FDD Massive MIMO - Antenna Duplex Pattern an-Reciprocity : A Missing Brick

FDD MM studies generally recognize that instant CSI reciprocity between UL and DL does not readily apply or does not exist [3, 6, 5, 4, 7, 8, 9]. However, in average sense some spatio-frequency correlation is assumed¹¹1previous MM channel sounding campaigns [4, 5, 10, 6, 9], have used simple UE antennas which can impose the same spatial duplex illumination between UL and DL, i.e. the duplex separation is within the coherence angles and bandwidth of the channel [3, 6, 5, 4, 7, 8, 9].

This assumption means identity of the average UL and DL scattering cluster directions, which facilities relaxed CSI loop-back. However, if the radiation patterns of the UE antenna at the frequency bands of UL and of DL are diverging, then there is a good chance for significant different illumination of (or at least part of) scattering clusters. Since this inherent pattern reciprocity assumption is impacting average directional responses and thus extent of needed MM DL CSI to obtain optimal beam directions, it is crucial to assess its validity. The latter is the issue addressed in this paper.

From both antenna and propagation perspective, duplex pattern reciprocity is questionable if it can be generalized, even in the average sense - and this paper fills this gap with practical knowledge. While pattern reciprocity is achievable at base-station (BS) side (free propagation conditions), the story at the user equipment (UE) handset side may be very different and is of interest in this paper. The fast change of the radiation pattern over frequency, mainly depends on the size of the effective radiating structure. I.e., small simple antennas by them selves cannot change radiation pattern fast²²2fundamental antenna structures with size below ca. one wave length [13]. Thus, variation of the radiation pattern over frequency is partly due to the antenna element and partly due to the handset body and the user presence [11, 12].

We will discuss three situations considering UE antenna duplex patterns:

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  different antenna elements used for UL and DL.

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  multiple antennas used in (typically) DL direction (i.e. receive diversity). For SAR issues also different transmit (i.e. UL) elements could be used - even dynamically.

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  same antenna element used for UL and DL, but pattern changes noticeably over the duplex separation.

while the two first situations have obvious potential for an-reciprocal duplex patterns, the latter situation is an overlooked culprit for not meeting the aforementioned assumptions.

In line-of-sight (LOS) we essentially have an antenna pattern illumination, approaching an angular Dirac’s delta function. Thus no UL vs DL angular discrimination effects will be observed. On the contrary, as illustrated in Fig. 1, pronounced angular discrimination can occur at the BS side in obstructed propagation conditions - non-line-of-sight (NLOS), due to divergent UL vs. DL UE patterns in multi modal (i.e. several separated scattering clusters) or widely distributed scatterings scenarios.

As shown in the paper, FDD duplex pattern an-isotrophy does exist for practical handsets and at a level strong enough to expect noticeable impact in systems studies or operation. Throughout the paper, the normal spherical convention with azimuth $\phi$ and inclination $\theta$ - unless specifically noted, the elevation $\theta_{e}=\pi/2-\theta$ [13] is used (see Fig. 1). Furthermore, the variable dependencies of probability density distributions (pdf) $f$ is understood.

The paper is organized as follows. In Section II we discuss the duplex pattern similarity metrics. Section III contains analysis of power patterns from a wide range of measured commercial mobile phones. Section IV contains analysis of measured complex patterns of antennas in a mock-up handset. Section V concludes the paper.

Often antenna performance is based only on power ($p$) measures, i.e. $p\propto|h|^{2}$. We use the basic scalar descriptors for UE antenna efficiency as provided in [14]: 1) the effective isotropic radiated power is $p_{\mathrm{Tx}}|h_{\mathrm{Tx}}(\Omega)|^{2}=EIRP_{\Omega}=EIRP_{\theta}(\theta,\phi)+EIRP_{\phi}(\theta,\phi)$; and 2) effective isotropic sensitivity (for a given output signal-to-noise ratio SNR) is $(p_{\mathrm{Rx}}|h_{\mathrm{Rx}}(\Omega)|^{2})|_{\mathrm{SNR}}=EIS_{\Omega}=EIS_{\theta}(\theta,\phi)+EIS_{\phi}(\theta,\phi)$.

