Interference-Aware Accurate Signal Recovery in sub-1 GHz UHF Band Reuse-1 Cellular OFDMA Downlinks

OFDM channel estimation typically consists of obtaining the initial estimates at the pilot locations and then interpolating these estimates over the data subcarriers. The channel interpolation can be done using various methods such as linear interpolation, transform domain techniques, Wiener filtering, etc. [20]. The initial estimate quality will affect the quality of the interpolated channel.

The initial channel estimates can be obtained using frequency or time-domain least-squares, the linear minimum mean squared error (LMMSE) approach [21], the maximum likelihood (ML) approach [22] or the Bayesian MMSE approach [23]. The ML and time-domain least squares solutions (also called modified least squares or mLS) are found to be equivalent, and the MMSE solution reduces to ML at high signal-to-noise ratios (SNRs) [20, 23]. Thus, the mLS/ML is a minimum variance unbiased estimator that yields the best performance without knowledge about the channel correlation matrix. The mLS typically uses implicit DFT interpolation but can also work with other interpolation methods.

Signal detection in the presence of interference requires estimates of the channels of the interfering signals and that of the desired signal. These channels can be estimated by allotting them non-intersecting sets of frequency orthogonal pilot subcarriers like those described in [24]. However, such designs are not flexible as they would have to reserve pilot sets for the maximum number of BS towers that the user equipment (UE) is likely to detect. The number of such towers is calculated based on inter-site distances and path loss calculations alone. The combination of shadowing, fading, and dynamic interference control techniques can reduce the number of towers that interfere with the UE. A design based on the maximum number of BS towers in a region would be spectrally inefficient as it would require more pilot subcarriers in total.

The pilot-on-pilot allocation scheme multiplexes the pilot positions of the desired signal and interferers [24]. The pilots originating from different towers would then be separated with the help of codes rather than frequency orthogonality. Interfering pilots are either suppressed or cancelled out altogether in such an allocation [25, 26, 27]. The 5G-NR standards [28], for example, define the demodulation reference signal (DM-RS) sequence with such a pilot-on-pilot allocation by using orthogonal cover codes (OCCs). The channel is assumed to be static over the time and frequency resources over which the OCC is applied. This assumption makes DM-RS channel estimation suffer from performance degradation in channels with moderate to high selectivity [29, 30].

The sounding reference signal (SRS) in 5G also uses pilot-on-pilot arrangement [28]. However, the ports use distinct phase-shifted pilot sequences [31] rather than relying on OCC to separate the ports. The phase-shifted pilots result in time-shifted CIR for each port, which can then be separated by windowing the CIR [32]. However, this approach suffers from an error floor caused due to interpolation error that arises from zero padding in the CIR [33].

Co-channel interference must either be avoided or suppressed to decode the received signal. The transmitter powers at the different towers can be optimized by solving a system of equations as in [34] to minimize the CCI. The idea is to reduce the interference power while keeping the quality at the desired receiver at an acceptable level. While this method utilizes knowledge of channel states of the neighboring cells, recent works like [4] have proposed strategies that do not require this knowledge. CCI is suppressed in [7] by a combination of interference coordination and beamforming. Beamforming-based techniques use multi-antenna systems and cannot be practically deployed in the sub-1 GHz band. Power control faces limitations in the presence of multiple high-power interferers, as the transmitted power of a tower cannot be reduced without the associated cost of reduced throughput in its home cell.

Thus, either successive interference cancellation (SIC) or joint detection has to be employed to deal with interference at the receiver [35]. When the signal-to-interference ratio (SIR) is very high, the signal can be decoded satisfactorily by ignoring the interference. On the other hand, SIC can be employed when interference power exceeds the signal power by a large margin [36]. A joint detector such as the one described in [35, 37] is the best option when the signal and interference powers are comparable. Such detectors typically utilize a joint loglikelihood ratio (JLLR) metric [38] that accounts for the interferer constellations and the signal constellation in the minimum distance calculation.

