Timely CSI Acquisition Exploiting Full Duplex
Abstract
In this paper, we propose a method for acquiring accurate and timely channel state information (CSI) by leveraging fullduplex transmission. Specifically, we propose a mobile communication system in which base stations continuously transmit a pilot sequence in the uplink frequency band, while terminals use selfinterference cancellation capabilities to obtain CSI at any time. Our proposal outperforms its halfduplex counterpart by at least 50% in terms of throughput while ensuring the same (or even lower) outage probability. Remarkably, it also outperforms using full duplex for downlink data transmission for low values of downlink bandwidth and received power.
I Introduction
In mobile wireless communications, the transmitting end needs to adjust its transmission parameters based on channel information (namely channel state information at the transmitter  CSIT) that may not match the actual conditions at the moment of transmission. For instance, when the user equipment (UE) selects its modulation and coding scheme (MCS), it does so based on the latest feedback from the base station (BS); such feedback often consists of a quantized version of the channel, as estimated from pilot symbols previously transmitted by the UE. Leaving aside the distortion introduced by quantization, or even the noise inherent to any channel estimation process, the delay between estimation and exploitation alone severely impacts the system performance.
To deal with this problem, we take an alternative and novel approach for leveraging fullduplex capabilities at the UE [1]. Fullduplex radio, that is, transmitting and receiving simultaneously in the same frequency band, is made possible through recent advances in selfinterference cancellation (SIC). If selfinterference can be suppressed, possibly well below the noise level [2, 3], then simultaneous uplink and downlink transmission could take place, potentially doubling the net throughput. Most of the proposed applications of full duplex have followed this path and have focused on boosting the throughput.
However, some alternative uses of full duplex have already been proposed in the literature. In [4], it was targeted at enhancing spectrum sensing in a cognitive radio context. In [5], it was exploited to improve crosstier intercell interference suppression in an heterogeneous network by allowing pico BSs to simultaneously transmit their desired signal and forward the listened interference. Reference [6] realized the potential of continuous feedback through the fullduplex channel in multipleinput multipleoutput (MIMO) communications; the proposal therein substantially reduces the feedback power required to achieve the same multiplexing gains as its halfduplex counterpart. In [7], such fast feedback was also exploited to improve AMC in backscatter communications, allowing the transmitter to adapt to a fastvarying channel. More related to our proposal is [8], where full duplex is used to continuously train a BS in open loop and update its precoding matrix.
In this paper, we exploit full duplex in order to provide terminals with timely CSIT. To do so, each BS continuously broadcasts a distinct pilot sequence in the same frequency band used for uplink reception; thanks to their fullduplex capabilities, terminals are able to use the received pilot sequence for estimating the channel at any time. In other words, we exploit fullduplex capabilities to enhance openloop training. Such training provides timely CSIT that is used to select the most convenient transmission rate.
We explore the potential of our proposed scheme and we compare it with state of the art alternatives. We start by formulating a simplified mathematical model for an uplink where UEs select their transmission rate based on delayed CSIT. We then obtain analytical expressions of throughput and outage probability for different CSIT acquisition schemes. Our numerical results evince that our proposed scheme outperforms halfduplex CSIT acquisition by at least 50% in terms of throughput while ensuring the same  or even lower  outage probability. Moreover, it can also outperform fullduplex downlink data transmission in cases with low values of downlink bandwidth and received power.
Ii System model
Consider a mobile cellular communication system where downlink and uplink frequency bands are different, i.e. a frequency division duplex (FDD) system; in fact, our proposal also applies to downlink and uplink decoupling architectures, where UEs can associate to different BSs for each direction [9]. We assume both UE and BS to have a single antenna, even though the proposed idea can be directly extended to MIMO systems.
We propose that each BS continuously transmits a pilot sequence in the frequency band used for uplink transmissions; see Figure 1. UEs with fullduplex radios will be able to estimate their channel based on these pilot sequences, thanks to their SIC capabilities and to the reciprocity of the communication medium. In the following we detail the uplink and downlink signal model, the channel estimation assumed, and the rate selection at the UE.
Iia Downlink signal model
The th block of signals received by a UE is given by
(1) 
where is the pilot sequence transmitted by the th BS, which consists of symbols and is received with average signaltonoise ratio (SNR) ; is the noise vector ; is the channel remaining after selfinterference mitigation, through which the transmitted vector of symbols contaminates the received signal, and is the residual selfinterference over noise ratio after cancellation.
We assume to be a Gaussian random variable [2]. However, since the strongest selfinterfering paths will be severely attenuated after cancellation (sometimes below the noise level [2, 3]), in the remainder we set . Note that we can emulate different selfinterference cancellation capabilities by changing the value of .
