## Description

# A Low Complexity I/Q Imbalance Calibration Method for Quadrature Modulator

**Existing System:**

Analog quadrature modulator (direct conversion transmitter) offers compact and low-cost implementation. The simplicity of the topology makes it attractive for high level of integration. However, imperfections from gain and phase mismatches as well as dc offset deteriorate the out-of-band emission performance. Therefore, it requires the compensation for these errors, either with a digital signal processor (DSP) or analog circuits. Many works based on the DSP techniques were proposed to compensate for I/Q imbalance. Sen et al. utilized equation-based optimum test stimulus and power detection based on nonlinear phaseto-amplitude conversion. Witt and van Rooyen presented an I/Q imbalance extraction algorithm utilizing the Cholesky decomposition of the signal’s covariance matrix. Valkama et al. proposed special reference signal generation to adaptively compensate for I/Q imbalance. However, DSP-based compensation is computationally intensive so that it requires extensive resources.

Furthermore, extraction of mismatch parameters relies on nonlinear estimation, and thus convergence is not guaranteed. Analog techniques for I/Q imbalance compensation can be done with either loop-back receiver measurement or baseband signal tuning based on the spectrum measurement. In phase and quadrature baseband signals are transmitted sequentially and this time-sequenced injection method enables the calculation of quadrature mismatch parameters by measuring quadrature loopback receiver outputs. Similarly, the work in utilized two consecutive measurements with different attenuation settings. However, extraction of transmitter I/Q imbalance with the loop-back method is disturbed by the limited residual sideband (RSB) performance of the receiver. Coupling between the loop-back receiver and the transmitter further degrades the accuracy of the loop-back method. In local-oscillator (LO) feed through is first canceled by compensating signal due to on-chip digital to analog converter (DAC). I/Q imbalance is then compensated manually by adjusting the gain and phase of quadrature baseband signals. Patent from depicts the same idea of adjusting the gain and phase of the quadrature baseband signals. Note that the works in compute (extract) the gain and phase imbalance parameters with specially designed input sequence and the loop-back receiver. On the other hand, it cannot compute the imbalance parameters but manually adjust the baseband signals to improve the RSB performance based on the spectrum measurement.

**Disadvantages:**

- Have more Calibration in gain
- Have more interference and frequency extraction in reception.
- Not yet tested bit error rate measurement
- Have more phase mismatches signal

**Proposed System:**

In a recent technology of digital and analog signal processing applications will have lot of interference will occurs due to signal transmission traffic in air medium, thus transmission and reception of any RF signal will have more interference, calibration, jitter noise in reception part. In this digital modulation and demodulation technique of Quadrature transmission will have I/Q based differential signal method to reduced this calibration imbalance but some error will occur in gain and phase mismatches on high frequency range transmission, due to this problem, here the proposed work will designed a Quadrature amplitude modulation in phase shift keying method of QAM-QPSK modulation and demodulation in 4, 8, 16 quadrant in differential signal processing with using technique of digital frequency calibration with carrier signal generation. This method is fully design with digital quadrature method in FPGA with using VHDL, these output will measure in the extraction, calibration of gain and phase mismatch and also verified in the compared terms of bit error rate, area, delay and power with using Xilinx FPGA S6LX9-2FG144.

**PROPOSED I/Q IMBALANCE CALIBRATION METHOD:**

In general, all the analog components such as filter, up-conversion mixer, and DAC of the I/Q branches contribute to the imbalance.

Sources of all the gain mismatches can be aggregated into a single parameter g. Similarly, a parameter θ denotes the amalgamated phase mismatch of the transmitter. Then, a generalized block diagram of a direct-conversion transmitter is presented in Fig. 1. Up-converting signal xLO(t) due to the quadrature modulator is expressed as

xLO(t) = cos(ωLOt) + j(1 + g)sin(ωLOt + θ )

= K1e jωLOt + K2e−jωLOt ……(1)

where the imbalance coefficients K1 and K2 are given by

K1 = 1 2 (1 + (1 + g)e j θ ) …..(2)

K2 = 1 2 (1 − (1 + g)e−j θ ). ……(3)

With positive baseband signal (xBB(t) = e jωBBt), the transmitter output signal (xRF(t)) is written by

xRF(t) = Re[xBB(t) · xLO(t)]

= Re[K1] cos(ωusbt) − Im[K1]sin(ωusbt) + Re[K2] cos(ωlsbt) + Im[K2]sin(ωlsbt) …(4)

where ωusb = ωLO + ωBB and ωlsb = ωLO − ωBB denote the transmitted signal located at the upper sideband and lower sideband frequencies with respect to ωLO. With no mismatches (g = 0 and θ = 0) between I/Q branches, K1 and K2 are set to 1 and 0, respectively. Then, the transmitted signal has only the single tone at the upper sideband frequency of ωLO as desired. The power ratio between upper sideband and lower sideband signal is RSB suppression ratio whose expression is

