Design and Calibration of Wideband Multiport ... - IEEE Xplore

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 66, NO. 12, DECEMBER 2017

Design and Calibration of Wideband Multiport Homodyne Wireless Receivers Weiwei Zhang, Graduate Student Member, IEEE, Abul Hasan, Graduate Student Member, IEEE, Fadhel M. Ghannouchi, Fellow, IEEE, Mohamed Helaoui, Member, IEEE, Yongle Wu, Senior Member, IEEE, and Yuanan Liu, Member, IEEE Abstract— Complexity and computation effective design of multiport-based receiver system is proposed in this paper, and a simple calibration algorithm based on modified memory polynomial for the five-port receiver is used to demodulate the desired baseband signals from the received radio frequency signals. The theoretical foundation for the baseband signal recovery for the multiport system, basic circuit theory of the five-port receiver, and the proposed algorithm about how to retrieve the baseband signals from three output voltage signals are discussed. Finally, common modulated signals are used in the five-port receiver to validate the proposed calibration algorithm, and the measured performance in terms of error vector magnitude between the transmitted and the received signals are all less than 2%. Also, the performance comparison with the state-of-the-art multiport receivers is made to conclude that the five-port receiver with the proposed model can be one of the best cost and computation effective choices to accurately complete the signal recovery.

TABLE I A PPLICATIONS S UMMARY OF THE M ULTIPORT S YSTEMS

Index Terms— Calibration algorithm, error vector magnitude (EVM), five-port receiver, modified memory polynomial (MMP), modulated signals.

I. I NTRODUCTION INCE the six-port correlator was used for the reflectometer in 1977 by Engen [1], multiport techniques and systems have attracted more and more attention because of its low cost, easy fabrication, and wideband applications. Besides the reflectometers [1]–[4], the applications of the

S

Manuscript received November 18, 2016; revised June 27, 2017; accepted July 24, 2017. Date of publication September 12, 2017; date of current version November 8, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61422103 and Grant 61671084, in part by the National Key Basic Research Program of China (973 Program) under Grant 2014CB339900, in part by the BUPT Excellent Ph.D. Students Foundation under grant CX2016303, in part by the China Scholarship Council, in part by the Alberta Innovates Technology Future (AITF), in part by the National Science and Engineering Research Council (NSERC) of Canada, and in part by the Canada Research Chairs (CRC) program. The Associate Editor coordinating the review process was Dr. M. Pastorino. (Corresponding author: Weiwei Zhang.) W. Zhang is with the Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China, and also with the Intelligent RF Radio Laboratory, Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada (e-mail: [email protected]). A. Hasan, F. M. Ghannouchi, and M. Helaoui are with the Intelligent RF Radio Laboratory, Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada (e-mail: [email protected]; [email protected]; [email protected]). Y. Wu and Y. Liu are with the Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2017.2746458

multiport correlators, which have been summarized in Table I. Apart from the metrology applications [5], [6], six-port techniques can also be used in active millimeter load-pull measurement [7], low-velocity measurement [8], beam direction finding application [9], high-frequency phase-locked loop [10], phase discriminator [11], and zero-intermediate frequency (IF) receivers [12]–[24]. As we know, the radio frequency (RF) receiver plays a key role in the communication systems [25], and it takes charge of receiving the RF information and recovering the desired inphase and quadrature-phase (I /Q) baseband signals. Among the various kinds of RF receivers, the multiport receiver, shown in Fig. 1(a), features more advantages over the classical zeroIF receiver using two mixers and one 90° phase shifter (PS) shown in Fig. 1(b). Other advantages of multiport receivers are enumerated here [14], [15]. First, the circuit mentioned above and system nonidealities can be easily compensated for by using the appropriate calibration algorithms in the

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ZHANG et al.: DESIGN AND CALIBRATION OF WIDEBAND MULTIPORT HOMODYNE WIRELESS RECEIVERS

Fig. 1.

