V. Ramon

Low-complexity linear frequency domain equalization for continuous phase modulation

In this paper, we develop a new low-complexity linear frequency domain equalization (FDE) approach for continuous phase modulated (CPM) signals. As a CPM signal is highly correlated, calculating a linear minimum mean square error (MMSE) channel equalizer requires the inversion of a nondiagonal matrix, even in the frequency domain. In order to regain the FDE advantage of reduced computational complexity, we show that this matrix can be approximated by a block-diagonal matrix without performance loss. Moreover, our MMSE equalizer can be simplified to a low-complexity zero-forcing equalizer. The proposed techniques can be applied to any CPM scheme. To support this theory we present a new polyphase matrix model, valid for any block-based CPM system. Simulation results in a 60 GHz environment show that our reduced-complexity MMSE equalizer significantly outperforms the state of the art linear MMSE receiver for large modulation indices, while it performs only slightly worse for small ones.

Joint Transmit and Receive Analog Beamforming in 60 GHz MIMO Multipath Channels

Analog BeamForming (ABF) with one scalar weight per antenna is an attractive technique for low-cost, low-power 60 GHz multi-antenna wireless communication systems. However, the design of the corresponding joint transmit and receive (Tx/Rx) ABF optimization algorithms is still challenging in the case of multipath channels due to the constraint of having only one scalar weight per antenna. In this paper, we aim at maximizing the average Signal to Noise Ratio (SNR) at the input of the equalizer and analytically derive close-to-optimal Tx/Rx scalar weights. We show that the required Channel State Information (CSI) for joint Tx/Rx ABF weights computation is the inner product between all Tx/Rx channel impulse response pairs. Taking the channel length into account, a training-based estimation strategy of this CSI is proposed. Simulation results carried out in a typical 60 GHz multipath environment show that the proposed scheme outperforms the existing ABF schemes in term of BER performances.

A New Symbol Block Construction for CPM with Frequency Domain Equalization

We present a new symbol block construction which yields a cyclic continuous phase modulated (CPM) signal to enable frequency domain equalization. It is known that in addition to a cyclic prefix, a subblock of data-dependent symbols has to be inserted in each block to cope with the memory in the CPM signal. We propose a new subblock, called intrafix, valid for any CPM scheme. Our intrafix is shorter than what is currently known in the literature, reducing the overhead. Moreover, it can be calculated on a per-block basis, without knowledge of previous blocks. We also prove that there are constraints on the length of both the intrafix and the total block by studying the influence of the modulation index. Simulation results in a 60 GHz environment show that our new block construction satisfies all requirements.

Spectrum Sensing over SIMO Multi-Path Fading Channels Based on Energy Detection

One of the techniques for spectrum sensing is the energy detection of signals from primary transmitters. However, when detecting in a certain frequency band, this technique suffers from the random fading introduced by the channel. This problem can be alleviated by the use of multiple antennas introducing spatial diversity. The performance of the energy detector with multiple antennas has already been analytically analyzed for flat fading channels. In this paper, we propose analytical expressions for the performance of multi-antenna energy detector with multi-paths fading channels. These expressions will enable to compare for different channel power profiles the gains brought by the two sources of diversity: spatial (or antenna) diversity and multi-path diversity. This analytical performance is compared to simulations to show the validity of the used approximations.

Maximum SINR-Based Beamforming for the MISO OFDM Interference Channel

We address the problem of co-channel interference (CCI) in wireless mesh networks (WMNs). In such networks, multiple nodes communicate concurrently using the same time/frequency resources. This is recognized as the interference channel (IFC) because the CCI is a major impairment in such a scenario. To mitigate the CCI, non-cooperative beamforming techniques can be employed. Non-cooperative beamformers are simpler to implement than their cooperative counter-parts because they require neither synchronization nor the sharing of information data between the transmit nodes. In this paper, we then propose a non-cooperative beamforming scheme to improve the performance of WMNs with frequency-selective channels. We present an iterative algorithm that maximizes the signal-to-interference-and-noise ratio criterion over all subcarriers of the orthogonal frequency division multiplexing system. The performance of this algorithm is evaluated through simulations.

