received power in a classical DFE scheme. As an example we apply the introduced detection algorithm to the K-symmetric multiuser channel and compare the results to both the classical block decision feedback equalizer and to maximum likelihood equalization.

Detection method for MC-CDMA based on a recurrent neural network structure

A detection method based on a recurrent neural network structure is derived for a multi carrier code division multiple access communication system with multi path propagation. Contrary to other neural network approaches, the RNN has the advantage, that network size as well as the coefficients of the network can be derived from parameters which characterize the communication system. The energy function of the RNN is identical to the log-likelihood function of the maximum likelihood detector. Different iteration algorithms for the RNN with an emphasis on parallel processing are discussed. Performance results are given for the Rayleigh fading channel and a typical mobile radio channel. Performance and complexity of the RNN detector are compared with other iterative detection algorithms, specifically a block decision feedback equalizer.

Convergence behavior of iterative equalization and decoding schemes with equalization and memory

In recent years, there has been a growing interest in applying turbo algorithms to enhance performance in communication systems. Among them, iterative equalization and decoding, turbo equalization, has proven to be a powerful technique to mitigate intersymbol interference. In this paper, we propose a soft interference canceler with memory, suitable for general complex symbol alphabets, as part of a turbo equalization scheme and investigate its convergence behavior using the extrinsic information transfer (EXIT) chart tool. Although the true behavior of the trajectory of the iterative process cannot be perfectly predicted, we obtain useful information to reduce computational complexity of the turbo scheme.

Multiuser detection in DS-CDMA systems based on a lattice code decoder

Usually, multiple access interference in DS-CDMA systems represents the capacity limiting factor. In this paper, we propose a multiuser detection algorithm based on a lattice code decoder that offers moderate computational complexity. The bit error rate converges asymptotically to the maximum-likelihood curve for large signal-to-noise ratios. Numerical results verify the performance in comparison to conventional detection schemes.