IQ imbalance estimation using broadcast signals
The present disclosure is described in the exemplary context of a Long Term Evolution (LTE) cellular network and is directed to a method and apparatus for estimating a gain and phase imbalance between an in-phase path and a quadrature path of a receiver operating in such a network. The method and apparatus specifically exploit channel coherence in time and frequency, and the properties of the Primary Synchronization Signal (PSS), and/or the Secondary Synchronization Signal (SSS), and/or information in the Physical Broadcast Channel (PBCH), all of which are defined by the LTE standard, to estimate the gain and phase imbalance of the receiver while it remains connected to a base station to receive data.
1. A method for estimating a gain and phase imbalance between an in-phase path and a quadrature-phase path of a receiver, the method comprising:
for each of a plurality of subcarrier pairs, adding a first symbol received over a first subcarrier of the subcarrier pair with a complex conjugate of a second symbol received over a second subcarrier of the subcarrier pair to form a statistic, wherein the number of subcarrier pairs in the plurality of subcarrier pairs is determined based on one or more signal-to-noise ratios associated with the plurality of subcarrier pairs;
determining two channel estimates using the statistics formed for the plurality of subcarrier pairs and using known values of the first and second symbols received over each of the plurality of subcarrier pairs; and
estimating the gain and phase imbalance using at least the two channel estimates and the first and second symbols received over each of the plurality of subcarrier pairs.
2. The method of claim 1 , wherein the first and second subcarriers of each of the plurality of subcarrier pairs are located at equal distances from a direct current (DC) subcarrier and on opposite sides of the DC subcarrier.
3. The method of claim 1 , wherein the number of subcarrier pairs in the plurality of subcarrier pairs is determined based on a coherence bandwidth associated with channels over which the plurality of subcarrier pairs are received.
4. The method of claim 1 , wherein a difference in time between when the first and second symbols of a first one of the plurality of subcarrier pairs are received and when the first and second symbols of a second one of the plurality of subcarrier pairs are received is constrained based on one or more signal-to-noise ratios associated with the plurality of subcarrier pairs.
5. The method of claim 1 , wherein a difference in time between when the first and second symbols of a first one of the plurality of subcarrier pairs are received and when the first and second symbols of a second one of the plurality of subcarrier pairs are received is constrained based on one or more coherence times associated with channels over which the plurality of subcarrier pairs are received.
6. The method of claim 1 , wherein the first and second symbols received over one or more of the plurality of subcarrier pairs are associated with a primary synchronization signal, a secondary synchronization signal, or a physical broadcast channel.
7. The method of claim 1 , further comprising:
using linear processing on subcarriers of a signal down-converted by the in-phase path and the quadrature-path of the receiver to compensate for the estimated gain and phase imbalance.
8. The method of claim 1 , wherein the determining the two channels using the statistics further comprises:
using an overdetermined system of the statistics.
9. A method for determining an imbalance parameter for an in-phase path and a quadrature-phase path of a receiver, the method comprising:
for each of a plurality of subcarrier pairs, adding a first symbol received over a first subcarrier of the subcarrier pair with a complex conjugate of a second symbol received over a second subcarrier of the subcarrier pair to form a statistic, wherein the number of subcarrier pairs in the plurality of subcarrier pairs is determined based on signal-to-noise ratios associated with the plurality of subcarrier pairs;
solving for channel estimates using the statistics formed for the plurality of subcarrier pairs and using known values of the first and second symbols received over each of the plurality of subcarrier pairs; and
solving for an imbalance parameter using the channel estimates and the first and second symbols received over each of the plurality of subcarrier pairs,
wherein the first and second subcarriers of each of the plurality of subcarrier pairs are located at equal distances from a direct current (DC) subcarrier and on opposite sides of the DC subcarrier.
10. The method of claim 9 , wherein the number of subcarrier pairs in the plurality of subcarrier pairs is determined based on a coherence bandwidth associated with channels over which the plurality of subcarrier pairs are received.
11. The method of claim 9 , wherein a difference in time between when the first and second symbols of a first one of the plurality of subcarrier pairs are received and when the first and second symbols of a second one of the plurality of subcarrier pairs are received is constrained based on one or more signal-to-noise ratios associated with the plurality of subcarrier pairs.
12. The method of claim 9 , wherein a difference in time between when the first and second symbols of a first one of the plurality of subcarrier pairs are received and when the first and second symbols of a second one of the plurality of subcarrier pairs are received is constrained based on one or more coherence times associated with channels over which the plurality of subcarrier pairs are received.
13. The method of claim 9 , wherein the first and second symbols received over one or more of the plurality of subcarrier pairs are associated with a primary synchronization signal, a secondary synchronization signal, or a physical broadcast channel.
14. The method of claim 9 , further comprising:
using linear processing on subcarriers of a signal down-converted by the in-phase path and the quadrature-path of the receiver to compensate for the estimated gain and phase imbalance.
15. An apparatus comprising:
an adder module configured to add, for each of a plurality of subcarrier pairs, a first symbol received over a first subcarrier of the subcarrier pair with a complex conjugate of a second symbol received over a second subcarrier of the subcarrier pair to form a statistic, wherein the number of subcarrier pairs in the plurality of subcarrier pairs is determined based on signal-to-noise ratios associated with the plurality of subcarrier pairs;
a channel estimator configured to estimate channels using the statistics formed for the plurality of subcarrier pairs and known values of the first and second symbols received over each of the plurality of subcarrier pairs; and
an imbalance estimator configured to estimate a gain and phase imbalance using the channel estimates and the first and second symbols received over each of the plurality of subcarrier pairs.
16. The apparatus of claim 15 , wherein the first and second subcarriers of each of the plurality of subcarrier pairs are located at equal distances from a direct current (DC) subcarrier and on opposite sides of the DC subcarrier.
17. The apparatus of claim 15 , wherein the first and second symbols received over one or more of the plurality of subcarrier pairs are associated with a primary synchronization signal, a secondary synchronization signal, or a physical broadcast channel.
18. The apparatus of claim 15 , further comprising:
a compensator configured to perform linear processing on subcarriers of a signal down-converted by an in-phase path and a quadrature-path of a receiver to compensate for the estimated gain and phase imbalance.
19. The apparatus of claim 15 , wherein the apparatus is implemented in a Long Term Evolution receiver.
20. The apparatus of claim 15 , wherein the channel estimator is configured to estimate the channels using an overdetermined system of the statistics.