An obvious UL vs. DL pattern comparison is via the isotropic power balance ($IPB$) as $IPB\propto EIRP(\theta,\phi)\cdot EIS(\theta,\phi)$. $IPB$ will be a perfect sphere if UL and DL patterns are identical. However, deviations from a sphere can suggest exaggerate³³3for example, DL pattern nulls (i.e. high $EIS$) will exhibit large relative differences but result in little absolute signal difference. importance.

A better metric to compare patterns is a difference construct of normalized UL vs. DL isotropic patterns, as

with the normalizing means taken over $\Omega_{r}$ (i.e. spherical region of investigation). This normalization typically gives $0.4\lesssim\overline{\Delta IP}\lesssim 1$ and is not strictly bounding the metric, but it is simple and largely suppresses variations due to absolute levels.

A very compact dual-direction metric, compares DL vs. UL selectivities at maximum (DL) power azimuth direction ($\phi_{max,DL}\forall~{}\theta$ ) with its opposing (i.e. $\phi_{max,DL}+\pi$) direction, i.e. the cross link front to back ratio (FB)

This indicator shows whether the links focus on clusters in opposing directions. The maximization in (2) is taken across the elevation span of $\Omega_{r}$.

For scalar patterns, some polarimetric insight can be gained from the shear polarimetric power decomposition, i.e. cross polarization discrimination $\mathrm{XPD}=p_{\theta}/p_{\phi}$. The XPD expresses the purity of the linear polarization, but is not so suitable⁴⁴4as the logarithmic mapping in the dBs is double sided open scale, it becomes ambiguous to compare e.g. (near co-polar) $\Delta_{XPD}=XPD_{DL}(+20\mathrm{dB})-XPD_{UL}(+10\mathrm{dB})=10\mathrm{dB}$ vs. (near orthogonal) $\Delta_{XPD}=XPD_{DL}(+5\mathrm{dB})-XPD_{UL}(-5\mathrm{dB})=10\mathrm{dB}$. Similarly for the linear singled side open scale. for comparative purposes. Instead we use the linear polarization tilt $\psi\equiv\alpha=\arctan(E_{\theta}/E_{\phi})=\arctan(\sqrt{p_{\theta}/p_{\phi}})$, where $\alpha$ is the help angle in the full polarization description in section II-B2. When XPD is large or small we are close to linear polarization and the tilt will be close to $90^{o}$ or $0^{o}$, respectively. XPD close to 1 (0 dB) means $\psi\approx 45^{o}$, but the polarization can be anything from pure linear to circular, depending on actual phase relationships. We can though make a rough polarization discrimination assessment by looking at the tilt angle difference, as

As the scalar pattern fields have no sign or phase, $\psi$ and $\Delta\psi$ are restricted to the range $0-90^{o}$. Polarization mismatch reveals an extra signal difference influence on top of the directional gain impacts.

Global population (all phones and bands) statistics of correlations and other metrics, are taken either over the sphere (or rather down to the measurement limit $\Omega_{r}(\theta)\leq 150^{o}$, see next section) - or over a subset girdle above the horizontal plane ($0^{o}\leq\Omega_{r}(\theta_{e})\leq 30^{o}$).

Details about the handset measurement campaign, which results are used in this paper, can be found in [14]. Here, antenna radiation patterns in terms of EIRP and EIS of 16 contemporary mobile phones have been measured over-the-air (OTA) in 2G, 3G and 4G bands for both vertical and horizontal linear polarization. The operating bands [14],[2, Table 5.5-1] we use are (UL/DL center frequencies [MHz]) : UMTS900 (897.5/942.5); UMTS2100 (1950/2140); LTE800 (847/806); LTE1800 (1747.5/1842.5) and LTE2600 (2535/2655).

