Ilia Iofedov

MIMO–OFDM With Nonlinear Power Amplifiers

The influence of nonlinear power amplifiers (PAs) on the performance of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is investigated. A “full” MIMO scheme with transmitters (TX) precoding and receivers (RX) decoding is considered. It is shown, under assumption of high order OFDM and frequency selective channel, that the ratio between the useful signal and the nonlinear distortions is proportional to the number of TX antennas, i.e., the influence of the nonlinear distortions decreases as the number of TX antennas increases. The distortion reduction factor (DRF) is proposed as a performance metric for MIMO-OFDM systems with nonlinear PAs. A general formula for signal to distortion and noise ratio is obtained for the nonlinear PA with memory, described by the Wiener-Hammerstein (WH) model. Special cases of MIMO, such as maximum ratio transmission (MRT) and maximum ratio combining (MRC), are considered. A full agreement between the theoretical and simulation results is obtained. The main contribution of this paper is in a statement that TX processing reduces the effect of nonlinear distortions. This is obtained by novel approach for analysis of the MIMO-OFDM systems with nonlinear PAs with memory.

Iterative Decoding of Iterative Clipped and Filtered OFDM Signal

A communication system with non-linear power amplifier (PA) is considered. We introduce three major performance criteria of the system: (i) power efficiency of the PA, (ii) spectral purity of the transmitted signal expressed by adjacent channel interference, and (iii) transmission performance expressed by mutual information or symbol error rate. In order to fulfill the first two criteria it is proposed to use iterative clipping and filtering (ICF) at the transmitter together with low input back-off, while the third criterion is obtained by modified iterative receiver (MIR). The proposed MIR is based on the well-known iterative receiver, but with ICF in the feedback path. The obtained results show that the proposed system is better than its competitors when considering the three performance criteria together. The analysis and results are focused on OFDM; however, the proposed approach may be applied to single carrier.

Performance Analysis of Communication System with Nonlinear Power Amplifier

A communication system with nonlinear Power Amplifier (PA) is considered. The PA nonlinearity forces the designer of communication system to choose proper Back-Off, which influences three major parameters of the communication system: (i) power efficiency, (ii) Adjacent Channel Power Ratio (ACPR), and (iii) bit rate expressed by Mutual Information (MI). Having these three parameters, we propose to evaluate the performance of a communication system with nonlinear PA using the fact that ACPR is dictated by the regulator/communication standard. In what follows we propose to find power efficiency and MI as a function of ACPR. To illustrate the usefulness of the proposed method, the Solid State Power Amplifier (SSPA), and two linearized versions of SSPA are considered. The first version is a perfectly linearized PA using pre-distortion resulting with Soft Envelope Limiter (SEL), and the second is the Feed-Forward (FF) architecture based on SSPA. For each of the PAs ACPR, power efficiency and MI are found. While the analysis of SSPA and SEL is mainly based on the existing literature, the analysis of FF may be considered as a new contribution. From the results of the analysis it is concluded that linearization improves the overall performance of communication system. It is also shown that the pre-distortion method (SEL) shows better performance than FF.

Iterative precoding of OFDM-MISO with nonlinear Power Amplifiers

A novel iterative algorithm for transmitter (TX) precoding for a Orthogonal Frequency Division Multiplexing - (OFDM-) Multiple Input Single Output (MISO) system with nonlinear Power Amplifiers (PAs) is proposed. Having a plurality of PAs at the TX, it is possible to synthesize peak power limited signals, transmitted at each TX branch, such that the total distortions seen at the receiver (RX) will be minimal. Two versions of the algorithm are proposed. The first one reduces nonlinear distortions seen at the RX antenna without considering the spectral purity requirements. The second one reduces nonlinear distortions at the RX and also keeps the out-of-band radiation of the TX signals at a low level in order to satisfy spectral purity requirements. For a low Back-Off (BO) scenario, where the nonlinear distortions are strong, the proposed algorithms show a much lower Symbol Error Rate (SER) and much higher power efficiency than the well known Maximum Ratio Transmission approach.

On OFDM-MRT with nonlinear power amplifier

The influence of a nonlinear power amplifier on the performance of OFDM-MRT is investigated. It is shown that the ratio between the useful signal and the nonlinear distortions is proportional to the number of TX antennas, i.e., the influence of the nonlinear distortions decreases as the number of TX antennas increases. The Distortion Reduction Factor (DRF) is proposed as a performance metric for multi-antenna systems with nonlinear power amplifier. Considering the nonlinear power amplifier in each transmitting branch, a general formula for signal to distortions and noise ratio in the receiver is obtained and symbol error rate is computed. The MRT is compared to MRC and SISO. It is shown that for a low noise scenario the performance of MRT is much better than that of MRC. Full agreement of the theoretical and simulation results is obtained.