Low-Complexity Frequency Domain Equalization Receiver for Continuous Phase Modulation

A new approach for frequency-domain equalization of continuous phase modulated (CPM) signals is presented. In contrast with state-of-the-art receivers, we separate channel equalization on the one hand and CPM demodulation on the other. This separation enables us to calculate independently of the CPM scheme a new low-complexity zero-forcing channel equalizer. We also present a new high-performance minimum mean square error (MMSE) channel equalizer for any CPM scheme and a method to lower its complexity for a popular class of CPM schemes. Simulations show that our new MMSE equalizer significantly outperforms state-of-the-art linear receivers in a 60 GHz multipath environment.

A Flexible Antenna Selection Scheme for 60 GHz Multi-Antenna Systems Using Interleaved ADCs

We present a new scheme for maximizing the signal-to-noise ratio (SNR) in wideband multi-antenna receivers that employ time-interleaved analog-to-digital converters (ADCs). Current wideband receivers interleave a fixed number of slower ADCs into one fast ADC and assign this latter to one antenna according to an antenna selection algorithm. However, this does not always guarantee an optimal trade-off between thermal noise and quantization noise. This results in an overall SNR that is lower than what could be obtained with the same number of ADCs, assigned in a more optimal way. Therefore, we propose to adjust the number of slower ADCs assigned to a certain fast, interleaved ADC dynamically, according to the SNR of every individual antenna. Our proposed algorithm can be implemented at the expense of a very limited hardware complexity increase. The SNR gain of our new scheme can exceed 7 dB, depending on channel conditions and ADC specifications.

Applying frequency domain equalization to precoded CPM

We show how to apply frequency domain equalization (FDE) to precoded continuous phase modulation (CPM) systems. It is well known that differential precoding can be applied to the specific, popular class of CPM schemes with modulation index h = 1/2Q, where Q is any integer. This precoding halves the bit error rate (BER) compared to nonprecoded CPM without any overhead or complexity increase. We apply FDE to a block-based precoded CPM system. Therefore, we show that in addition to a cyclic prefix, two subblocks of data-dependent symbols have to be inserted in each block to cope with the memory in the CPM signal and to enable correct decoding by the receiver. We explain how to calculate these subblocks. Simulation results in a 60 GHz environment confirm that the BER is halved by precoding, and that this precoding is compatible with FDE using our new technique.

Training Sequence Versus Cyclic Prefix for CPM with Frequency Domain Equalization

Frequency domain equalization (FDE) of continuous phase modulations (CPM) has been thoroughly investigated lately. To enable this low-complexity FDE, all known techniques use a cyclic prefix (CP). However, using a training sequence (TS) of known symbols instead of a CP offers some advantages: the additional known symbols can be used to improve synchronization and channel estimation, with the same performance of a CP. Nevertheless, using a TS for CPM-FDE is not trivial because the memory in a CPM waveform has to be taken into account to guarantee cyclicity and phase continuity after insertion of the TS into a block of input symbols. In this paper, we therefore propose a technique for constructing a TS for CPMFDE. Simulation results in a 60 GHz environment show that the proposed technique satisfies all requirements. The 60 GHz case is chosen because CPM with FDE has recently been proposed for communications at 60 GHz and the latest IEEE and ECMA standards for these frequencies mandate the use of a TS rather than a CP.

A CramÉr-Rao Bound Characterization of the EM-Algorithm Mean Speed of Convergence

This paper deals with the mean speed of convergence of the expectation-maximization (EM) algorithm. We show that the asymptotic behavior (in terms of the number of observations) of the EM algorithm can be characterized as a function of the Cramer-Rao bounds (CRBs) associated to the so-called incomplete and complete data sets defined within the EM-algorithm framework. We particularize our result to the case of a complete data set defined as the concatenation of the observation vector and a vector of nuisance parameters, independent of the parameter of interest. In this particular case, we show that the CRB associated to the complete data set is nothing but the well-known modified CRB. Finally, we show by simulation that the proposed expression enables to properly characterize the EM-algorithm mean speed of convergence from the CRB behavior when the size of the observation set is large enough.