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Zero-IF receivers based on (a) multiport correlator and (b) two mixers and one 90° PS.

multiport receivers. Moreover, broadband system performance can be easily realized using multiport correlators. Furthermore, the multiport receivers have low cost and low power consumption because no active nonlinear mixers are required in the system, and therefore they can be easily integrated on chip. Hence, the multiport receivers, including the five-port receivers [13]–[18] and the six-port receivers [19]–[21], have been a hot area of research. Among the multiport receivers [12], as obvious from the nomenclature, the five-port receiver has one less output port than the six-port receiver and uses only three output voltage signals to recover the desired I /Q signals. Consequently, it possesses the reduced complexity as well as the system resources, and this aspect will be discussed in this paper even though the six-port receivers are more popular in the published literature. Also, the methods on how to recover the I /Q signals are of critical importance during the implementation of the five-port receiver. The digital methods have been adopted in most of the recently published works [13]–[17], however, none of these different approaches consider all system impairments, such as the nonideal performance of the five-port correlator, local oscillator (LO) leakage, direct current (dc) offset, I /Q signals imbalance, nonlinearity, and memory effect of the diode detectors (DDs). Moreover, the system performance will degrade further when the receiver system is used to receive wideband RF modulated signals. Therefore, a new calibration algorithm based on the modified memory polynomial (MMP) for the wideband five-port receiver is proposed to retrieve the I /Q signals from three output voltage signals, and it turns out to be one of the best choices to realize the I /Q signals demodulation. The remainder of this paper is organized as follows. Theoretical foundation of the baseband signal recovery for the multi-port receiving system and the calibration procedures about how to realize the MMP are discussed in Section II. The experimental setup, the measured results of the five-port receiver based on the MMP, and the traditional calibration algorithm (TCA) are discussed and compared in Section III. In addition, the performance comparison of the state-of-theart six-port and five-port receivers is presented in Section IV. A conclusion is drawn in Section V. II. T HEORY A BOUT THE M ULTIPORT R ECEIVER The block diagram of a generalized zero-IF receiver based on multiport architecture, which has one RF input port, one LO input port, and (K − 2) output ports for signal recovery,

is shown in Fig. 1(a). This receiver system essentially consists of one multiport correlator, (K − 2) DDs, (K − 2) low-pass filters (LPFs), (K − 2) analog-to-digital converters (ADCs), and one digital signal processor (DSP). A. Theoretical Foundation of the Baseband Signal Recovery It can be seen that one input port of the multiport correlator is fed with the RF signal having a complex envelope (X I + j X Q ). The LO signal, of which the frequency is the same as the carrier frequency of the RF signal and its amplitude is stable, goes into the other input port as shown in Fig. 1(a). The mathematical expressions [20] of the RF and LO signal phasors are defined as follows: aRF = X I + j X Q

(1a)

j ϕLO

(1b)

aLO = |aLO |e

.

The power Pk s (k = 1, 2, . . . , K ) [20] detected by (K − 2) identical diode detectors (DDk ), with which the outputs of the multiport correlator are terminated, can be written in terms of the scattering parameters (Sk1 and Sk2 ), the RF signal (aRF ), and the LO signal (aLO ) pk = |Sk1 aLO + Sk2 aRF |2 = Ak + Bk X I +Ck X Q + Dk X 2I + X 2Q (2) where Ak = |Sk1 |2 |aLO |2

(3a)

Bk = 2|Sk1 ||Sk2 ||aLO | cos(ϕLO + ϕk1 − ϕk2 )

(3b)

Ck = 2|Sk1 ||Sk2 ||aLO | sin(ϕLO + ϕk1 − ϕk2 ) Dk = |Sk2 |2 .

(3c) (3d)

Then, we can find that the mathematical expression of the power Pk s, which contains the I signal (X I ), the Q signal (X Q ), and the quadratic sum of I and Q signals (X 2I + X 2Q ), is a circle equation that can alternatively be written as (X I − E xk )2 + (X Q − E yk )2 = Rk2

(4)

where Ck 2Bk Dk E yk = − 2B k Dk2 Ck2 pk − A k + + . Rk = Bk 4Bk2 4Bk2 E xk = −

(5a) (5b) (5c)

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Fig. 2.


Graphical solutions based on (a) ideal and (b) nonideal conditions.