The local oscillators of the different towers seen by the receiver induce frequency offsets with varying signs and magnitudes on the receiver. The total frequency synchronization error is comprised of the error in local oscillator frequencies and the relative Doppler of the mobile UE relative to the BS [39]. The term carrier frequency offset (CFO) will be used in our work to denote this combined error. CFO error is the major contributor²²2Inter-Block Interference (IBI) can also contribute to ICI in OFDMA cellular systems. In our work, we assume that there is sufficient cyclic prefix available on the downlink ITI signals from GPS synchronized BS to ensure that the UE determines an IBI-free window. to inter-carrier interference (ICI) in an OFDM or OFDMA system.

ICI cancellation literature focuses on removing or suppressing ICI in the time or frequency domains. Frequency domain approaches are limited and more complex as they mostly require reconstructing the ICI to cancel them [40]. On the other hand, a time-domain algorithm reduces the CFO before it is formed by the FFT operation [41]. Some methods, like [42], combine time domain and frequency domain approaches. Other methods for multi-transmitter CFO compensation involve singular value decomposition [43], lattice filtering [44], iterative design [45], etc. Complete compensation for the CFOs is not possible when multiple transmitters are present, as in the case of a reuse-1 system [45].

The downlink multi-transmitter CFO problem is distinct from CFO correction in the absence of co-channel interferers for uplink OFDMA links [46, 47]. CCI comes into the picture on the uplink in MIMO systems that use spatial multiplexing [48, 40]. Based on the downlink CFO estimate, the uplink compensation schemes generally assume some amount of precompensation by the UE [40]. UE-specific precompensation is not possible in the downlink as the towers simultaneously cater to multiple UEs.

The ICI contribution of multiple CFOs in the downlink is studied extensively in Coordinated Multi-Point (CoMP) literature [49, 50, 51, 52, 53]. A receiver in a CoMP system sees multiple towers from nearby cells that transmit desired information as a form of diversity [49]. The degradation due to multi-transmitter CFO is studied in [50]. The ICI that arises from downlink transmitters is an issue that reuse-1 systems share with CoMP schemes. The ICI compensation proposed in [51] utilizes a time-domain derotation factor that is a nonlinear function of the CFOs. Some corrections are proposed to this derotation factor in [52]. These methods assume that the difference between the minimum and maximum CFOs is less than half of the subcarrier bandwidth. The CFO correction is shifted to the transmitter side in [53] by first de-biasing the various CFOs at the receiver and then feeding back the residual to the respective towers. However, [53] assumes a quasi-static, non-selective channel and a single-carrier system.

Bold symbols denote vectors or matrices. Uppercase letters usually indicate the frequency domain, and lowercase letters are for the time domain. A hat on top of a parameter (e.g., $\hat{x}$) will represent an estimate of the parameter $x$. The subscripts $k$ and $m$ are used to denote the $k^{th}$ subcarrier and $m^{th}$ tower, respectively. Finally, the OFDM symbol index shall be denoted by $i$, and $j$ shall be reserved for the unit imaginary number.

The pilots are assumed to be equally spaced in the frequency domain from band-edge to band-edge to derive the CRLB. The residual ICI term $\mathbf{\tilde{I}}$ is merged with the noise term $\mathbf{\tilde{W}}$. Under these assumptions, following the steps given in Appendix 6, CRLB of the total variance of an unbiased joint estimator of $\mathbf{\tilde{h}^{\prime}}_{N_{cp}M}$ is given by

where $Tr(.)$ denotes the trace of a matrix. If the pilot spacing is assumed to be a power of 2, as given in Appendix 6, then

where the number of joint estimator pilots $N_{p}^{(J)}=N/2^{i}$, $i$ being a non-negative integer. Equation (12) is only approximate since the inverse will not be a pure identity matrix in the presence of guard subcarriers. Equation (11) can be used in such cases.