Rate increase in digital communications by using master-slave power amplifiers

In this paper we propose to use a so-called “Slave” power amplifier (PA) to remove the distortions caused by the non-linear “Master” high power amplifier (HPA) in multicarrier systems. We derive the mutual information (MI) expressions for the proposed scheme and perform simulations to obtain the spectral mask. It is shown that by adding an additional “Slave” PA we increase the MI and improve the spectral mask, while maintaining the same supplied power as in regular multicarrier system with a single “Master” HPA.

Linearization of nonlinear MISO channel

A Multiple Input Single Output (MISO) system based on Maximum Ratio Transmission (MRT) precoding with nonlinear Power Amplifiers (PAs) is considered. The nonlinear PAs distort the transmitted signal causing performance degradation. The common approach to mitigating nonlinear distortions is linearization of the PAs. For the MISO system we propose to apply a more generic approach in the form of an entire nonlinear MISO channel linearization, applied jointly for all PAs. It is shown that the results of this approach outperform those of the approach based on local linearization of each PA separately. An iterative technique is proposed to implement the entire MISO channel linearization. This technique requires knowledge of the channel state information and a model of the PAs at the transmitter. The performance of separate local and collective joint linearization is evaluated and compared in terms of the Symbol Error Rate (SER).

Distortion cancellation precoding for OFDM-SDMA downlink with nonlinear power amplifiers

In this work we consider an OFDM-SDMA downlink with a real life, nonlinear Power Amplifier (PA). It is well known that a nonlinear PA produces nonlinear distortions. We propose a novel iterative algorithm based on Zero Forcing (ZF) precoding to cancel the nonlinear distortions seen at the mobile devices while preserving the interference-free reception due to ZF. The proposed algorithm also keeps the out-of-band radiation of the transmitted signals low, in order to satisfy spectral purity requirements. For a low Back-Off (BO) scenario, where the nonlinear distortions are strong, the proposed algorithm shows a much lower Symbol Error Rate (SER) and much higher power efficiency than the well known ZF-SDMA with a real life PA.

Maximum Likelihood Detection of Nonlinearly Distorted OFDM Signal

This paper deals with a Maximum Likelihood receiver for a nonlinearly distorted OFDM signal over a flat channel with AWGN. The nonlinearity destroys the orthogonality between subcarriers, consequently, a per subcarrier decision, used when the linear PA is considered, is no longer optimal. We propose a sub-optimal receiver based on the Maximum Likelihood (ML) criterion. The ML receiver has to find the minimum Euclidean distance between the received vector and a set of all possible OFDM symbols passed through the same nonlinearity. This approach has exponential complexity. To reduce the complexity, we propose a sub-optimal receiver that minimizes the Euclidean distance, seen as a cost function, by the gradient descent algorithm. Unfortunately, due to the nonlinearity, the cost function is non-convex. In order to overcome this obstacle, we propose a method to classify the solution, i.e., to decide if the achieved minimum is local or global. We modify the gradient descent algorithm to avoid convergence to a local minimum. It is shown that the proposed receiver outperforms the simple OFDM and iterative receivers in terms of symbol error rate (SER) performance.

Optimization of OFDM system with nonlinear power amplifier and modified iterative receiver

OFDM signal suffers from high Peak to Average Power Ratio (PAPR). This dictates the necessity to drive the nonlinear power amplifier with high back-off, which leads to low power amplifier efficiency. In this paper we consider system that contains Iterative Clipping and Filtering (ICF) at the transmitter for PAPR reduction and modified iterative receiver (MIR) for demodulation. The MIR demodulate the distorted received signal. The distortions are created by the ICF and the nonlinear PA. The system architecture provides two main degrees of freedom given by the two back-offs: BO1 for ICF and BO2 for the power amplifier. We suggest to exploit these degrees of freedom in order to optimize the system performance expressed by a triplet: power efficiency (PE), adjacent channel power ratio (ACPR) and symbol error rate (SER). The optimal pair [BO1 BO2] depends on the priority among ACPR, SER and PE. Once the priority is determined, the optimal pair [BO1 BO2] that optimizes the system performance is found. An example of a hierarchy is given.