It can be seen that the center of each circle is decided by the scattering parameters of the five-port correlator and the LO signal, however, the radius is decided by not only the scattering parameters and the LO signal, but also the RF signal. If these three different circles intersect at one point as shown in Fig. 2(a), the I /Q signals (X I and X Q ) can be determined uniquely, and this is the theoretical foundation for the baseband signal recovery from a multiport receiver, of which the number of output ports should be more than or equal to three for unique determination of an I /Q point. It is worth mentioning that three circles always intersect at one point by adjusting the amplitudes of the RF and the LO signals. However, given many unpredictable circuit and system behavior, including the nonlinearity as well as the memory effects of the power detectors, the diode noise, the nonideal characteristics of the multiport correlator, and the RF and the LO signals, three circles usually have an intersection area, instead of an intersection point, making it very hard for the system to uniquely recover the desired signals as shown in Fig. 2(b). More information about this approach of modeling can be found in [26] and [27]. Hence, for this reason, an appropriate calibration algorithm is needed for the receiver system, and this algorithm decides the performance of the multiport system directly. Though the four-port receivers and their corresponding algorithms are reported in [22]–[24], it is very difficult for the system to decide which solution is uniquely adopted because two independent circles intersect at two points. One way to decide the unique solution under the certain conditions is discussed in [12]. In addition, the linear process cannot be used in the four-port receiver systems [12]. Therefore, the five- and the six-port receivers are more practical than the four-port receivers from the calibration and unambiguous I /Q signals recovery point of view. B. Basic Theory of the Five-Port Receiver The block diagram of a five-port receiver is shown in Fig. 3. It can be seen that the five-port correlator [12], which lies at the heart of the circuit, essentially consists of three PDs (PD1 –PD3 ) and one quadrature coupler (QC). The RF signal is fed into port 2, and the LO signal, of which the frequency is the same as the carrier frequency of the RF signal, goes into port 1 of the correlator circuit. Three outputs are terminated

Fig. 3.

Block diagram of the five-port receiver.

with identical DDs, LPFs, and ADCs, as shown in Fig. 3. The desired I /Q signals can be retrieved under an appropriate recovery algorithm by using the DSP. Power expression (2) can be written in a matrix form as follows: ⎤ ⎡ ⎤⎡ ⎤ ⎡ XI B 3 C 3 D3 p3 − A 3 ⎣ p 4 − A 4 ⎦ = ⎣ B 4 C 4 D4 ⎦ ⎣ X Q ⎦ . (6) X 2I + X 2Q p5 − A 5 B 5 C 5 D5 After some linear matrix transformation, we can easily get the desired baseband signals, that is ⎤ ⎡ ⎤⎡ ⎤ ⎡ XI α3 α4 α5 p3 − A 3 ⎣ X Q ⎦ = ⎣ β3 β4 β4 ⎦ ⎣ p 4 − A 4 ⎦ (7) X 2I + X 2Q γ3 γ5 γ5 p5 − A 5 where

⎡

α3 ⎣ β3 γ3

α4 β4 γ5

⎤ ⎡ B3 α5 β4 ⎦ = ⎣ B 4 γ5 B5

C3 C4 C5

⎤−1 D3 D4 ⎦ . D5

(8)

The I /Q signals can be written as the linear combination of (Pi − Ai ) with different coefficients and are listed as follows: XI = XQ =

5 k=3 5 k=3

αk ( pk − Ak )

(9a)

βk ( pk − Ak ).

(9b)


Fig. 4.

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Block diagram of the whole system.

Here, the coefficients (αk and βk ) should be constant under the fixed operating frequency. The parameters Ak , which are the average of the Pk , represent the dc component [13]. Therefore, if the coefficients (αk and βk ) and three voltages are known, it will be very easy to retrieve the desired I /Q signals. However, the coefficients are frequency dependent, and this method can only be applied to narrowband RF signal cases. Also, the six parameters are not enough to characterize the whole system and many of the known system imperfections should also be taken into account by means of a suitable calibration method [20] and [21]. C. Simplified Calibration Method Based on MMP

Fig. 5. Block diagram of the simplified calibration algorithm based on MMP.

As shown in Fig. 4, the five-port receiver system can be modeled as a nonlinear system, and we need to build its inverse model to make the whole system linear, namely, an appropriate calibration algorithm to model the inverse five-port receiver system is needed to make the whole system quasi-linear. Hence, the system imperfections and signal distortions, such as the nonideal characteristics of the multiport correlator, dc offset, I /Q signals imbalance, the nonlinearity, and the memory effects of the power detectors, have been taken into account when the inverse model cascaded after the system. Here, the calibration algorithm of the MMP [20] is adopted and listed as follows:

where

IEST (n) =

N M 5

q

akq p

v k [n − p]

Q EST (n) =

.