The JmLS estimator can be shown to be unbiased by simply substituting (5) into (9a) and performing the expectation operation. The MVUE property of an unbiased estimator can be proven if its MSE is shown to be equal to the CRLB. The total MSE of the JmLS estimates is now computed as follows:

The following expression is obtained by applying the steps given in Appendix 7. For unit amplitude pilots,

Equation (14) is the same as the CRLB expression (12) except for the regularization factor. When pilots are band-edge to band-edge, and the pilot spacing is assumed as per the CRLB derivation, regularization is unnecessary. For $\alpha=0$, (14) becomes equal to (11). Thus the proposed JmLS estimator in (9a) achieves CRLB and is an MVUE as well as an efficient estimator.

The CRLB of the joint estimator can now be compared to the mLS algorithm with a null-on-pilot allocation. An orthogonal pilot pattern with $N_{p}^{(O)}$ pilots per BS tower can be compared to the JmLS pilot-on-pilot pattern with a total of $N_{p}^{(J)}$ pilots. This orthogonal scheme can estimate CIR using mLS for each tower. This algorithm shall be called orthogonal modified least squares (OmLS) to distinguish it from the joint estimation scheme. The OmLS estimate is described by

$\mathbf{Y}^{(D)}_{p,m}$ is the vector consisting of only those subcarriers in $\mathbf{Y}^{(D)}_{p}$ that correspond to the $m^{th}$ tower as per the null-on-pilot scheme. The CRLB of OmLS is the special case of JmLS with $M=1$, except for a pilot boosting factor which shall be explained shortly. The CRLB of the total variance of the estimate for the $m^{th}$ user is then

The number of BS towers $M$ seen by the UE changes with time and location. OmLS can then only be designed for $N_{T}>M$ towers, the maximum number a UE is likely to see at the cell edge. Since $(N_{T}-1)N_{p}^{(O)}$ subcarriers are nulls in OmLS, the power of the $N_{p}^{(O)}$ pilot subcarriers can be boosted by a factor $\beta=N_{T}$. This means $E\left[{\mathbf{X_{m}}}^{H}{\mathbf{X_{m}}}\right]=\beta\mathbf{I}$. The expression in (16) can be further simplified in terms of the pilot boosting factor and the number of OmLS pilots.

JmLS and OmLS are allotted the same total number of pilot subcarriers to enable a fair comparison. That is, for $N_{T}$ BS towers, $N_{p}^{(O)}=N_{p}^{(J)}/N_{T}$. The aggregate CRLB for the CIRs of all the users is obtained by substituting the value of $\beta$.

This CRLB is identical to the CRLB derived for JmLS in (12) and it shows that there is no degradation by going for a joint estimator instead of using orthogonal pilots. The next subsection shows that JmLS has an advantage over OmLS in terms of the number of pilots needed.

The model in (5) can be rewritten as a system of equations.

This is a system with $MN_{p}^{(J)}$ equations and $MN_{cp}$ unknowns. As $N_{p}^{(J)}=N_{T}N_{p}^{(O)}$, JmLS would be solvable when $N_{p}^{(O)}N_{T}>N_{cp}$. When $N_{p}^{(O)}<N_{cp}$, the OmLS estimator is underdetermined as it would have fewer equations than the number of unknowns. This means that the matrix inverted in (15b) will not be full rank. Thus, JmLS will be able to perform better than OmLS whenever the following set of inequalities hold true.

It follows that JmLS can work with fewer pilots than OmLS when multiple towers are present.