IiB Uplink signal model
When a UE transmits the th block to BS, the received signal is given by
(2) 
where contains unitpower transmitted symbols, contains the received symbols, and . Constant is the average received SNR, and we will hereafter refer to as the instantaneous SNR with a slight abuse of terminology. As for the channel, we take . The autocorrelation between channel samples is given by , where is the Doppler frequency and is the time between the two samples. Note that, differently from UEs, BSs are assumed to have perfect SIC capabilities.
UEs select their transmission rate at the th slot (discrete time) based on the latest available channel information, given by
(3) 
We note that, with respect to the true instantaneous SNR , the available knowledge is both delayed and noisy: delayed because and are different (but correlated) as a consequence of the timevarying nature of the channel, and noisy because the underlying channel estimation is affected by an error . Consistently with conventional dataaided channel estimation, we assume ; we will elaborate more on this in Section IIC.
In a realistic system, UEs would use their available CSIT to select the most suitable MCS from a finite set; the transmission rate is then determined by the chosen MCS, and an outage occurs if the actual quality of the channel is below the MCS operating threshold.
For tractability, in this work we assume a simplified version of the aforementioned operation. Based on an estimate , the transmitter encodes data at a rate
(4) 
where is a backoff factor emulating the selection of a more protected MCS to guarantee a low packet error rate^{1}^{1}1This parameter would in reality be a function of the estimated SNR[10], or could be changed over time as the result of an outer loop control [11], but for our purposes it suffices to consider it fixed., and represents the SNR gap from Shannon capacity realworld systems exhibit [12] (due to finite constellations, nonideal channel coding, etc.).
Transmission is successful if the actual is above the one assumed upon encoding. We can write this event as where denotes the indicator function. Then, the outage probability conditioned on an estimation reads as
(5) 
We further define the effective rate as
(6) 
and the average effective rate and outage probability, respectively, as
(7) 
In Section III, we obtain analytical expressions for the above metrics, and introduce an additional one to assess the performance of our proposal. Next, we provide some additional explanations on the channel estimation process.
IiC Channel estimation
As explained before, the model adopted in (3) is consistent with traditional dataaided channel estimation. For the expression of we assume[13]
(8) 
Here, is a constant that accounts for practical imperfections in the channel estimation process and comprises the training sequence length. As for , it represents the signal to interference plus noise ratio (SINR) experienced by pilot sequences at the moment of estimation. Let us provide some examples.
IiC1 Estimation from uplink signaling
In the conventional case in FDD, the uplink channel is estimated at the BS from pilot sequences sent by the UEs. Thus, in the absence of interference we simply have .
IiC2 Fullduplex estimation from downlink pilot sequences
In our proposal, the channel can be estimated from the pilot signal BSs constantly broadcast thanks to the fullduplex capabilities of the UE. If pilots from different BSs are orthogonal, that is, if is nonzero only when , then terminals can distinguish between the channels of different BSs with no interference; for instance, in the case of leastsquares channel estimation, we have from (1):
(9) 
and we easily obtain
(10) 
From (10) we see that when estimating the channel in full duplex, we incur in a penalty given by the residual selfinterference, thus the term in the denominator. Our key finding is that, in many cases, the reduction in estimation delay greatly compensates for this noise enhancement. We will demonstrate this in subsequent sections.
Before doing so, let us recall that , and define the following normalized correlation coefficient:
(11) 
Also recall that, as defined in (3), is exponentially distributed with mean .
Iii Performance analysis
Iiia Outage probability and average effective rate
We start by obtaining an explicit expression for , which is given by
(12) 
where is the Marcum function [14], is the normalized correlation coefficient (11), and we recall that ; see Appendix A for a detailed explanation. The outage probability is then given by
(13) 
after plugging (12) into the integral and using [15, Eq. B.48].
This expression tells us that, in order to make smaller than 0.5, we need . Figure 2 numerically evaluates (13). We can corroborate that increasing allows us to decrease , but we know from (4) that this will decrease the rate; for this reason, increasing becomes crucial. Our proposed method achieves this by reducing the delay with respect to the last estimated channel value leveraging full duplex.
As for , we can express it as
(14) 
IiiB Throughput
A fair assessment of our proposal requires taking into account its bandwidth occupancy in the downlink. To do this, let us define the throughput at 1 MHz bandwidth as
(15) 
Here, represents the average SNR affecting data decoding (see (4)), is the SINR affecting the channel estimation process (see Section IIC), and is the delay experienced by the CSI, so that .
We must remark that, in defining (15), we are implicitly assuming all power values relative to a bandwidth of 1 MHz. If we scale the bandwidth by a factor , we will assume that

SNR values are divided by (thus increased). The power budget at the transmitter is the same, but the noise bandwidth is reduced, so that .