(14a) (14b)

The inverse model in (13) is depicted in Fig. 5 for better understanding. It can be observed that three output voltage signals v k (n) captured from the ADCs are the inputs to the model, and the retrieved signal SEST (n) = IEST (n)+ j Q EST (n) is the output. The dc-offset cancellation [13] can easily be realized by subtracting the average of the voltage signals as shown in the following equation: (15)

D. Calibration Procedures q

bkq p

v k [n − p]

(10b)

where M is the memory depth, N is the nonlinearity order of the inverse model, and the coefficients (akpq and bkpq ), which are decided by the five-port correlator, the amplitude of the LO signal, and the DDs, are real constants. For simplification, (10) can also be written as SEST (n) =

NM , . . . , C5 NM ]

v k = v k − average(v k ).

k=3 q=1 p=0

M 5 N

C = [C301 , C302 , . . . , C3

T

(10a)

k=3 q=1 p=0 N M 5

v 3 (n − 1), . . . ,

v 3N (n − M), . . . ,

v 5N (n − M)] V(n) = [

v 3 (n),

q

ckpq

v k [n − p]

(11)

k=3 q=1 p=0

where SEST (n) = IEST (n) + j Q EST (n) ckpq = akpq + j bkpq .

(12a) (12b)

Equation (11) can also be written in the matrix form as shown in (13) for easy calculation SEST (n) = V(n) · C

(13)

The MMP and its block diagram have been described in Section II-C. The calibration procedures, involving the determination of the coefficients and the recovery of desired I /Q signals, are explained in this section. The memory depth and the nonlinearity order are assumed to be equal for three DDs to simplify the calibration process. The entire calibration approach is summarized in the following five steps. 1) Time Alignment: Align three voltage signals with the transmitted I or Q signals. Let us assume that the numbers of samples in the transmitted I /Q signals and three voltage signals are all equal to L 0 . 2) DC-Offset Cancellation: Obtain the alternating current (ac) voltages by subtracting the average, as shown in (15). 3) Fixing System Orders: Determine the memory depth M (from 0 to 6) and the nonlinearity order N (from 1 to 6), and use a series of known training data from the transmitted signals [18], which has L 1 samples or entries, to determine the coefficients C = V1−1 · S1

(16)

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where

⎡

⎢ ⎢ V1 = ⎢ ⎣

V1 (M + 1) V1 (M + 2) .. .

⎤ ⎥ ⎥ ⎥ ⎦

(17a)

V1 (M + L 1 ) S1 = [STrain (M+1), STrain (M+2), . . . , STrain (M+ L 1 )]T. (17b) Here, the V−1 is the Moore–Penrose pseudo inverse 1 matrix of V1 according to matrix laboratory (MATLAB) software from the MathWorks. 4) I/Q Signals Recovery: Retrieve the estimated I /Q signals according to the following equation: S0 = V0 · C

(18)

where

Fig. 6.

Complete measurement setup of the five-port systems.

T

S0 = [SEST (M + 1), SEST (M + 2), . . . , SEST (L 0 )] (19a) ⎤ ⎡ V0 (M + 1) ⎢ V0 (M + 2) ⎥ ⎥ ⎢ (19b) V0 = ⎢ ⎥. .. ⎦ ⎣ . V0 (L 0 ) 5) Performance Evaluation: Calculate the performance metric in terms of error vector magnitude (EVM)

1 N |SEST (n)− STMT (n)|2 EVM = N n=1 ×100% (20) N 1 2 n=1 |STMT (n)| N where SEST (n) represents the estimated signals by using (18), and STMT (n) denotes the ideal transmitted signals. III. M EASUREMENT AND D ISCUSSION OF THE F IVE -P ORT R ECEIVER The measurement setup, which is shown in Fig. 6, has been built to verify the performance of the calibration algorithm based on the MMP. The baseband modulated signals with different bandwidths, such as quadrature amplitude modulation (QAM) signals, wideband code division multiple access (WCDMA) signals, wireless local area network (WLAN) signals, and long-term evolution (LTE) signals, are downloaded into the vector signal generator N5182A by using the MATLAB. Then, the RF signal with a preset carrier frequency is fed into the port 2 of the system. The LO signal, of which the frequency is the same as the carrier frequency of the RF signal and the amplitude is stable, is generated by ESG series signal generator E4422B and supplied to the port 1 of the system. The five-port correlator, which is shown in the dotted-line box in Fig. 6, consists of three PDs and one QC. Three output voltage signals from the DDs, which go into the Mixed Signal Oscilloscope MSO9404A (8 bit), are captured by the vector signal analyzer (VSA 89600) software. The desired I /Q signals are retrieved according to the calibration procedures discussed in Section II-D. Besides, the power of

