Impact of Hardware Impairments in Wireless, MIMO OFDM Communication Systems

Transcription

1 119 TERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY Impact of Hardware Impairments in Wireless, MIMO OFDM Communication Systems Stephan Lang, Member IEEE, Babak Daneshrad, Member IEEE University of California, Los Angeles, California 99 Abstract- Hardware impairments are critical when building a wireless communication system. A key problem for a designer is to estimate the effect of certain hardware impairments on the overall performance of a system before building it. In this paper, the impact of hardware impairments such as phase noise, I/Q mismatch, power amplifier nonlinearity and noise from switched power supplies is studied thoroughly for MIMO OFDM based wireless communication systems. Results from extensive simulations on the impact of hardware impairments are presented. The impact is presented as a loss in SNR in the demodulation process at the receiver and is used as a figure of merit for all impairments studied here. This loss in SNR can be integrated into the link budget calculation of the system. The results are presented in graphs and tables and are approximated with rather intuitive formulas. The paper presents results for up to MIMO systems, for outages of 1%, % and 1% and for 4QAM, 16QAM and 64QAM constellations. Index Terms- Hardware Impairments, MIMO OFDM, Wireless Communication Systems, I/Q mismatch, Phase Noise, Power Amplifier Non- Linearity, Switched Power Supply Noise I. TRODUCTION The impact of hardware impairments can be serious for the overall performance of high complexity MIMO OFDM (Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing) based wireless communication systems. Many impairments have been studied in literature and theoretical derivation show the impact of these impairments. In [1], the impact of carrier phase noise on M-QAM modulated OFDM signals in an additive white Gaussian noise (AWGN) channel is analytically evaluated for a SISO (Single Input Single Output) system in terms of bit error rate sensitivity. Effects from phase noise such as Inter-carrier interference (ICI) and common phase error (CPE) are discussed in [2] for a SISO system. In [3], the degradation in SNR (Signal to Noise Ratio), when adding phase noise to an SISO OFDM system with an AWGN channel, is derived and simulated. A correction technique to reduce phase noise is presented as well. I/Q mismatch has been analyzed in SISO OFDM systems in [] and MIMO OFDM systems with a rich scattering channel in [6]. In [7], the impact of non-linear amplifiers in SISO OFDM systems on the transmit spectrum and the bit error rate has been analyzed and simulated. Most of these analyses focus on SISO systems with AWGN channels. The analysis for MIMO systems operating over frequency selective channels is often tedious and not solvable in a closed form solution. This paper tries to fill this gap with extensive results from simulations with real world simulation models derived from actual measurements on testbeds. The results allow the designer to quickly estimate the impact of hardware impairments on the overall performance. The designer will know before building a system how much phase noise, I/Q mismatch, PA non-linearity and noise from switched power supplies can be tolerated for a desired throughput. One of the most common hardware impairment is phase noise [1]-[4], which arises from the generation of the needed local oscillator (LO) signals in the transmitter and receiver RF subsystem for up- and down-conversion respectively of the signal of interest. The LO signal can not be generated perfectly from a pure clock source with a phase locked loop (PLL). Jitter in the time domain signal translates into phase noise in the frequency domain signal which then affects the performance of the RF