The estimator matrix $\mathbf{J}_{M}$ in (9a) is an $MN_{cp}\times N_{p}^{(J)}$ matrix. Both $\mathbf{X_{p}}$ and $\mathbf{F}_{pN_{cp}M}$ are required to calculate this matrix. These are computed with the individual pilot matrices $\{\mathbf{X_{m}}\}$, and the subsampled DFT matrix $\mathbf{F}_{pN_{cp}}$. Since the transmitted pilot sequence and their locations are known at the receiver, $\mathbf{J}_{M}$ can be precalculated and stored. $\mathbf{J}_{M}$ should be computed for different $M$ values and the various tower combinations that the receiver is likely to see. The appropriate estimator matrix can then be chosen by determining which $M$ out of the $N_{T}$ possible bands in the banded preamble (as explained in footnote 3 and the simulation section) contain signals of significant strength. The OmLS estimator matrices for the $N_{T}$ towers can also be precalculated and stored using similar logic.

The OmLS and JmLS estimations reduce to matrix multiplications by employing the precalculated estimator matrices at the receiver. A well-determined OmLS-based estimator requires $N_{p}^{(O)}=N_{cp}$ subcarriers per tower and $N_{T}N_{cp}$ subcarriers in total. However, JmLS can work with slightly more than $N_{cp}$ pilots. The total number of pilots in OmLS and JmLS are kept equal in this work for a fair comparison of the schemes. This means that JmLS is well-determined and will perform well, while OmLS is underdetermined. For this design, the complexity of JmLS in terms of complex multiplications is $O(MN_{cp}N_{p}^{(J)})$. The corresponding complexity of OmLS to estimate the CIR for all the channels is $M\times O(N_{cp}N_{p}^{(O)})=O(MN_{cp}N_{p}^{(O)})$.

In the case described above, $N_{p}^{(J)}=N_{T}N_{p}^{(O)}=N_{cp}$ which implies $N_{p}^{(O)}=N_{cp}/{N_{T}}$. Although OmLS is less complex than JmLS, the estimates are meaningless as $N_{p}^{(O)}<N_{cp}$. Thus, JmLS requires more complex multiplications to produce reliable channel estimates. On the other hand, OmLS is less complex but underdetermined. This higher complexity can be justified as the JmLS estimator can work with fewer pilots than OmLS. If the total number of pilots of both estimators are fixed such that the equations are well determined in either case, $N_{p}^{(J)}$ becomes equal to $N_{cp}$ and $N_{p}^{(O)}=N_{cp}$. In this case, OmLS and JmLS would have the complexity of the order of $O(MN_{cp}^{2})$. However, OmLS would require $N_{T}$ times more pilots in total.

Time-domain compensation is a computationally simple first step towards reducing the ICI power at the receiver. The CFOs should be estimated at the receiver as their true values are unknown. This work estimates CFOs using a banded preamble, as explained in the simulation section. These estimates are then used to perform offset correction in the time domain. Some of the choices for the compensation factor are:

1. 1.

   Desired signal CFO [41].

2. 2.

   A function of the arctan of the CFOs as proposed in CoMP literature [51, 52].

3. 3.

   Mean or weighted mean of the CFOs can also serve as a near-optimal derotator as proposed in this work.

In CCI-free systems, ICI is mostly removed with the help of the time-domain scheme described in [41]. In this algorithm, the received time domain signal (1) is multiplied with the conjugate of $c_{i,0}(n)$ to remove the effect of CFO. This is equivalent to “de-rotating” the signal that was rotated by the CFO, and hence this approach is called signal derotation (SD). Some amount of ICI shall remain as an estimate of $\epsilon_{0}$ is used in practice.

Although the optimal time-domain derotation factor for a co-channel interference system has not been explored in the literature, there are several studies made in the related field of downlink CoMP. These studies have been outlined in the literature survey. In [51], the derotator proposed is the arctan of the ratio of the weighted sum of sines and cosines of the normalized CFOs. A later study [52] corrected this expression and found that even for the case of $M=2$, certain cross terms should be accounted for within the arctan expression. It is shown that for $M=2$ and similar fading conditions, the derotator reduces to the mean of the normalized CFOs. For dissimilar fading conditions, the derotator CFO shall move towards the CFO of the signal with the larger fading factor, i.e., lower path loss. This corrected expression has not been derived for $M>2$.