Fig. 7. (a) Constellation and (b) power spectrum of the 16-QAM signal with 10-MHz bandwidth.

the RF and LO signals need to be set in advance. The mean power of the RF signal is set to be 7 dBm, and the LO power is 12 dBm in our experiments. Particularly, two signal generators, the oscilloscope and the VSA 89600 software, are all from the Agent Keysight Technologies. A. Measured Results of the Five-Port Receiver The 20 000 samples of the 16-QAM data, of which the bandwidth is 10 MHz and the sampling frequency is 80 MHz, are generated by MATLAB randomly, and the first 1000 training


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Fig. 8. Power spectra of (a) WCDMA signal with 3.84-MHz bandwidth and (b) LTE signal with 3-MHz bandwidth.

samples are used to determine the calibration coefficients. The experiment is carried out at a carrier frequency of 2 GHz. The constellation and the power spectrum of a transmitted and received 16-QAM signal are shown in Fig. 7. The EVM is only 1.14% when the memory depth is 2 and the nonlinearity order is 3. In addition, there are 20 491 samples of WCDMA signal, of which the bandwidth is 3.84 MHz and the sampling frequency is 61.44 MHz, and the first 1500 training samples are used to calibrate the coefficients. Similarly, 15 360 samples of the LTE signal are used to test the MMP calibration model and the first 1000 training data are used to calibrate for the model parameters. Its bandwidth is 3 MHz and the sampling frequency is 15.36 MHz. The carrier frequency of the WCDMA (LTE) signal is set to be 2.1 GHz (2.6 GHz). The power spectra of the transmitted and the received WCDMA and LTE signals are shown in Fig. 8. The EVM is 1.59% (1.5%) for the WCDMA (LTE) signal when the memory depth is 2 (3) and the nonlinearity order is 3 (3). B. Performance Comparison With the Five-Port Receiver Based on the Traditional Calibration Algorithm The TCA [13] is adopted here to be compared with the proposed MMP model and its model expression can be listed as follows: IEST (n) = Q EST (n) =

5 k=3 5 k=3

dk

v k [n]

(21a)

ek

v k [n]

(21b)

Fig. 9. (a) Constellation of the 64-QAM signal based on the MMP. (b) Constellation of the 64-QAM signal based on the TCA. (c) Power spectra of the 64QAM signal based on the MMP and TCA.

where

v k = v k − average(v k ).

(22)

It can be seen from (21) and (22) that the nonlinearity and the memory effects of the DDs are not taken into consideration in the traditional calibration algorithm [13], which is just a special case for the proposed MMP when M = 0 and N = 0. Different kinds of baseband modulated signals are tested based on the MMP and TCA, and the final measured results are calculated and summarized in Table II. The number of the parameters, which are used to characterize the whole system, is only six for the TCA. However, the number is different for the MMP with different modulated signals. Though the

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TABLE II S UMMARY OF THE M EASURED R ESULTS OF F IVE -P ORT R ECEIVER BASED ON THE MMP AND TCA

proposed calibration approach is more complex than the conventional approach, the measured results based on the proposed MMP are much better than those based on the TCA. The constellation of a 64-QAM signal with 4-MHz bandwidth based on the MMP and TCA are illustrated in Fig. 9(a) and (b), respectively. The corresponding power spectra are shown in Fig. 9(c). It can be seen that the constellation points match very well in Fig. 9(a), however, the received signals in Fig. 9(b) based on the TCA are very bad. The performance comparison can also be seen from their power spectra in Fig. 9(c). For LTE signals with 5-MHz and 10-MHz bandwidths, the power spectra based on the proposed MMP are much better than those based on the TCA as shown in Fig. 10. The received signals based on the MMP match very well with the transmitted signals; however, there are some spectrum regrowth for the received signals based on the TCA. C. Discussion About the Nonlinearity Order and the Memory Depth LTE signal with 20-MHz bandwidth is used to explain the effect of the nonlinearity order (N) and the memory depth (M) on the final results. The performance in terms of EVM versus different memory depth (from 0 to 6) and nonlinearity order (from 1 to 6) is plotted in Fig. 11. It can be seen that the performance is poor when the memory depth is zero, namely, the memory effects of the diodes and the frequency response of the correlator are not considered during the calibration. However, the EVMs are larger than 15% when the nonlinearity order is fixed to one (N = 1), namely, the nonlinearity of the diode is not taken into