2 12 subsystem. Another common hardware impairment is I/Q mismatch generated during I/Q modulation at the transmitter and I/Q demodulation in the receiver. I/Q mismatch is composed of three parts: I/Q gain, I/Q delay and I/Q phase mismatch [][6]. The gain and delay difference between the I-rail and Q-rail contributes to the I/Q gain and I/Q delay mismatch respectively. I/Q phase mismatch emerges from the 9 phase shifter in the analog I/Q modulator and demodulator. As for nonlinearity, the main contributor in wireless communication systems is the power amplifier (PA) on the transmitter side [7]. The challenge in biasing power amplifiers is the trade off between power efficiency and non-linearity. For maximum power efficiency, the mean output power delivered by the PA should be close to its saturation power. For best linear behaviour, the mean output power should be within the linear region of the PA. The last hardware impairment is noise from switched power supplies. Very sensitive analog circuits in the baseband and RF subsystem should be powered by a linear, clean power source. This is often not possible and therefore the noise generated from the switched power supplies can degrade the performance of the system or even prevent reasonable transmissions (i.e. in the case of unlocking a PLL circuit). Noise from switched power supplies is present in most systems but there is sparse research and literature available that discusses its impact on real wireless communication systems. This paper quantifies the impact of hardware impairments on the performance of wireless, MIMO OFDM communication systems. The results from extensive simulations show how much loss in Signal to Noise Ratio (SNR LOSS ) is incurred for a given amount of phase noise, I/Q mismatch, PA non-linearity and switched power supply noise. The results are summarized in graphs and tables. Moreover, for phase noise, PA non-linearity and switched power supply noise, polynomial fits to the data are presented which provide relatively accurate predictions of SNR LOSS. The paper is organized as follows. In section II, the Matlab based MIMO OFDM simulator and the concept of SNR LOSS is presented. The calibration procedure for the simulator, as well as the packet structure used in this study is explained. Sections III to VI show the results from the simulations of the 4 afore mentioned hardware impairments. The results are analyzed and summarized and important conclusions and trends are highlighted. Section VII concludes the paper. II. SIMULATION SETUP The simulations are performed for spatial multiplexing nxn ( to ) MIMO systems. For each MIMO configuration the constellation varied from 4QAM to 16QAM and 64QAM, resulting in 12 unique cases. For each case, the input at the receiver side was either high (), medium () or low () which brings the total number of scenarios to 36. The simulation results are then analyzed for outages of 1%, % and 1% readings from the resulting CDF (Cumulative Distribution Function) of SNR LOSS. For each simulation point in the CDF, 2 independent, randomly generated frequency selective channels were simulated and averaged. The simulations were performed for a fixed number of 26 subcarriers. For MIMO systems, the total output power was constant and equal to a SISO system (Single Input Single Output) independent of the number of transmitter antennas. This is referred to as power constrained. A. MIMO OFDM Simulator The MIMO OFDM simulator used in this study is a Matlab based simulator used in a non real time testbed previously developed at UCLA [4]. This simulator was used for the analysis of the hardware impairments by implementing a model for phase noise, I/Q mismatch, power amplifier non-linearity and switched power supply noise. The packet structure used in the simulator is shown in Fig. 1

3 121 Fig. 1 Packet Structure The first OFDM block (preamble) is used for acquiring the block boundary. The implemented block boundary detection algorithm is described in [1] for a SISO-OFDM system and was adapted for a MIMO-OFDM system. The preamble has a PN (pseudo noise) sequence on alternate subcarriers. At the receiver, a correlation is performed between the received samples and the known PN sequence which peaks if the received samples match with the PN sequence. This peak signal is used for the block boundary detection. After the block boundary detection algorithm follow 2 OFDM blocks for channel training. During the training, an RLS based, adaptive channel inverse estimator is implemented for MIMO decoding [8]. The channel is Rayleigh fading and has an rms delayspread RMS of 4ns. The training overhead is significant in this packet structure but it guarantees that all the algorithms have settled before the transmission of the actual data. Training overhead in this simulator was optimized and is discussed in [9]. The remaining of the 1ms long packet are OFDM blocks of payload data. In the frequency domain, the bandwidth of 2MHz was split into 26 subcarriers. 