Ferkans — Interactive Telecom Tutor

Two Directions, One Channel

All the multiple access techniques discussed so far address the uplink (users to base station) and downlink (base station to users) separately. But a real system must support both directions, and the spectrum allocated to a cell must be shared between them. This sharing is called duplexing. The two dominant approaches — Frequency Division Duplex (FDD) and Time Division Duplex (TDD) — have profoundly different implications for channel estimation, spectral efficiency, and massive MIMO operation. The choice of duplexing mode is one of the most consequential system design decisions, particularly as the number of antennas grows.

Definition:
FDD, TDD, and Channel Reciprocity

FDD (Frequency Division Duplex): The uplink and downlink use separate frequency bands, separated by a guard band to prevent self-interference. Each direction operates continuously.

Uplink band: $[f_1, f_1 + W]$ , downlink band: $[f_2, f_2 + W]$ with $|f_2 - f_1| > W + W_{\text{guard}}$ .
Total spectrum consumed: $2W + W_{\text{guard}}$ .
Channel estimation: the uplink channel $\mathbf{h}_{\text{UL}}$ and downlink channel $\mathbf{h}_{\text{DL}}$ are independent because they occupy different frequencies. The BS must learn $\mathbf{h}_{\text{DL}}$ from downlink pilot feedback: it sends pilots, users estimate the channel, quantise it, and feed it back.

TDD (Time Division Duplex): The uplink and downlink share the same frequency band, separated in time. Each frame is divided into uplink and downlink sub-frames.

Single band: $[f_1, f_1 + W]$ .
Total spectrum consumed: $W$ (no guard band).
Channel estimation exploits channel reciprocity: since both directions use the same frequency, $\mathbf{h}_{\text{DL}} = \mathbf{h}_{\text{UL}}^*$ (after calibrating hardware differences). The BS learns the downlink channel from uplink pilots alone — no feedback required.

Channel reciprocity holds because the electromagnetic propagation channel is reciprocal (by the Lorentz reciprocity theorem). Hardware non-reciprocity (different TX/RX chains) is corrected by periodic calibration.

FDD has historically dominated cellular deployments because it avoids the guard period overhead and synchronisation complexity of TDD. However, TDD is increasingly preferred for massive MIMO and 5G NR deployments because channel reciprocity eliminates the feedback bottleneck that would otherwise scale as $O(M)$ with the number of BS antennas.

,

Theorem: CSI Overhead Scaling in FDD vs. TDD

Consider a base station with $M$ antennas serving $K$ single-antenna users, with coherence time $T_c$ symbols.

TDD overhead: The BS needs uplink pilots from each user. With orthogonal pilot sequences of length $\tau_p \geq K$ :

$\eta_{\text{TDD}} = 1 - \frac{K}{T_c}$

The pilot overhead scales as $O(K)$ and is independent of $M$ .

FDD overhead: The BS sends $M$ downlink pilot symbols (one per antenna), and each user feeds back the estimated $M$ -dimensional channel vector. The total overhead is:

$\eta_{\text{FDD}} = 1 - \frac{M + M_{\text{FB}}}{T_c}$

where $M_{\text{FB}} \geq K \cdot B_{\text{fb}}$ symbols are needed for feedback ( $B_{\text{fb}}$ bits per user per antenna coefficient). The overhead scales as $O(M)$ .

For $M \gg K$ , TDD is dramatically more efficient: $K/T_c \ll M/T_c$ .

In TDD, the BS learns the $M \times K$ channel matrix from just $K$ uplink pilot symbols (each pilot is received on all $M$ antennas simultaneously). In FDD, the channel matrix must be communicated explicitly: $M$ downlink pilots plus $MK$ feedback coefficients. As $M$ grows (massive MIMO), the FDD overhead eventually consumes the entire coherence interval, while TDD overhead remains constant at $K$ symbols. This is the fundamental reason why massive MIMO overwhelmingly uses TDD.

Proof

TDD pilot overhead

Each of $K$ users sends an orthogonal pilot of length $\tau_p = K$ symbols. The remaining $T_c - K$ symbols are available for data:

$\eta_{\text{TDD}} = \frac{T_c - K}{T_c} = 1 - \frac{K}{T_c}$

This is independent of $M$ : adding more BS antennas does not increase the pilot overhead because all antennas receive the same uplink pilots simultaneously.

FDD pilot and feedback overhead

The BS transmits $M$ downlink pilot symbols (one per antenna dimension). Each user estimates the $M$ -dimensional channel and feeds back the estimate. With $B$ bits per complex coefficient, the feedback requires $MB$ bits per user, or $KMB/R_{\text{fb}}$ symbols on the uplink.

Total overhead: $M + KMB/R_{\text{fb}}$ symbols. Even with generous compression ( $B = 4$ bits, $R_{\text{fb}} = 1$ bit/symbol), this is $M + 4KM$ symbols, growing linearly in $M$ .

For $M = 64, K = 10, T_c = 200$ :

TDD: overhead $= 10/200 = 5\%$
FDD: overhead $\geq 64/200 = 32\%$ (pilots alone)

For $M = 256$ : FDD overhead exceeds $100\%$ — impossible to estimate the channel within one coherence interval. $\blacksquare$

TDD vs FDD: CSI Overhead as Antennas Grow

Watch the CSI overhead fraction as the number of BS antennas

M

sweeps from 4 to 256. TDD overhead stays constant at

K/T_c = 5\%

(independent of

M

), while FDD overhead grows linearly, crossing 100% at

M = T_c = 200

and becoming infeasible for massive MIMO.