An example of power patterns in the horizontal plane ($\theta_{e}=0^{o}$) is shown in Fig. 2 for one of the tested smartphones (using $\Delta\phi=30^{o}$ for both UL and DL). The DL (EIS) data have been inverted (negation in dB) so they represent proportionality with antenna gain, just as the UL (EIRP) does. It is noticed how the total power (i.e. both polarization fully exposed) is a well behaved round shape. However, even in this case there is a front-to-back (FB) ratio difference between UL and DL patterns of order 10dB for the UMTS bands. This can cause emphasis on different scattering clusters.

The individual polarization patterns exhibit significant differences between DL and UL. This is quantified in Table I for all 16 phones tested where the DL field strength ($|E|\propto\sqrt{p}$) has been linearly interpolated to give same grid resolution of $15^{o}$ as for the UL, to use all data available. Only two phones (Doro 7070 and Huawei P9 Lite mini) do not have any marked high ($\Delta\mathrm{FB}$) pattern divergence in any band. Those two phones also exhibit lower end standard deviations of $\Delta IP$ and $\Delta\psi$, albeit the differences here between phones is not pronounced (therefore not included in Table I).

An example of $IPB$ for the horizontal plane is presented in Fig. 5, showing the tendency to a round (circle) shaped response, but also significant deviations for some bands and directions. The over all cross link gain behaviors via $\Delta{IP}$ and $\Delta{FB}$ metrics, are shown in Fig. 3 and 4.

The metric $\Delta IP$, shows population medians of $\overline{\Delta IP}+\sigma_{\Delta IP}$ around 0dB, while deciles are around the $\pm$2dB marks. So a noticeable portion of phones and bands have duplex pattern imbalances.

A very revealing and sensitive gain based metric is the $\Delta FB$, as it is a single maximization value and not a distribution over $\Omega_{r}$ (as $IPB$ and $\Delta IP$). The median of $\Delta\mathrm{FB}$ are modest around the 2.5dB mark. However, the upper decile for the girdle case, is around 12dB. I.e ca. 10% of the phones and bands exhibit a strong UL to DL divergent focus in environments simultaneously illuminating from opposing directions. This is a potential trouble maker situation for FDD-MM CSI UL to DL translation.

The polarization state variation in the horizontal plane via the XPD and tilt $\psi$ is shown by an example in Fig. 5. As discussed in Section II, we resort to only using $\psi$ for analysis. Here we observe significant occurrences of UL and DL exposing orthogonal tilts, i.e. strong depolarization if close to linear polarization is present.

The overall cross link polarization matching aspect is shown in the $\Delta\psi$ statistics in Fig. 6.

While the median of $\overline{\Delta\psi}+\sigma_{\Delta\psi}$ in the girdle case is around $24^{o}$, the upper decile of the maximum $\Delta\psi$ approaches $56^{o}$. In linear polarization conditions, this poses corresponding matching losses of order 0.8 dB and 5 dB, respectively. Thus the maximum $\Delta\psi$ represents noticeable diverging CSI for the duplex links.

Despite the lack of phase information in the data from [14] we use a correlation analysis which will include directional gain and to some extent the polarimetric state as well (when links are close to linear polarization, but differ in tilt). The result will be an optimistic UL-DL signal correlation (i.e. higher or equal to that of complex patterns). Consequently, we can use these correlations for worst case assessment.

We have performed high density ($\Delta\phi=\Delta\theta=3^{o}$) measurements of the two element antenna array mock-up phone (in the presence of a right hand phantom [11, Fig. 3(b)]) - in the same bands as [14], i.e. using the center link frequencies given in Section III-A. Antenna 1 is located at the top left corner of the mock-up phone, while antenna 2 at the bottom right corner as shown in [11, Fig. 3(b)]. Furthermore, to test effect of reduced duplex spacing, two extra frequencies are measured at the LTE2600 band, yielding three modified duplex cases, a: ($\overline{f_{UL}}+20\mathrm{MHz}$), b: ($\overline{f_{UL}}+20\mathrm{MHz}$ and $\overline{f_{DL}}-20\mathrm{MHz}$) and c: ($\overline{f_{DL}}-20\mathrm{MHz}$).