2 subcarriers are used for pilots. 16 subcarriers at each edge of the band and 18 subcarriers in the center (a total of subcarriers) are not used for testbed implementation purposes resulting in a useable bandwidth of 2MHz. The MIMO OFDM simulator was first calibrated by comparing its performance with theory for an AWGN and Rayleigh flat fading channel. For each SNR simulation point, 2 channel realizations were averaged. The calibration shows that the performance of the simulator perfectly matches the theoretical values up to a symbol error rate of 1-6 for AWGN channel and 1-4 for the Rayleigh fading channel. Matching lower symbol error rates would require averaging more channel realizations. Secondly, the performance of the hardware impairment models were compared with results of actual wireless measurements [1]. It was shown that the simulator mimics the wireless measurements within 1dB of difference and thus the results presented in this paper are comparable with actual wireless measurements. This calibration was the baseline for the simulations to follow. B. SNR LOSS The figure of merit for all the hardware impairment simulation results is SNR LOSS. SNR LOSS is defined as the difference between the input and output SNR OUT as shown in Fig. 2. Fig. 2 SNR loss The input is measured after the A/D converters and is computed by measuring the energy of the noise on each subcarrier (i.e. when there is no signal transmitted) and the energy of the signal plus noise on each subcarrier (during the payload). To measure the energy of the noise, many zero blocks are transmitted before the actual data stream. The zero blocks are just OFDM blocks with zeros on all subcarriers. is defined as follows: Energy( Signal + Noise) SNR = 1 (1) Energy( Noise) The output SNR OUT is measured at the input of the QAM slicer (equivalently at the output of the MIMO decoder). The SNR LOSS is then defined as: SNR LOSS =SNR SNR (2) OUT The SNR LOSS is basically a measure for the system performance loss due to the presence of

4 122 hardware impairments that are not corrected for by the MMSE based decoder. III. PHASE NOISE The phase noise model used in the simulation was derived based on phase noise measurements carried out on an actual local oscillator at 1KHz offset. The measured phase noise and the model are shown in Fig. 3. Phase Noise [dbc/hz] Fig Phase Noise Model α = GHz (top) 1.74GHz (bottom) 1/f α Approx. Model α = 2 α = Frequency Offset [Hz] Phase noise model The phase noise of a 1.74GHz and 3.48GHz local oscillator signal was measured and can be modeled with 1/f approximations. For very small frequency offsets, a 1/f 3 approximation closely models the actual phase noise. The phase noise at medium frequency offsets are best approximated with a 1/f 2 behavior and larger frequency offset closely with a 1/f 1 approximation. This results in a very complex model as shown in Fig. 3. For the simulation, a simplified model with a 1/f approximation was used which models the phase noise closely over a large frequency range. The simulation results for a 16QAM constellation with % outage in an nxn (n=1,2,3,4) MIMO setup are presented in Fig. 4. Fig Phase Noise Simulation: 16QAM, % outage Phase Noise [dbc/hz] Phase noise simulation results In general, a MIMO setup has higher SNR LOSS in comparison to a SISO setup because the power was not constrained in the phase noise simulation setup. Thus the added phase noise on the transmitter and receiver side in a MIMO setup was larger as it scales with the transmitted signal power Also, in the MIMO case, the receivers receive noise from several spatial streams. For a nxn MIMO setup, the SNR LOSS in 9% of all the cases will be upper bounded by 7dB provided that = and the phase noise power spectral density is -1dBc/Hz at 1kHz offset. In % of the cases, the SNR LOSS will be higher. As a second example, the maximum tolerable phase noise for an SNR LOSS of 1dB in 9% of all cases in the case is between -97dBc/Hz to -94.dBc/Hz, depending on the nxn setup. Observing the results in Fig. 4 for different shows that they are very similar in shape (just shifted along the x-axis). Therefore the results from the phase noise simulation could be summarized in a formula based on a polynomial approximation of the simulated results: SNRLOSS ( db) PN, SNR = a ( PN + SNR )^4 + b ( PN + SNR )^3 + c ( PN + SNR )^2 + d ( PN + SNR ) + e+ ( n 1) corr Constraints: dbc dbc PN : Hz Hz dbc PN < 8 SNR SNRLOSS = db Hz SNR :4 db... SNR < SNR 7.dB LOSS The polynomial formula in (3) allows calculating the SNR LOSS for a given phase noise and (3)

