IQ-Imbalance Compensation for OFDM in the Presence of IBI and Carrier-Frequency Offset

In this paper, we propose a frequency-domain equalization technique for orthogonal frequency division multiplexing (OFDM) transmission over frequency-selective channels. We consider the case where the receiver analog front-end suffers from IQ-imbalance and the local oscillator suffers from carrier-frequency offset (CFO). While the IQ-imbalance results in a mirroring effect, the CFO induces inter-carrier interference (ICI). In addition to ICI, we consider the channel delay spread is larger than the cyclic prefix (CP). This means that inter-block interference (IBI) is present. The frequency-domain equalizer is obtained by transferring a time-domain equalizer (TEQ) to the frequency-domain resulting in a per-tone equalizer (PTEQ). Due to the presence of IQ-imbalance the conventional TEQ (where only one TEQ is applied to the received sequence) is not sufficient to cope with the mirroring effect. A sufficient TEQ consists of two time-domain filters; one applied to the received sequence and another applied to a conjugated version of the received sequence. For the case of IQ-imbalance and CFO, the TEQs are designed according the basis expansion model (BEM) which showed to be able to cope with the ICI problem. Finally, in addition to the frequency-domain PTEQ design procedure, a training-based RLS type initialization scheme for direct per-tone equalization is also proposed     

Equalization for OFDM over doubly selective channels

In this paper, we propose a time-domain as well as a frequency-domain per-tone equalization for orthogonal frequency-division multiplexing (OFDM) over doubly selective channels. We consider the most general case, where the channel delay spread is larger than the cyclic prefix (CP), which results in interblock interference (IBI). IBI in conjunction with the Doppler effect destroys the orthogonality between subcarriers and, hence, results in severe intercarrier interference (ICI). In this paper, we propose a time-varying finite-impulse-response (TV-FIR) time-domain equalizer (TEQ) to restore the orthogonality between subcarriers, and hence to eliminate ICI/IBI. Due to the fact that the TEQ optimizes the performance over all subcarriers in a joint fashion, it has a poor performance. An optimal frequency-domain per-tone equalizer (PTEQ) is then obtained by transferring the TEQ operation to the frequency domain. Through computer simulations, we demonstrate the performance of the proposed equalization techniques.     

Turbo equalization of doubly selective channels

In this paper, turbo equalization for transmission over doubly selective channels is proposed. The maximum a posteriori probability (MAP) algorithm is used for channel detection as well as for channel decoding. The detection/decoding constituents can exchange soft information in an iterative manner resulting in the so‐called turbo equalization. The time‐varying multi‐path fading channel is modeled using the basis expansion model (BEM). In this BEM, the time‐varying channel is viewed as a bank of time‐invariant finite impulse response filters, and the time variation is captured by means of time‐varying complex exponential basis functions. Therefore, the time‐varying transition tables that characterize the time‐varying channel can also follow a similar BEM. The complexity of the MAP channel detector is rather prohibitive for practical applications. This motivates the search for lower‐complexity soft‐output channel detectors. For this purpose, soft‐output linear minimum‐mean square error (LMMSE)‐based channel detectors are proposed for single carrier as well as for multi‐carrier systems. With the use of Gaussian approximation, expressions for the a posteriori and extrinsic log‐likelihood ratios have been derived. The performance of the proposed turbo equalization schemes are evaluated using numerical simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

MLSE and MAP Equalization for Transmission Over Doubly Selective Channels

In this paper, equalization for transmission over doubly selective channels is discussed. The symbol-by-symbol maximum a posteriori probability (MAP) equalizer and the maximum-likelihood sequence estimation (MLSE) are discussed. The doubly selective channel is modeled using the basis expansion model (BEM). Using the BEM allows for an easy and low-complexity mechanism for constructing the channel trellis to implement the MLSE and the MAP equalizer. The MLSE and the MAP equalizer are implemented for single-carrier transmission and for multicarrier transmission implemented using orthogonal frequency-division multiplexing (OFDM). In this scenario, a complexity-diversity tradeoff can be observed. In addition, we propose a joint estimation and equalization technique for doubly selective channels. In this joint estimation and equalization technique, the channel state information (CSI) is obtained in an iterative manner. Simulation results show that the performance of the joint channel estimation and equalization approaches the performance when perfect CSI is available at the receiver.     

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.     

Optimal training design for MIMO OFDM systems in mobile wireless channels

This paper describes a least squares (LS) channel estimation scheme for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on pilot tones. We first compute the mean square error (MSE) of the LS channel estimate. We then derive optimal pilot sequences and optimal placement of the pilot tones with respect to this MSE. It is shown that the optimal pilot sequences are equipowered, equispaced, and phase shift orthogonal. To reduce the training overhead, an LS channel estimation scheme over multiple OFDM symbols is also discussed. Moreover, to enhance channel estimation, a recursive LS (RLS) algorithm is proposed, for which we derive the optimal forgetting or tracking factor. This factor is found to be a function of both the noise variance and the channel Doppler spread. Through simulations, it is shown that the optimal pilot sequences derived in this paper outperform both the orthogonal and random pilot sequences. It is also shown that a considerable gain in signal-to-noise ratio (SNR) can be obtained by using the RLS algorithm, especially in slowly time-varying channels.