In an ideal case, results derived from I/Q demodulation performed by a receiver are further processed (e.g. filtered or amplified) through the receiver's I path and Q path respectively, to output a signal I and a signal Q, where the signal I and the signal Q are orthogonal. In a real case, in contrast to the ideal case, the signal I and the signal Q mentioned above are respectively re-defined as a signal I′ and a signal Q′, where the signal I′ and the signal Q′ are not orthogonal.
where ε is utilized for representing a gain error, and θ is utilized for representing a phase error. The above equations are well known in the art. Please refer to “RF Microelectronics” written by BEHZAD RAZAVI (published by Prentice Hall PRT, Page 135) for detailed descriptions.
First, it is assumed that the variation var(I(t)) of I(t) and the variation var(Q(t)) of Q(t) are equivalent to each other. Then, the variation var(I′(t)) of I′(t) and the variation var(Q′(t)) of Q′(t) can be derived according to the equations mentioned above, as listed in the following:
In addition, two gain compensation parameters KQ and KI can be further defined as follows:
Thus, different embodiments of the present invention methods and devices are capable of respectively estimating the power of the signal I′ and the power of the signal Q′ (i.e. estimating a square value of the signal I′ and a square value of the signal Q′) and adjusting at least one of the gain of the signal I′ and the gain of the signal Q′ in real time according to the estimation mentioned above, to balance the power outputted through the I path and the power outputted through the Q path, in order to correct the gain error. According to this embodiment, after the gain adjustment mentioned above, the corresponding signals I″ and Q″ are respectively generated on the I path and the Q path, where the signal I″ and Q″ can be written as respective functions of time t, i.e. I″(t) and Q″(t). Please note that I′(t), Q′(t), I″(t), and Q″(t) have relationship(s) as shown in the following equations:
That is, in this embodiment, the gain error can be corrected by adjusting at least one of the gain of the signal I′ and the gain of the signal Q′, where the two gain compensation parameters KQ and KI are respectively utilized for adjusting the signals Q′ and I′.
Additionally, regarding correction of the phase error, an average value mean(I′(t) Q′(t)) of a product (I′(t) Q′(t)) of I′(t) and Q′(t) can be calculated first, as shown in the following:
Given:
as the value of the cosine function cos(θ/2) approaches 1 when θ is very small, the above equation can be re-written as follows:
By substituting Equation (7) into Equation (9), the following equation can be derived:
as (ε/2)2 is much smaller than one, the above equation can be written as follows:
By utilizing the above equations, sin(θ/2) and cos(θ/2) can be estimated, and therefore correction of the phase error by utilizing matrix operations can be further implemented.
Here, the corresponding signals respectively generated on the I path and the Q path after the phase adjustment are defined as a signal I′″ and a signal Q′″. According to the descriptions mentioned above, I(t), Q(t), I′(t), Q′(t), I″(t), Q″(t), I′″(t), and Q′″(t) have relationships as shown in the following equations:
Two of the matrixes to the right of the last equal sign in the above equation can be simplified according to Equation (3) as follows:
Equation (12) can be re-written as follows:
Regarding specific values of the gain error ε and the phase error θ, C is constant. Therefore, the signal I′″ and the signal Q′″ derived according to embodiments of the present invention methods are, respectively, the recovered versions of the signal I and the signal Q in an ideal case.
According to different embodiments of the present invention, the gain error can be corrected by adjusting the power of the signal Q′ (e.g. adjusting the power of the signal Q′ by utilizing the gain compensation parameter KQ) or adjusting the power of the signal I′ (e.g. adjusting the power of the signal I′ by utilizing the gain compensation parameter KI). In addition, by estimating sin(θ/2) and cos(θ/2), the phase error can be corrected through matrix operations. Thus, the signal I and the signal Q in the ideal case can be recovered.
As shown in
The square operation units 122-1 and 122-2 respectively calculate a square value of the signal I′ and a square value of the signal Q′. The arithmetic unit 124 calculates a difference between the square value of the signal I′ and the square value of the signal Q′, and the filter 128-1 performs filtering on the difference to generate the gain compensation parameter KQ. In addition, the arithmetic unit 126 adds the square value of the signal I′ and the square value of the signal Q′ to generate a sum, and the average operation unit 132-1 performs an average operation on the sum to generate a first average value. On the other hand, the multiplier 130 calculates a product of the signal I′ and the signal Q′, and the average operation unit 132-2 performs an average operation on the product to generate a second average value. As a result, the division operation unit 134 divides the first average value by the second average value to generate a quotient, and the filter 128-2 performs filtering (more particularly, loop filtering) on the quotient to generate the phase compensation parameter A_sin. Additionally, the calculation unit 138 receives the phase compensation parameter A_sin to generate the phase compensation parameter A_cos. According to the architecture shown in
In a variation of this embodiment, the multiplier within the gain compensation module 112 is positioned on the I path, rather than being positioned on the Q path, where the multiplier is utilized for performing gain compensation on the I path according to the gain compensation parameter KI, where the gain compensation parameter KI can be derived by calculating 1/KQ. In addition, the components to which the positive and negative input terminals of the arithmetic unit 124 are respectively coupled can be exchanged in this variation, where the positive and negative input terminals are respectively coupled to the square operation units 122-2 and 122-1. In this situation, the gain compensation parameter that is generated by utilizing the filter 128-1 to perform loop filtering on the difference calculated by the arithmetic unit 124 is KI. Similar descriptions are not repeated for this variation.
The positive/negative sign detection unit 136 detects a positive/negative sign of the product calculated by the multiplier 130 to generate a positive/negative sign detection result, and the filter 128-2 performs filtering on the positive/negative sign detection result to generate the phase compensation parameter A_sin′. Additionally, the calculation unit 138 generates the phase compensation parameter A_cos′ according to the phase compensation parameter A_sin′.
According to another embodiment of the present invention, the signal I′ and the signal Q′ inputted into the left of the closed loop architecture shown in
According to yet another embodiment of the present invention, the signal I′ and the signal Q′ inputted into the left of the closed loop architecture shown in
According to other embodiments of the present invention, the gain compensation parameter KQ and KI can be derived by estimation performed by open loop architecture for implementing Equation (3) and Equation (4) respectively. In another embodiment, the phase compensation parameters A_sin and A_cos (and the corresponding sin(θ/2) and cos(θ/2)) can be derived by estimation performed by open loop architecture for implementing Equation (10) and Equation (11) respectively. In another embodiment, the phase compensation parameters A_sin and A_cos (and the corresponding sin(θ/2) and cos(θ/2)) can also be derived by operations performed on the signal I″ and the signal Q″.
While compensating IQ imbalance according to the embodiment(s) of the present invention, the errors on the I path and the Q path have been considered at the same time when deriving the equations mentioned above as the basis of the descriptions disclosed above, so the present invention indeed provides general solutions for compensating IQ imbalance in receivers. The present invention can be widely applied to various kinds of wireless communication systems, without any limitation of being merely applied to Orthogonal Frequency Division Multiplexing (OFDM) architecture. Therefore, regarding communication systems of non-OFDM architecture, the present invention is capable of conquering application bottlenecks of imbalance between different paths.
In addition, preferred embodiments of the present invention, such as the embodiments mentioned above, generate the phase compensation parameters A_sin and A_cos by estimating sin(θ/2) and cos(θ/2), where θ is utilized for representing the phase errors of the I path and the Q path, as shown in
Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims.
Number | Date | Country | Kind |
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095119865 | Jun 2006 | TW | national |