5 123 with the coefficients a through e of a polynomial. A correction term, corr, was added to correct for different QAM constellations and outages. The variable n refers to the nxn MIMO setup. The constraints apply to the range of phase noise and. Also, a minimum SNR OUT of 7.dB is needed for the simulator to produce reliable results. The coefficients and correction terms are summarized in Table 1. Table 1 Phase Noise Simulation: Polynomial Approximation 4 th order 3 rd order 2 nd order a b c d e rmse.27db.4db.63db outage corr (4QAM) corr (16QAM) corr (64QAM) 1%.3dB.dB.4dB %.6dB.7dB.7dB 1%.9dB 1.dB 1.dB For a 4 th order polynomial, the SNR LOSS can be estimated with an accuracy of.27db rmse (root mean square error). For a 3 rd order polynomial the accuracy decreases to.4db rmse and for a 2 nd order polynomial the rmse is.63db. The following conclusions can be drawn from the phase noise simulations: PN < -8dBc/Hz - has no impact on the performance (SNR LOSS is negligible). The QAM constellation has negligible impact on the SNR LOSS. The performance degradation for an nxn system is < n*1db in SNR LOSS. VI. I/Q MISMATCH I/Q mismatch occurs in the analog I/Q modulator and demodulator. Between gain, phase and delay I/Q mismatches, I/Q gain mismatch has the biggest impact on the performance of a wireless communication system [6]. Thus, only I/Q gain mismatch was considered in the simulation. The I/Q gain mismatch reported in the following simulation results was applied to all the transceivers in an nxn MIMO setup split equally between transmitter and receiver. The power was constrained in the MIMO case. The simulation results for a 16QAM constellation with 1% outage in an nxn (n=1,2,3,4) MIMO setup are presented in Fig.. Fig I/Q Gain Mismatch Simulation: 16QAM, 1% outage IQ Gain Mismatch [db] I/Q mismatch simulation results In general, a SISO setup has higher SNR LOSS in comparison to a MIMO setup because the power was constrained. Also, since the same I/Q gain mismatch was added to all the transceivers, MIMO setups perform better because the receivers profit from the spatial diversity. I/Q gain mismatches from practical I/Q modulator and demodulator are much smaller than shown in the simulations. Typical values are in the tenths of dbs. Therefore, even for high cases, I/Q gain mismatch does not have a severe impact on the performance of the system. V. PA NON-LEARITY A rather prominent hardware impairment present in any wireless communication transmitter is the non-linearity of the power amplifier. The PA, when driven close to saturation, behaves as a non-linear device and distorts the spectrum (spectral re-growth)[11]. On the other hand, from a power conservation point of view, it is desired to operate the PA as close to its saturation power as possible. Thus a balance between linearity and power efficiency must be maintained. An ideal, linear gain stage shows the following output to input relationship: A OUT = gain A (4)

6 124 The output amplitude A OUT is linearly dependent on the input amplitude A. Any practical gain stage experiences a saturation behavior for large input amplitudes. This can be modeled with the following output to input relationship [12]: A OUT gain A = gain A 1+ ASAT 1 2 p 2 p () The p-exponent in the denominator introduces the saturation behavior of the non-linear stage. Practical values for p are in the range of one to three. A SAT is the saturation amplitude. The exponent p was chosen to be one as it closely matches the saturation behavior of the PAs implemented on actual testbeds. The mean power P MEAN is backed off a certain amount from the saturation power P SAT to prevent non-linear distortions. The PA backoff (BO) is defined as: (6) PSAT BO[ db] = 1 log1( ) PMEAN The backoff value presented in the simulations is per PA in the individual transceiver. The power was constrained for MIMO simulations. The simulation results for a 4QAM constellation with % outage in an nxn (n=1,2,3,4) MIMO setup are presented in Fig Power Amplifier Non-Linearity Simulation: 4QAM, % outage Power Amplifier Non-Linearity Simulation: 