RSBraw = (Power)lsb /(Power)usb = Re2[K2] + Im2[K2] /Re2[K1] + Im2[K1] = |K2|2 |K1|2

= 1 − 2(1 + g) cos(θ ) + (1 + g)2/ 1 + 2(1 + g) cos(θ ) + (1 + g)2 ……. (5)

Under small imbalance conditions (e.g., g < 0.1, θ < 3◦), RSBraw can be approximated as

RSBraw ≈ (g)2 + (θ )2 4 …… (6)

The derivation mentioned earlier includes the implicit assumption that there is no I/Q mismatch due to the baseband signal. The assumption is valid since the digital baseband can generate very accurate quadrature signal in contrary to analog quadrature transmitter. Note that the power amplifier does not create any quadrature mismatch and its transfer function can be assumed to be unity here, i.e., xRF(t) = xmod(t). With the mismatch parameters at the baseband (−gerr and θerr for gain and phase mismatches, respectively), the baseband signal is evaluated in the following. Negative sign of the gain mismatch parameter (−gerr) is introduced for computational convenience

xBB(t) = cos(ωBBt) + j(1 − gerr)sin(ωBBt + θerr)

= J1e jωBBt + J2e−jωBBt …..(7)

where the baseband imbalance coefficients J1 and J2 are given by

J1 = 1 2 (1 + (1 − gerr)e j θerr) …..(8)

J2 = 1 2 (1 − (1 − gerr)e−j θerr) …… (9)

With imbalanced baseband signal (xBB(t)) and up-converting signal (xLO(t)), the transmitter output signal (xRF(t)) can be derived as

xRF(t) = Re[J1K1 + J2K2] cos(ωusbt) + Im[−J1K1 + J2K2]sin(ωusbt) + Re[J1K2 + J2K1] cos(ωlsbt) + Im[J1K2 − J2K1]sin(ωlsbt)….. (10)

Following the same procedure with the ideal baseband signal case (4) and (5), RSB for transmitter output (xRF(t)) including the mismatches at both baseband signal and up-converting signal can be written as

RSB= 1 − 2(1 + g)(1 − gerr) cos(θ − θerr) + [(1 + g)(1 − gerr)] 2 1 + 2(1 + g)(1 − gerr) cos(θ + θerr) + [(1 + g)(1 − gerr)]2 ….. (11)

With small imbalance conditions for both baseband and up-converting signal I/Q branch, RSB is approximated as

RSB ≈ (g − gerr)2 + (θ − θerr)2 /4 ….. (12)

Equations (6) and (12) indicate that RSB in (g,θ) plane is represented as a circle with radius (2√RSB) centered at (gerr, θerr). With the aim of obtaining gain and phase mismatch parameters (g, θ) in the form of a circle, three measurements are necessary to be performed. While many permutations of test stimulus exists, Fig. 2 shows the mismatch parameter extraction and its calibration method [Fig. 2(a)], and the mismatch parameter extraction procedure [Fig. 2(b)–(d)] without loss of generality.

The first measurement with no baseband mismatch condition [Fig. 2(b)] dictates that any gain and phase mismatches of the transmitter on the same radius can be a possible solution. The second measurement with baseband gain mismatch introduced [Fig. 2(c)] gives the definite solution for the gain mismatch but an indefinite solution for the phase mismatch parameter, whose solutions are derived as follows:

g = gerr 2 + 2 gerr (RSBraw − RSBshift1) …..(13)

θ = ± 4RSBraw − g2…… (14)

RSBraw = RSBshift1 dictates that the gain mismatch solution is g = (gerr/2). Otherwise, RSBraw ≷ RSBshift1 gives g ≷ (gerr/2). Finally, using the third measurement with both gain and phase imbalances of the baseband [Fig. 2(d)], the indefinite solution for the phase mismatch is determined without ambiguity. RSBshift2 ≷ RSBshift1 dictates that the phase mismatch is θ = ∓(4RSBraw − g2)1/2 (sol2 and sol1 in Fig. 2).

** Advantages:**

- Reduced the calibration imbalance and get a accurate gain.
- Have less interference and frequency extraction in reception.
- Tested bit error rate measurement
- Reduced the phase mismatches signal

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# A Low Complexity I/Q Imbalance Calibration Method for Quadrature Modulator

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