In this work, a simple linear function of the CFOs is shown to be a near-optimal derotator by using a slightly different set of approximations than the ones used in [51] and [52]. The proposed derotator is a weighted mean of the normalized CFOs and shall be called the weighted mean derotator (WMD). The formulation of the optimization problem and the steps to arrive at this solution is given in Appendix 8. When the user equipment is near the cell edge, the desired and interferer channels have similar path loss. The weighting factors of the CFOs of the different towers become equal in such scenarios, and the WMD reduces to a simple mean derotator (MD). Their expressions are given by

and

As mentioned at the start of this subsection, the normalized CFOs used in the MD and WMD expressions are replaced by their estimates obtained using a preamble described in section 4-4.3. The simulation section explains how the weights used in the WMD formulation can also be obtained from this preamble. It will be shown through simulations that there is no loss in terms of block-error rate (BLER) by using the mean derotator over WMD.

ICI compensation can be carried out using either the proposed derotation factor or the arctan-based derotator. For any derotation factor $\epsilon_{d}$, the time-domain derotation is given by

Here $i$ is the OFDM symbol index. $i$ is 0 for OFDM symbols in which channel estimation takes place (pilot-containing symbols). For symbols that do not contain pilots, $i$ increments by 1 for every symbol until the next pilot-containing symbol is reached. In place of (3), the following new equation is obtained after derotation

$Y_{D}$ is the frequency domain received signal that has undergone time-domain derotation and $\tilde{C}_{m}^{\prime}:=e^{j2\pi\frac{i(N+N_{cp})}{N}(\epsilon_{m}-\epsilon_{d})}$. The tilde in the above terms indicate that $\epsilon_{m}$ has been replaced with $\epsilon_{m}-\epsilon_{d}$.

The desired signal is modulated with 4-QAM. Three ITI signals are also present with powers of 3, -3, and 0 dB relative to the desired signal, each modulated with 4-QAM. This means that the interferer powers are high and comparable to the desired signal power. The ITI signals are assumed to arrive at the time of flights given in Table 2. In pilot-carrying OFDM symbols, a comb-type pilot arrangement interlaced with data is assumed with a pilot subcarrier separation of 3. The number of used subcarriers and the number of pilots per OFDM symbol are given in Table 2. A TDL-B channel, as defined in [67] and scaled with an RMS delay spread of 300 ns (long delay spread channel), is assumed. In this scenario, the UE is assumed to have low mobility with speed restricted to below 10 kmph.

The performance of the OmLS, JmLS, and DMRS-MMSE channel estimation schemes are compared in terms of coded block error rate in Fig. 6. The SRS-DFT approach is not simulated here since its performance is found to be flooring similar to OmLS in Fig. 5. The performance of the joint detector fed with the true channel knowledge is also plotted for reference.

It is seen that at low delay spreads, DMRS-MMSE is superior and is close to the performance for the case of true channel knowledge. This is unsurprising as the robust-MMSE interpolation is known to be near-optimal. The true values of the delay spread and SNR are given to the MMSE interpolator. Because of this, it can achieve near-ideal performance at low delay spreads. However, even at an rms delay spread of $300$ ns, DMRS-MMSE fails as the number of estimates becomes insufficient.

By comparing Fig. 5 and Fig. 6, it is seen that the BLER performance of JmLS improves at high delay spreads even though there is no improvement in the MSE performance. This is because high frequency selectivity is known to be beneficial for the performance of error correction codes [68]. A similar BLER improvement is also seen in the case of true channel knowledge when the delay spread increases.

The ICI compensation scheme proposed in this work comprises both a time-domain derotation scheme and the offset correction in the joint detector. It was found in Fig. 2 that WMD performs close to the optimum time-domain derotator, and the MD performs close to the arctan derotator proposed in [51]. The SD has the worst performance among the time-domain derotators. The simulations results that follow shall only contain the results for SD, MD, and WMD schemes to avoid confusion. Further, only the OmLS and JmLS channel estimation schemes shall be included in future comparisons.