4QAM, % outage Linearization Focal Point Backoff [db] Fig. 6 PA non-linearity simulation results In general, a SISO setup has higher SNR LOSS in comparison to a MIMO setup because the total power for a SISO system is the same as in a MIMO system (power constrained) and the maximum power of the PA was constant. As an example, the SNR LOSS for a nxn MIMO setup with 1dB backoff will be in 9% of all cases in the range of 4.dB to 1.dB given that =. As a second example, the minimal backoff needed for a SNR LOSS of maximum 1dB in 9% of all cases is between.db to 1.dB in the case. Fig. 6 also unveils an interesting trend that when extending the curves they all meet at a single focal point. This observation was exploited to condense the results from the PA non-linearity simulation into the equation shown below: SNRloss( db) BO, SNR = (2 BO[ db]) m corr (7) Constraints: BO : db...2db SNR :4 db,2 db, SNRLOSS < db SNRLOSS = db The formula in (7) allows calculating the SNR LOSS for a given backoff and. A correction term, corr, was added to correct for different outages and input. The factor m is the slope of the linearizations (Table2) and the constraints reflect the valid range of the backoff and Backoff [db] Table 2 Power Amplifier Non-Linearity Simulation: slope m

7 12 setup slope slope slope outage corr corr corr 1% db db db %.8 db 1.7 db 1.7 db 1%. db 1.1 db 1.2 db Important to realize is that the simulations were conducted with a fixed number of subcarriers although the number of subcarrriers has a big impact on the linearity of the PA. This has been analyzed and discussed in numerous publications [9] and is beyond the scope of this paper. VI. SWITCHED POWER SUPPLY NOISE Switched power supplies are very power efficient but generate a lot of noise degrading the performance of any wireless communication system. The switched power supply noise at the output of a switched power supply implemented on one of the testbeds [13] was captured with an oscilloscope. The frequency content of this captured signal is shown in Fig. 7. Power Fig. 7 34kHz Frequency [MHz] Switched power supply (frequency spectrum) The figure shows a strong peak at the switching frequency of 34kHz. The captured time domain samples of the switched power supply noise were added to the data stream in the transceiver for the simulation. The assumption is that all transceivers (in SISO and MIMO) are built on the same PCB and supplied by the same switched power supply so that the added switched power supply noise is common to all transceivers. The switched power supply noise figure of merit SIR (Signal to Interference Ratio) refers to a single transceiver. The power was constrained in the MIMO case. The simulation results for a 16QAM constellation with % outage in an nxn (n=1,2,3,4) MIMO setup are presented in Fig. 8. Fig Switched Power Supply Noise Simulation: 16QAM, % outage SIR [db] Switched power supply (simulation results) In general, a SISO setup has higher SNR LOSS in comparison to a MIMO setup because the power was constrained. Also the same switched power supply noise was applied to each transceiver in the MIMO setup and thus could easily be corrected during the demodulation process. As an example, the SNR LOSS for 3dB SIR will be in 9% of all cases between 4dB to 1dB in a case depending on the nxn setup. As a second example, the maximum tolerable SIR for an SNR LOSS of 1dB in 9% of all cases is between 27dB to 3dB (depending on the nxn setup) in the case. Observing the results in Fig. 8 for different values of shows that they are very similar in shape (just shifted along the x-axis). Therefore the results from the switched power supply noise simulation could again be summarized in a formula based on a polynomial approximation of the simulated results:

