Spectral broadening effects of high-power amplifiers in MIMO–OFDM relaying channels
© Ahmad et al.; licensee Springer. 2013
Received: 14 June 2012
Accepted: 10 November 2012
Published: 15 February 2013
The combination of MIMO–OFDM is a very attractive solution for broadband wireless services. Thus, the two prominent fourth-generation (4G) cellular systems, WiMAX and LTE-advanced, have both adopted MIMO–OFDM transmission at the physical layer. OFDM signal however suffers from nonlinear distortions when passed through high-power amplifier (HPA) at the RF stage. This nonlinear distortion introduces out-of-band spectral broadening and in-band distortions on the transmitted signals. 4G cellular standards have placed strict limits on the allowable spectral broadening in their spectrum mask specifications, to insure that data transmission on a given channel is not interfering significantly with an adjacent channel user. In this article, we characterize the out-of-band spectral broadening introduced by HPA when MIMO–OFDM signals are transmitted over multiple relaying channels. Expressions for the power spectral density of MIMO–OFDM signals are derived over multiple relay channels, and the cumulative effects of HPA on the spectrum of the transmitted signals are estimated. It is shown that depending on the number of relays and the relaying configuration employed, it may happen that a transmitted MIMO–OFDM signal with the transmit spectrum mask initially within the allowable set limit at the source node arrives at the destination violating this limit due to the cumulative effects of the multiple HPA’s in a multihop relaying channel.
KeywordsSpectral re-growth Amplifier nonlinearity Spectral mask MIMO–OFDM Relaying channels
Banelli and Cacopardi derived analytical expressions for the correlation function of the output of nonlinear HPA when the input to the amplifier is an OFDM signal. The power spectral density (PSD) of the signal is then calculated using the Fourier transform of the correlation function. Grad et al. studied spectral re-growth due to HPA nonlinearity in code-division multiple access (CDMA) systems. They obtained analytical expressions for the power spectrum of the CDMA signal at the output of the HPA, using a complex power-series model for the HPA characteristics. The out-of-band emission for the time division synchronous CDMA system is presented in, in terms of third-order intercept point (IP3). Cottais et al. derived expressions for the PSD of a general multicarrier signal at the output of a memoryless HPA. They also obtained a closed-form expression for the PSD of the special case of single-carrier signals. Helaly et al. examined the effects of the characteristics of the input CDMA signal on the resulting out-of-band spectral re-growth at the output of the HPA. They pointed out that, in addition to the HPA saturation level, the input signal’s threshold crossing rate and the variance of the clipped signal also contribute to the spectral re-growth. It is important to note that OFDM signals share some similarities with CDMA signals in this regard. Recently also, Gregorio et al. proposed a MIMO-predistortion (MIMO-PD) system that tries to compensate crosstalk and IQ imbalance in single-hop MIMO–OFDM communication systems, where they have shown that some reduction in the spectral re-growth can be achieved using the proposed MIMO-PD system. The effectiveness of such a compensation scheme in a multihop environment is however not yet known.
All the above-cited studies, and several others in the literature however, focused on the spectral re-growth due to HPA nonlinearity in a single-hop communication system. Recently, the two prominent 4G cellular systems, WiMAX and LTE-advanced, have defined relaying as an integral part of the network design[18, 19]. Thus, MIMO–OFDM signals transmitted in the 4G systems will frequently pass through one or more relay hops from source node to the destination node. Investigating the level of adherence to set limits on spectral broadening in cellular systems employing relaying technologies is therefore a deployment imperative. To the best of the authors’ knowledge, no work has presented a detailed study of the broadening effects of HPA nonlinearity on the spectrum of MIMO–OFDM signals in multihop relaying channels.
In this article, we characterize for the first time in the literature, the cumulative spectral broadening effects of multiple HPAs when MIMO–OFDM signals are transmitted over multihop relaying channels. Expressions for the PSD of a MIMO–OFDM signal are presented over multihop relay channels, each equipped with nonlinear HPA’s. It is shown that due to the cumulative effect of the multiple HPA’s in a MIMO link, and the cascade effect of many relaying channels in a multihop relay link, significant broadening effect occur which is much more than what would be observed in a single-hop transmission such as those characterized in[11–15]. We also show that for the amplify-and-forward (AF) and demodulate-and-forward (DemF) relaying options, the resulting cumulative re-growth may lead to spectral mask violations after a few relaying hops is traversed by the transmitted OFDM signal, even though the set limits were initially met at the source node [at the base station (BS) for downlink transmission, or at the mobile station (MS) for uplink transmission]. For the decode-and-forward (DF) relaying option, it is observed that less severe spectral broadening are observed. However, due to the latency problems associated with the DF relaying option which degrades quality of broadband signals, AF or DemF are the preferred candidates for broadband transmissions over relaying channels and therefore the spectral broadening issues observed here must be given considerable attentions in the design of broadband multihop relaying systems.
