Almost all the deployed and successful communication strategies till date are half duplex (HD). That is, we don’t have simultaneous transmission and reception on the same frequency band, aka, full duplex (FD). For example, 802.11 WiFi uses a time switch (TDD) between transmit and receive mode.  Both transmission and reception takes place over the same frequency band as well. A single antenna is (typically) used for both tx and rx in this case. It is always either transmit or receive (or none!) that happen at any given time. In the cellular world, such as LTE the popular scheme is to have the frequency slice shared (FDD). In that case the up-link (link from a cell phone to base station) takes place in a range of frequency band different from that on link receiving signal from base station, while both transmit and receive can take place simultaneously. In both TDD and FDD cases, there is no overlap between the transmit and receive signals at a given frequency at the same time.

Let us posit this question. In a given frequency band,  is it feasible at all to have simultaneous transmission and reception? One way of course is to find a domain where these two (transmit and receive) signals stay perfectly distinct. Say use some orthogonal codes. In theory yes, but there is an important practical hurdle here. It is the issue of the loudness (aka self interference) from own transmit signal! An analogy is like one tries to decipher a whisper coming from someone, while he/she is simultaneously shouting at top of his/her voice. In reality, the desired signal comes from a distant source after traveling through adverse medium/channel. More than anything else, the signal intensity level would have got severely degraded by the time signal arrives at the receiver unit. Well, let me put some numbers from a practical setup. In a (typical) WiFi scenario the incoming signal (from an AP) at your receiver antenna (of say tablet) may be around -70dBm, whereas, the power of (tablet PC’s) concurrent transmission power could be $20$ dBm!  The task to fulfill the full duplex goal is really to recover the information from the relatively week signal in the presence of a self interference stronger by 80 to 90dB! In other words, we should hit a mechanism to suppress the self interference by 90dB! Getting a 90dB suppression is no easy, especially when we are constrained chip and board area to get deployed in portable devices! Traditional board layout tricks such as isolation, beam steering etc alone wouldn’t get us there.

OK, now what? the reason I suddenly brought this up is largely due to the increased momentum this one is gathering off later in both academia as well as industry. It still has enormous challenges ahead. Realizing FD on the other hand will bring in enormous benefits. Historically, we always mulled over capacity and throughput, with the strong assumption that all resources in the lot are available. Say for a given channel bandwidth $W$, the capacity is $C(W)$ and throughput is so much and so on. The reality is that, in most cases, to have information exchange, we need two way communication and that means double resources. Spectrum being pricey and scarce, getting the full duplex can potentially get up to double fold in throughput and several other benefits along the way such as remedy to the hidden node problem in current 802.11 MAC access. Now 802.11 standards front, we have a new study group on high efficiency wireless (HEW). I believe HD can play a role there too.

I am not prepared to discuss all the details involved here. Let me outline a rough problem formulation of FD.  More general versions exists, but let me try with a simple case. Much more detailed formulation of the problem can be seen here and elsewhere. I kinda used the notations and problem statement from this. Let $y_{a}$ be the desired signal from a distant sender, arriving  at the rx antenna. Simultaneously, a much high power signal $x$ is being sent . The signal $x$ is significantly higher power than $y_{a}$. Now, the signal $x$ leaks through some path $H$ and produce an interference $v_{a}$ at the receive antenna. In other words, the effective signal at the receiver antenna port is $z_a=x+y_a$. For sake of simplicity, let us assume that $H$ is modeled as a FIR filter. The sampled signal relationship can be then stated as follows.

$z_{a}[n]=y_{a}[n]+\underbrace{\sum_{k=0}^{\infty}{H[m] x[n-m]}}_{\triangleq u_{a}[n]}$.

Now here is the thing. We cannot simply pass the buck to digital domain and ask to recover the useful signal from powerful interference. Recall that, the A/D converter stands at the very interface of analog to digital partition. High power interference signal will severely saturate the A/D and result in irreversible clipping noise. So, first we must do a level of analog suppression of this interference and make sure that, the A/D is not saturated. Let us say, we go for an analog filter $C_{a}$ and do this job.  Post analog cancellation using a filter $C_{a}[n]$ we will have,

$\tilde{z}_{a}[n]=z_{a}[n]+\underbrace{\sum_{k=0}^{\infty}{C_{a}[m] x[n-m]}}_{\triangleq v_{a}[n]}$.

The A/D signal transformation can be decomposed to the following form (using Bussgang theorem for instance). $\tilde{z}_{d}[n]=\mathcal{A} \tilde{z}_{a}[n]+q[n]$. Now,

$\tilde{z}_{d}[n]={\mathcal{A}} z_{a}[n]+{\mathcal{A}} {\displaystyle \sum_{k=0}^{\infty}{H[m] x[n-m]}}$.

If we do a digital cancellation at the A/D output state with a filter $C_{d}[n]$, we can have $\hat{z}_{d}[n]=\tilde{z}_{d}[n]+\sum_{k=0}^{\infty}{C_{d}[m] x[n-m]}$. Incorporating all these, we will have

$\hat{z}_{d}[n]={\mathcal{A}} y_{a}[n]+ \displaystyle \sum_{m=0}^{\infty}{\left[\mathcal{A} \left(H[m]+C_{a}[m]\right)+C_{d}[m]\right] x[n-m]}+q[n]$.

Now if we can adapt and find $C_{a}[n]$ and $C_{d}[n]$ such that $\mathcal{A} \left(H[m]+C_{a}[m]\right)+C_{d}[m] \rightarrow 0$, then we can hope to have a near perfect self noise cancellation and produce $\hat{z}_{d}[n]={\mathcal{A}} y_{a}[n]+q[n]$!

So, in theory there is a way to do this, by a hybrid approach where in some correction is done in analog domain (before A/D) followed by a more easily realizable digital cancellation circuit. There are many more practical hurdles. Some of them are:

1. Performing correction/adaptation at RF frequency is not trivial
2. If we are to do this post mixer (after downconversion), then the LNA nonlinearity (and a potential saturation) will come into play
3. Channel/coupling path estimation error will degrade performance
4. Calibrating analog correction is a little more involved
5. A typical goal may be to have about 40dB suppression from analog correction and another 40dB from digital.
6. Digital and analog correction, calibration time should be reasonably fast, so as not to spoil the set goal of simultaneity!

Some of the recent results, published are indeed promising. Some prototypes are also being developed. More general version involving multiple antennas’s are also being talked about. In that case, some beam forming can provide additional support. Let us hope that, with some more push and effort, we get to realize this one day into real world.