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Orthogonal frequency division multiplexing-(OFDM-) based amplify-and-forward (AF) cooperative communication is an effective way for single-antenna systems to exploit the spatial diversity gains in frequency-selective fading channels, but the receiver usually requires the knowledge of the channel state information to recover the transmitted signals. In this paper, a training-sequences-aided linear minimum mean square error (LMMSE) channel estimation method is proposed for OFDMbased cooperative diversity systems with multiple AF relays over frequency-selective fading channels. The mean square error (MSE) bound on the proposed method is derived and the optimal training scheme with respect to this bound is also given. By exploiting the optimal training scheme, an optimal low-rank LMMSE channel estimator is introduced to reduce the computational complexity of the proposed method via singular value decomposition. Furthermore, the Chu sequence is employed as the training sequence to implement the optimal training scheme with easy realization at the source terminal and reduced computational complexity at the relay terminals. The performance of the proposed low-complexity channel estimation method and the superiority of the derived optimal training scheme are verified through simulation results.

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Multi-function wireless systems demand multi-channel transmit/receive (TR) modules, particularly as multiple functions are required to operate simultaneously. In each channel, passive components, including bandpass filters, must be compact, or at least transversely compact; thus, the entire circuitry of the channel will be slender, and consequently multiple channels can be parallel-arranged conveniently. In this work, single-ended and balanced bandpass filters for multi-channel applications are presented. As a unique resonator, the U-shaped stepped impedance resonator (USIR) can achieve size miniaturization compared with its corresponding uniform impedance resonator (UIR) counterpart. Hence, with the utilization of USIRs, the proposed bandpass filters are able to acquire compact transverse sizes. Moreover, by using the source-load coupling scheme, two transmission zeros (TZs) are respectively generated at the lower and upper sides of the passbands, which is useful for improvement of the selectivity performance. In addition, spurlines are introduced at the input and output ports to produce another TZ to further enhance the stopband performance, which cannot be acquired by the UIR or stepped impedance resonator (SIR). To verify the aforementioned idea, one single-ended and one balanced bandpass filter are implemented, with experimental results in good agreement with the corresponding simulations. Meanwhile, as compared with some similar works, the proposed balanced filter achieves compact transverse size, sharp selectivity skirt, and wide stopbands up to the fourth-order harmonic with suppression over 20 dB, which illustrates its suitability for differential signal transmission application in microwave circuits and systems.

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