It is seen in Fig. 7 that since the present design satisfies (20), the OmLS estimator has an unacceptable performance resulting in a BLER close to unity. This simulation shows that JmLS can perform well in scenarios where OmLS fails. The decoder fails in the absence of offset correction term as suggested by the proposed OC-JLLR in (26). All blocks will now be in error, irrespective of SNR. This is shown by the result indicated as “pure JLLR” in Fig. 7. As a benchmark for comparison, the BLER when CFO is absent and when perfect channel knowledge is available at the receiver is also plotted.

The simulation results show that WMD and MD do not differ much in terms of BLER. The weights for WMD are almost equal in the cell-edge scenario, as the path losses from the different towers are comparable. It is seen that there is a difference of just 0.5 dB in terms of ICI cancellation for the two schemes. However, both perform better than the signal derotation (SD) approach used in interference-free systems. The SD approach floors more at high SNRs than WMD or MD.

In this scenario, the desired signal is modulated with 16-QAM. Two ITI signals are also present with powers of 3 and -3 dB relative to the desired signal, each modulated with 4-QAM. The remaining assumptions in the previous section also hold here.

The inferences drawn from this result (shown in Fig. 8) are similar to the $M=4$ case. It is seen that 16-QAM with two 4-QAM interferers perform slightly better than 4-QAM with three 4-QAM interferers even though the super-constellation order is the same. One reason for this behavior is that 16-QAM has better minimum-distance properties than the irregular super-constellation formed by adding two faded 4-QAM signals. In addition, the detector for $M=3$ requires only 3 sets of channel estimates and hence has less estimation error.

The last scenario considered in the low mobility case is when the desired signal is modulated with 64-QAM. A single interfering signal whose power is 3 dB above the desired signal and modulated with 4-QAM is also present. This case is plotted in Fig. 9.

Although super-constellation remains the same, the performance for $M=2$ is superior to the previous two scenarios. This result also shows that a joint detector is feasible even for large constellation sizes like 64-QAM, but the number of interferers it can tolerate will reduce accordingly. For example, simulations show that it is not possible to accommodate two 4-QAM interferers on top of a 64-QAM desired signal for the code rate under consideration. Since high-order constellations are typically seen towards the center of the cell where interference is minimal, the results show that joint detectors can handle the interferences that are likely to be seen in the cell edge.

The final scenario uses a TDL-E channel model with a line-of-sight (LOS) Rician path and the usual non-line-of-sight (NLOS) Rayleigh multipaths. The UE is assumed to be mobile with a maximum speed of 100 kmph. The delay spread scaling factor considered for this channel is 100 ns since the TDL-E model is more spread out in terms of multipath. If a 300 ns scaling factor were to be considered as in the previous cases, this channel would have significant inter-block interference.

The results plotted in Fig. 10 consider a 4-QAM signal with 4-QAM interferer(s) for $M=$ 2, 3, and 4. WMD is not plotted in these results since previous simulations have shown no significant difference between WMD and MD in terms of BLER for the given interference profile. The performance of OmLS is similar to the results shown so far and is not plotted here.

The $M=4$ result (denoted by 4T in the figure) shows that the proposed MD is superior to SD even in the presence of a significant Doppler component. Referring back to Fig. 2, it is seen that when the BS oscillator error is 0.2 ppm, the residual ICI power is around -30 dB for SD. This means that the ICI is comparable to noise at an SNR of 30 dB. Hence, SD starts to floor near 30 dB SNR. SD would floor sooner for higher CFOs, as predicted by Fig. 2. The effect of the derotation factor is not as pronounced for this particular code rate when $M<4$.

The results show that the SNR required to reach a particular BLER increases with increasing $M$. The first reason for this is an increase in the order of super-constellation. A secondary reason is the accumulation of errors in channel estimation of both the desired and interferer channels. This error accumulates linearly with $M$.