8 126 SNRLOSS ( db) SIR, SNR = a ( SIR SNR )^4 + b ( SIR SNR )^3 + c ( SIR SNR )^2 + d ( SIR SNR ) Constraints: SNR + e corr ( n 1) 2.6dB SIR :13 db... db SIR > + SNR SNRLOSS = db SNR : 4 db... SNR < SNR 7.dB LOSS The polynomial formula in (8) allows calculating the SNR LOSS for a given SIR and input with the coefficients a through e of a polynomial. A correction term, corr, was added to correct for different QAM constellations and outages. The last term in equation (8) corrects for the nxn setup. The variable n refers to the nxn MIMO setup. The constraints reflect the valid range of SIR and. Also, a minimum SNR OUT of 7.dB is needed for the simulator to produce reliable results. The coefficients and correction terms are summarized in Table 3. Table 3 Switcher Power Supply Noise Simulation: Polynomial Approximation 4 th order 3 rd order 2 nd order a b c d e rmse.49db.6db.81db outage corr (4/16/64QAM) 1% 3dB % 1.8dB 1% db For a 4 th order polynomial, the SNR LOSS can be estimated with an accuracy of.49db rmse. For a 3 rd order polynomial the accuracy increases to.6db rmse and for a 2 nd order polynomial the rmse is.81db. The following conclusions can be drawn from the switched power supply noise simulations: SIR > + has no impact on the performance (SNR LOSS is negligible). The QAM constellation has negligible impact on the SNR LOSS. VII. COCNLUSIONS (8) This paper discussed the analysis, modelling and simulation of hardware non-idealities in MIMO OFDM wireless communication systems. The four impairments phase noise, I/Q mismatch, PA non-linearity and switched power supply noise were described along with the Matlab simulator. The simulator was used in several wireless testbeds, was calibrated and closely mimics the actual behaviour of these testbeds. The results from the simulation were thus considered to be very close to actual measured impacts of these non-idealities on the testbed. The simulations were done for to MIMO setups with 1%, % and 1% outages. The constellation varied from 4QAM to 16QAM and 64QAM. The figure of merit is the SNR LOSS which is the loss in SNR in the receiver demodulator between the A/D converter and the QAM slicer. The presented simulation results allow the designer to quickly estimate the anticipated loss in SNR depending on the hardware impairment before building the testbed. The simulation results were approximated with a formula for an easy calculation of the expected SNR LOSS. A lower bound for the phase noise and an upper bound of the SIR due to switched power supply noise were presented. VIII. ACKNOWLEDGEMENT The Author would like to thank Dr. Raghu Raghu for providing the Matlab based MIMO OFDM simulator and for his support in generating the simulation results. REFERENCES [1] T. Pollet, M. Van Bladel, M. Moeneclaey, BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise, IEEE Transaction on Communications, vol 43, iss. 234, pp , Feb/Mar/Apr 199. [2] P. Robertson, S. Kaiser, Analysis of the effect of phase-noise in orthogonal frequency division multiplexing (OFDM) systems, IEEE International Conference on Communications, vol 3, pp , June 199. [3] G. Armada, Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM), IEEE transactions on

9 127 TERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY Broadcasting, vol 47, no 2, pp 13-19, June 21. [4] Stephan Lang, Raghu Mysore Rao, Babak Daneshrad, Design and Development of a.2 GHz Software Defined Wireless OFDM Communication Platform, IEEE Communication Magazine (Radio communications supplement), vol. 42, no. 6, June 24, pp. S6-S12. [] A.Schuchert, R. Hasholzner, A Novel I/Q Imbalance Compensation Scheme for the Reception of OFDM Signals, IEEE Transactions on Consumer Electronics, August 21. [6] R. M. Rao, B. Daneshrad, Analysis and Correction of I/Q Mismatch in OFDM Systems, IST Communications Mobile Summit, Lyon, France, June 24. [7] Elena Costa, Michele Midro, Silvano Pupolin, Impact of Amplifier Nonlinearities on OFDM Transmission System performance, IEEE Communication Letters, vol. 3, iss. 2, pp [8] F. Tufvesson, O.Edfors, M. Faulkner, Time and Frequency Synchronization for OFDM using PN- Sequence Preambles, VTC-1999/Fall, vol. 4, pp , New Jersey, [9] R. M. Rao, S. Lang, B. Daneshrad, Overhead Optimization in a MIMO-OFDM Testbed Based on MMSE MIMO Decoding, VTC Fall 24, Los Angeles, September 26 th -29 th 24. [1] R. M. Rao, S. Lang, B. Daneshrad, Field Measurements with a.2ghz Broadband MIMO-OFDM Communication System, IEEE Transaction on Wireless Communications, VOL. 6, NO. 8, August 27. [11] B. Razavi, RF Microelectronics, Prentice Hall PTR, Upper Saddle River, [12] Christoph Rapp, Effects of HPA- Nonlinearity on a 4-DPSK/OFDM-Signal for a Digital Sound Broadcasting System, Second European Conference on Satellite Communications, October 22-24, Liège (Belgium) [13] Stephan Lang, Babak Daneshrad, The Development and Application of a Dual-Band, 8x8, MIMO Testbed with Digital IF and DDFS, AusWireless 26, Sydney, March 3 rd -6 th 26