HPA nonlinearity model for MIMO–OFDM relaying channel
where j = 0, 1, …, R denotes the number of relay hops, γ j represents the clipping ratio (CR), Ais,j represents the input saturation voltage of each and every HPA employed at the j th relay hop, and P j represents the average input power into the HPA’s at the j th hop. The frequency domain (FD) expression of the signal above is then obtained by taking its discrete Fourier Transform (DFT).
Effect of HPA nonlinearity on the spectrum of MIMO–OFDM relaying system
PSD of the nonlinearly amplified OFDM signal at the BS
Using the result from, Equation (16)], Equation (15) can be approximated as, where B denotes the bandwidth of the signal. This approximation is valid if the spectrum of w0 j is flat across the bandwidth, which is true for the subcarrier-based analysis considered here. As the variance of the nonlinear noise due to HPA increases, the spectral re-growth of the transmitted OFDM signal increases as can be observed from Equation (15). Since the analysis above gives estimate of the spectral re-growth due to HPA per transmitting antenna, then for MIMO–OFDM system with N transmitting antennas, the overall spectral re-growth that occur due to HPA nonlinearity is given by.
PSD of the nonlinearly amplified OFDM signals at RS’s
Next we calculate the PSD of the nonlinearly amplified OFDM signals at RS’s. For this analysis, we consider two cases. In the first case, we consider that each RS has ability to perform MIMO signal processing on the received signal before amplifying and forwarding it onto the next hop, and thus we could examine the spectrum of the OFDM symbols obtained at each receiving antennas of the RS. This case corresponds to the DemF relaying option. In the second case, we consider that the RS does not have ability to perform MIMO signal processing on the received signal before forwarding onto the next hop. The RS simply AF the received OFDM signals at the RF stage without demodulating the OFDM signal. This case corresponds to the AF relaying option. AF has the best latency performance, and is attractive for broadband transmissions over relaying channels. The case of DF relaying option where RS actually decode data transmitted on each OFDM subcarriers before re-encoding/forwarding it is not analyzed here because the existing single-hop analyses in and other references are valid for that case using hop-by-hop analysis. However, we later include the DF case in the simulation results as a reference.
Case I: DemF relaying system
Case II: AF relaying system
where is the PSD of the transmitted OFDM symbol at the output of the HPA at the l th transmitting antenna of the (P - 1)th RS.
Simulation results and discussions
1024-FFT/IFFT parameters in 20 MHz bandwidth
Number of DC subcarriers
Number of guard subcarriers, left
Number of guard subcarriers, right
Number of data subcarriers
Subcarrier frequency spacing, Δf
19.53125 KHz (= 20 MHz/1024)
IFFT/FFT period, TFFT
Cyclic prefix duration, TCP
6.4 μs (TFFT/8)
Total OFDM symbol duration, TS
This article presents new insights on the out-of-band spectral re-growth due to HPA nonlinearities when MIMO–OFDM signals are transmitted over multiple relay channels. Expressions for the PSD of a MIMO–OFDM signal are presented when it is transmitted from a BS to the MS via multiple RSs, all equipped with nonlinear HPAs. It is shown that significant spectral re-growth occurs for the AF and DemF relaying options as the OFDM signal traverse one or more relay hops. For MIMO–OFDM systems with large number of relay hops and MIMO antennas, the cumulative effects of this re-growth can result in significant spectral broadening exceeding specified limits on the spectral masks. Hence, it is concluded from our results that even though the general MMR system where data could traverse any number of relay hops from source to destination have widely been studied theoretically, only the 2-hop version proposed by the IEEE 802.16j group may be advised for any practical deployments in MIMO–OFDM transmissions because of the potentials for spectral mask violations when going beyond 2-hop transmissions.
This study was sponsored by a grant (No. 09-ELE928-02) from The National Plan for Science and Technology (NPST), King Saud University, Saudi Arabia.
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