consideration, too. Therefore, the conclusion that the memory effects and the nonlinearity of the diodes affect the system performance greatly can be drawn. The traditional calibration algorithm in [13] assumes that the system is static and linear which is a special case for the proposed algorithm (M = 0 and N = 1), and the final EVM reported is 18.21%. The model complexity and compensation capability can be controlled by its dimensions (M, N) as seen in Fig. 11. Therefore, a trade-off between the complexity and the performance can be achieved. For the proof-of-concept prototype, the case (M = 2, N = 4) for the LTE signal with 20-MHz bandwidth as shown in Fig. 11 can be chosen as the best complexity/performance trade-off. IV. P ERFORMANCE C OMPARISON W ITH THE S TATE - OF - THE -A RT M ULTIPORT R ECEIVER The measured results of the five-port receiver based on the proposed MMP and the performance comparison with the five-port receiver based on the TCA have been discussed in Section III to verify the correctness of the proposed calibration algorithm. Now, the performance comparison among the stateof-the-art multi-port receivers is made to verify that the fiveport receiver with the proposed MMP can be one of the best choices to realize the baseband signal recovery. A. Performance and Structure Comparison With the State-of-the-Art Six-Port Receivers It can be concluded that the performance of the fiveport receiver is much better than that of the six-port receivers [19], [20]. However, it is very close to that of the six-port receiver [21] from Table III. The calculated EVMs of


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TABLE III P ERFORMANCE C OMPARISON W ITH THE S TATE - OF - THE -A RT S IX -P ORT R ECEIVERS

Fig. 10. Power spectra of (a) LTE signal with 5-MHz bandwidth and (b) LTE signal with 10-MHz bandwidth.

B. Performance Comparison With the State-of-the-Art Five-Port Receivers

Fig. 11. EVM versus the nonlinearity order (N ) when memory depth (M) varies from 0 to 6 under the LTE signal with 20-MHz bandwidth.

the modulated signals are all less than 2% for the receivers in [21] and our work. Besides the performance in terms of the EVM, it can also be seen that the number of the DDs (LPFs and ADCs) for the five-port receiver is less than that of the six-port receiver, as listed in Table IV. In addition, the number of the unknown calibration parameters of the five-port receiver is also less than that of the six-port receiver [20], [21]. Hence, five-port receiver based on the MMP can be a better engineering choice that the six-port receiver since it features lower cost and less computation complexity.

It can be observed that the five-port receiver based on the proposed MMP model features better performance among the various implementations of the multiport receiver techniques. The TCA proposed in [13] has been tested and summarized in Table II, hence, it will not be listed in Table IV. The cost of the five-port receivers [17], [18], which consists of three mixers and three PSs, will be much higher than the five-port correlator in this paper. Besides, the results of this paper are much better than those in [17] and [18]. Furthermore, only five-port receiver in [18] is based on the hardware, and other receivers presented in [13]–[17] and [19]–[21], some of which have been listed in Tables III–V, are calibrated using software-based techniques. In [18], the detection circuit (called I /Q regeneration circuit) includes three amplifiers and eight resistors to retrieve the analog I /Q baseband signals before converting them into a digital format by two ADCs. It also takes lots of time to design and

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TABLE IV S TRUCTURE C OMPARISON B ETWEEN THE S IX -P ORT R ECEIVERS AND F IVE -P ORT R ECEIVER IN T HIS PAPER