INR values remain unaffected. If selfinterference has a frequencyflat power spectral density around the frequency of operation, then reducing the bandwidth scales both interference and noise power, leaving their quotient unaltered.
In the next section, we numerically evaluate this metric for a number of cases of interest.
Iv Numerical Results
In this section we evaluate (13) in order to plot , and (14) through numerical integration to plot . We compare our proposal to three benchmark curves described below.
Iva Description of the curves
Perfect CSI (PCSI)
As a halfduplex upper bound we consider the case of having perfect CSIT. In our model, this translates into unlimited acquisition SNR and zero delay:
(16) 
The outage probability is by definition zero.
Probing (PROBE)
As a halfduplex baseline we consider the case of the UE probing the channel before transmission; there is no selfinterference penalty when estimating the channel, but the delay equals at least the roundtrip delay, i.e.
(17) 
Fullduplex CSI acquisition (FDCSI)
Our solution, as previously described: channel estimation is affected by residual selfinterference, but delay is minimal :
(18) 
Full duplex for data transmission (FDDATA)
For comparison purposes, we evaluate the throughput of an alternative fullduplex solution that uses selfinterference cancellation capabilities to receive data. In this case we add up the throughput of both uplink (first term) and downlink (second term), assuming they both use probing to obtain their CSI:
(19) 
Note that we neglect interference from other BSs in the downlink.
IvB Examples
In all the examples that follow we have set GHz, dB, dB, ms, ms, dB. All power values are relative to 1 MHz bandwidth as explained in Section IIIB, and all the FDCSI curves have been obtained with ; the latter means we only use 100 kHz to send the downlink pilots^{2}^{2}2Some simple computations with the autocorrelation function of the channel show that, with a bandwidth of 100 kHz, more than 150 pilot symbols can be transmitted within the 80% coherence of the channel at a speed of 50 km/h, GHz.. Constant is set to 0.0544 [13].
Figure 3 plots the evolution of the desired performance metrics with respect to the . In this example we have set dB, the UE speed to 15 km/h, and dB; the latter has been chosen based on (13) to ensure the same asymptotic as with probing. Focusing on FDCSI, we see that its throughput quickly becomes constant with respect to the residual , roughly after dB; moreover, it outperforms PROBE by 53% in terms of throughput, and achieves the same performance as FDDATA when the latter occupies twice as much bandwidth in the downlink ().
IvC Discussion
Through the following items we highlight relevant details in the performance results and point out to some caveats.
IvC1 Downlink power and bandwidth
Figure 3 and Figure 4 suggest that our proposal is more bandwidth efficient than using full duplex for data transmission when the received downlink power is low. Conversely, they show that, when larger bandwidth and high powers are available in the downlink, full duplex for data makes a much more efficient use of them.
The observation above has been made taking into account the throughput of both links, but this might not be the best metric in certain relevant scenarios. If we exclusively focus on improving the uplink, FDCSI seems to be always a better choice.
IvC2 Unknown interference
In this paper we have focused on tracking the evolution of the channel over time and have disregarded the effect of timevarying interference. The underlying assumption is that interference events come from within the same cell, and that, when they happen, they can be regarded as collisions that will be dealt with by the MAC layer.
If there is outofcell timevarying interference, our solution FDCSI cannot track it directly, neither can the baseline PROBE unless interference changes very slowly over time. Both alternatives would probably need to resort to larger timevarying backoff values.
V Conclusions
We have proposed a mobile communication system where a BS continuously transmits a pilot sequence in the uplink frequency band, so that mobile terminals can acquire timely CSIT by leveraging full duplex and selfinterference cancellation capabilities. In all relevant evaluation scenarios considered here, our proposal outperforms its halfduplex counterpart by at least 50% in terms of throughput while ensuring the same (or even lower) outage probability. Interestingly, in cases with low values of downlink bandwidth and received power, it can also outperform fullduplex radios used for downlink data transmission.
Appendix A Derivation of
Both and are jointly exponentially distributed; equivalently, each of their doubles is chisquared distributed with two degrees of freedom. In consequence, we have that [15, Eq. 3.17]
(20) 
after applying a simple change of variables. Note that is the correlation coefficient between the underlying Gaussian random variables, and .
The probability distribution of conditioned on the last estimation is now given by
(21) 
which is the pdf of a scaled noncentral chisquared distribution with two degrees of freedom. The derivation continues as follows:
(22) 
Before plugging (21) into (22) we apply the following change of variables, , , so that
(23) 
where , and the last equality follows from the definition of the function [14].
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