Uplink Communication

The uplink reuses $N$, $N_\mathrm{CP}$, $\Delta f$, the frame-wide symbol index $m$, and the pilot positions, but has an independent grid $\boldsymbol B_\gamma^\mathrm{UL}$ and ZC root. The UE has already synchronized to the BS through the downlink; the uplink is a complete UE-to-BS communication link, not a separate initial-acquisition procedure or a reversal of downlink symbols. In TDD, the uplink grid is zero for $m\in\mathcal S_\mathrm{DL}\cup\mathcal S_\mathrm{G}$ and carries uplink symbols only for $m\in\mathcal S_\mathrm{UL}$.

Uplink Frame

Let $m_{\mathrm{UL},0}=\min\mathcal S_\mathrm{UL}$. The first active uplink OFDM symbol in the frame is full-band ZC:

$$b_{n,m_{\mathrm{UL},0},\gamma}^\mathrm{UL}=z_n^\mathrm{UL}.$$

The remaining symbols with $m\in\mathcal S_\mathrm{UL}\setminus\{m_{\mathrm{UL},0}\}$ carry known pilots on $n\in\mathcal P$ and coded QPSK on $n\in\mathcal D$:

$$b_{n,m,\gamma}^\mathrm{UL}= \begin{cases} p_{n,m}^\mathrm{UL},&n\in\mathcal P,\\ d_{n,m,\gamma}^\mathrm{UL},&n\in\mathcal D. \end{cases}$$

In TDD, this compact frame occupies $\mathcal S_\mathrm{UL}$ after the guard interval. A positive timing advance $t_\mathrm{TA,UE}$ moves the UE waveform earlier so that propagation places it in the BS uplink observation interval. In FDD, the uplink uses a continuous $M$-symbol frame on its own carrier.

Frequency-Domain Model at the BS

After frame-boundary alignment, cyclic-prefix removal, and the FFT,

$$Y_{n,m,\gamma}^\mathrm{UL} =b_{n,m,\gamma}^\mathrm{UL} H_{n,m,\gamma}^\mathrm{UL} +Z_{n,m,\gamma}^\mathrm{UL},$$ $$H_{n,m,\gamma}^\mathrm{UL} =\sum_{l=1}^{L_\mathrm{UL}} \alpha_l^\mathrm{UL}(t_{m,\gamma}^\mathrm{UL}) e^{j2\pi\left[ (f_{D,l}^\mathrm{UL}+\Delta\bar f_{c,\gamma}^\mathrm{UL}) t_{m,\gamma}^\mathrm{UL} -\kappa_n\Delta f (\tau_{l,\mathrm{prop}}(t_{m,\gamma}^\mathrm{UL}) +\tau_\mathrm{UL}^\mathrm{RF} -\tau_d^\mathrm{BS}(t_{m,\gamma}^\mathrm{UL})) \right]}.$$

$t_{m,\gamma}^\mathrm{UL}$ is the actual reference time of uplink symbol $m$ within the frame, and $\tau_d^\mathrm{BS}(t)$ is the time-varying offset of the BS’s current demodulation window relative to the uplink transmitter frame boundary. See the Signal Model for its relation to propagation delay, uplink RF group delay, and the locally observed TO.

The uplink ZC gives

$$\hat H_{n,0,\gamma}^\mathrm{UL,LS} =\frac{Y_{n,0,\gamma}^\mathrm{UL}}{z_n^\mathrm{UL}}.$$

Limiting its delay-domain support to the cyclic-prefix region and applying Wiener smoothing suppresses noise while retaining the multipath structure.

Uplink Phase Tracking

Let $\mathcal A_\mathrm{UL}$ contain indices for which two adjacent local-uplink symbols both carry pilots. When $M_\mathrm{UL}\ge3$ and all data symbols are consecutive, $\mathcal A_\mathrm{UL}=\{1,\ldots,M_\mathrm{UL}-2\}$. Then

$$\bar R_\gamma^\mathrm{UL}[n] =\frac{1}{|\mathcal A_\mathrm{UL}|} \sum_{m\in\mathcal A_\mathrm{UL}} (Y_{n,m,\gamma}^\mathrm{UL})^* Y_{n,m+1,\gamma}^\mathrm{UL},$$

with unwrapped phase

$$\arg\bar R_\gamma^\mathrm{UL}[n] \approx 2\pi\left( f_{o,\gamma}^\mathrm{UL}T_O -\kappa_n\Delta fN_s\Delta T_{s,\gamma}^\mathrm{UL} \right).$$

The same weighted fit used in the downlink gives

$$(\hat a_\mathrm{UL},\hat b_\mathrm{UL}) =\arg\min_{a,b}\sum_{n\in\mathcal P} |\bar R_\gamma^\mathrm{UL}[n]|^2 \left| \operatorname{unwrap}(\arg\bar R_\gamma^\mathrm{UL}[n])-a-b\kappa_n \right|^2,$$ $$\hat f_{o,\gamma}^\mathrm{UL} =\frac{\hat a_\mathrm{UL}}{2\pi T_O}, \qquad \Delta\hat T_{s,\gamma}^\mathrm{UL} =-\frac{\hat b_\mathrm{UL}}{2\pi\Delta fN_s}.$$

The channel is propagated as

$$\hat H_{n,m,\gamma}^\mathrm{UL} =\hat H_{n,0,\gamma}^\mathrm{UL} e^{j2\pi m( \hat f_{o,\gamma}^\mathrm{UL}T_O -\kappa_n\Delta fN_s\Delta\hat T_{s,\gamma}^\mathrm{UL})}.$$

If $\mathcal A_\mathrm{UL}$ is empty, the local frame provides no cross-symbol pilot fit. Residual CFO/SFO estimation and compensation have the same form in both directions, but each link uses its own references and observations; communication decoding does not rely on ideal reciprocity.

Equalization and Information Recovery

With ZF or MMSE coefficient $G_{n,m}^\mathrm{UL}$,

$$\hat d_{n,m,\gamma}^\mathrm{UL} =G_{n,m}^\mathrm{UL}Y_{n,m,\gamma}^\mathrm{UL}.$$

Equalized pilot residuals estimate $\hat\sigma_\mathrm{eq}^2$, which scales the QPSK LLRs. Soft deinterleaving, descrambling, and LDPC decoding then recover the UE information bits. All channel, frequency-offset, and noise estimates come from the uplink’s own references.

Relation to eRTM

The uplink also supplies the BS-side channel estimate $\hat H_{\mathrm{BS}}[n]$. When both directions are enabled, eRTM combines it with the UE-side downlink estimate $\hat H_{\mathrm{UE}}[n]$ and uses the relationship between the uplink and downlink channels to estimate the timing offsets at the two endpoints; see the eRTM option in Bistatic Sensing.