TABLE V P ERFORMANCE C OMPARISON W ITH THE S TATE - OF - THE -A RT F IVE -P ORT R ECEIVERS

basic theory applied to the five-port receiver along with the proposed impairment and distortion mitigation algorithm are presented and discussed. A proof-of-concept receiver was developed to validate the proposed approach and benchmarks it against published works. The system imperfections that include the nonlinear distortion of the diodes, the frequency response of the six-port correlator, crosstalk between the in-phase and quadrature-phase channels, as well as dc offset are all taken into consideration by the proposed algorithm. The measured results show that the measured EVM values for different 3G and 4G signals are all less than 2%. Based on the obtained results one can infer that five-port correlator augmented with robust and accurate MMP calibration algorithm is a viable alternative for wideband homodyne wireless receivers for 5G and beyond applications. ACKNOWLEDGMENT The authors would like to thank A. Kwan and A. Abdelhafiz, who are both with the iRadio Lab, University of Calgary, for their technical support and suggestions during the measurement. R EFERENCES

test the baseband regeneration circuit. However, we only need to change the memory depth and the nonlinearity order of the algorithm to improve the system performance, which is much more convenient. Receivers using either hardware or software calibration techniques are selected to benchmark the proposed technique against most relevant previous works. It is anticipated that the calibration using appropriate digital software-based methods usually outperform the analog hardware based ones. For fair comparison, techniques that fall in the same category have to be benchmarked against each other’s, and it has been done in in Tables III–V. The proposed software-based digital calibration technique for the five-port receiver in this paper outperforms the previous software-based ones in Table V, because it mitigates the sources of distortion and impairments of the receiver such that the static and dynamic nonlinearities of the diodes, frequency response of the six-port junction, and dc offset due to the LO oscillator leakage. Also, it is anticipated that the proposed software-based calibration technique (EVM < 2%) outperforms by far the hardware-based one (EVM = 14%) presented [18] as shown in Table V. V. C ONCLUSION A complexity and computation reduced design approach for the homodyne receiver using multiport technique and an accurate calibration algorithm based on the MMP is proposed in this paper. The theoretical foundation of the multiport receiver,

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Fadhel M. Ghannouchi (F’07) has held numerous invited positions with several academic and research institutions in Europe, North America, and Japan. He has provided consulting services to a number of microwave and wireless communication companies. He is currently a Professor and the iCORE/Canada Research Chair with the Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada, and the Director of the Intelligent RF Radio Laboratory. He has authored or co-authored over 650 publications. He holds ten U.S. patents with five pendings. His current research interests include microwave instrumentation and measurements, nonlinear modeling of microwave devices and communications systems, the design of power and spectrum efficient microwave amplification systems, and the design of intelligent RF transceivers for wireless and satellite communications.

Mohamed Helaoui (S’06–M’09) received the M.Sc. degree in communications and information technology from the École Supérieure des Communications de Tunis, Aryanah, Tunisia, in 2003, and the Ph.D. degree in electrical engineering from the University of Calgary, Calgary, AB, Canada, in 2008. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, University of Calgary. He has authored or co-authored over 60 publications and holds 7 pending patents. His current research interests include digital signal processing, power efficiency enhancement for wireless transmitters, switching mode power amplifiers, and advanced transceiver design for software defined radio and millimeter-wave applications. Mr. Helaoui is a member of the COMMTTAP chapter in the IEEE southern Alberta section.

Yongle Wu (M’12–SM’15) received the B.Eng. degree in communication engineering and the Ph.D. degree in electronic engineering from the Beijing University of Posts and Telecommunications (BUPT), Beijing, China, in 2006 and 2011, respectively. In 2010, he joined the City University of Hong Kong, Hong Kong, as a Research Assistant. In 2011, he joined BUPT, where he is currently a Full Professor with the School of Electronic Engineering. His current research interests include microwave components and wireless systems design.

Yuanan Liu (M’92) received the B.E., M. Eng., and Ph.D. degrees in electrical engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 1984, 1989, and 1992, respectively. In 1984, he joined the 26th Institute of Electronic Ministry of China, Langfang, China, where he was involved in the development of the inertia navigating system. In 1992, he joined the EMC Lab, Beijing University of Posts and Telecommunications (BUPT), Beijing, China, as a Post-Doctoral Researcher. In 1995, he joined the Broadband Mobile Lab, Department of System and Computer Engineering, Carleton University, Ottawa, ON, Canada, as a Post-Doctoral Researcher. Since 1997, he has been a Professor with the Wireless Communication Center, College of Telecommunication Engineering, BUPT, where he is involved in the development of nextgeneration cellular system, wireless LANs, Bluetooth application for data transmission, electromagnetic compatibility design strategies for high-speed digital systems, and electromagnetic interference and expected value of mean square measuring sites with low cost and high performance.