FDD overhead scales as

O(M)

and becomes infeasible for massive MIMO (

M > 100

). TDD overhead is

O(K)

— independent of

M

.

FDD vs. TDD Spectral Efficiency

Compare the effective spectral efficiency of FDD and TDD as functions of the number of BS antennas $M$ , coherence time $T_c$ , and number of users $K$ . Observe how TDD maintains high efficiency even with large $M$ , while FDD degrades rapidly as the CSI overhead consumes the coherence interval.

Parameters

M

(BS antennas)64

T_c

(coherence time in symbols)200

K

(number of users)10

FDD vs. TDD Comparison

Property	FDD	TDD
Spectrum usage	Paired bands (UL + DL)	Single band (shared)
Guard requirement	Frequency guard band	Time guard period (GP)
Channel reciprocity	Not available (different frequencies)	Available (same frequency, after calibration)
CSI acquisition	DL pilots + UL feedback: $O(M)$ overhead	UL pilots only: $O(K)$ overhead
Massive MIMO suitability	Poor (feedback bottleneck for $M \gg 1$ )	Excellent (overhead independent of $M$ )
UL/DL ratio	Fixed (paired spectrum)	Flexible (dynamic UL/DL split)
Latency	Continuous UL and DL	Half-duplex: UL/DL switching delay
Interference	UL and DL isolated by frequency	Cross-link interference if cells unsynchronised
Deployment history	Dominant in 2G/3G/4G FDD bands	Growing in 5G NR (esp. C-band, mmWave)
Hardware complexity	Duplexer filter required	TX/RX switch (simpler, cheaper)

Example: CSI Overhead in FDD vs. TDD

A 5G base station with $M = 64$ antennas serves $K = 16$ users. The coherence time is $T_c = 200$ OFDM symbols (corresponding to 10 ms at 20 kHz subcarrier spacing). Each FDD feedback coefficient requires 8 bits, and the feedback channel supports 1 bit per symbol.

(a) Compute the TDD pilot overhead fraction. (b) Compute the FDD pilot + feedback overhead fraction. (c) At what value of $M$ does FDD overhead reach 100%?

Solution

TDD overhead

TDD pilot length: $\tau_p = K = 16$ symbols.

Overhead fraction: $16/200 = 8\%$ .

Data efficiency: $\eta_{\text{TDD}} = 92\%$ .

FDD overhead

DL pilots: $M = 64$ symbols.

Feedback per user: $M \times 8$ bits $= 512$ bits $= 512$ symbols (at 1 bit/symbol).

Total feedback: $K \times 512 = 8192$ symbols.

Total FDD overhead: $64 + 8192 = 8256$ symbols.

But $T_c = 200$ symbols! The overhead far exceeds the coherence interval ( $8256 \gg 200$ ). FDD is infeasible at this scale without aggressive compression.

Even with ideal 4-bit feedback per coefficient: $64 + 16 \times 64 \times 4 / 1 = 64 + 4096 = 4160 \gg 200$ .

Critical antenna count for FDD

With just pilots (no feedback): $M/T_c = 1$ gives $M_{\text{crit}} = T_c = 200$ .

Including minimal feedback (1 bit/coefficient, 1 bit/symbol): $M + KM = M(1+K) = 200$ , so $M_{\text{crit}} = 200/17 \approx 12$ .

This shows that FDD with full CSI feedback is impractical for $M > 12$ antennas under these conditions. In practice, FDD systems use codebook-based feedback (Type I/II CSI in 5G NR) that compresses the feedback significantly, but the overhead still grows with $M$ . $\blacksquare$

Quick Check

A massive MIMO system has $M = 128$ antennas, $K = 8$ users, and coherence time $T_c = 300$ symbols. What fraction of the coherence interval is consumed by TDD uplink pilots?

2.7% (8 out of 300 symbols)

42.7% (128 out of 300 symbols)

45.3% (128 + 8 = 136 out of 300)

100% — not enough symbols for full CSI

Correction:

2.7% (8 out of 300 symbols)

With TDD, only $K = 8$ orthogonal pilot symbols are needed, regardless of $M$ . Overhead: $8/300 = 2.67\%$ . This leaves 97.3% of the coherence interval for data — the key advantage of TDD for massive MIMO.

Why This Matters: TDD in 5G NR

5G NR has embraced TDD for the majority of new spectrum allocations, particularly:

C-band (n77, n78): 3.3--4.2 GHz, the primary mid-band 5G spectrum globally. TDD with massive MIMO (64T64R) is the standard deployment configuration.
mmWave (n257, n258, n261): 24--40 GHz. All mmWave 5G bands use TDD, exploiting reciprocity with large antenna arrays (256--512 elements).

The 5G NR TDD frame structure supports flexible UL/DL configurations: each slot (14 OFDM symbols) can be designated as downlink, uplink, or flexible, with the ratio adjusted dynamically based on traffic patterns. The guard period (GP) between DL and UL is typically 1--2 OFDM symbols.

Channel reciprocity calibration in 5G NR uses SRS (Sounding Reference Signal) in the uplink, with the BS applying antenna-specific calibration factors updated every few seconds. This enables implicit CSI acquisition for massive MIMO precoding without any downlink CSI feedback.

Why This Matters: TDD Massive MIMO in the MIMO Book

The CSI overhead analysis in this section motivates the use of TDD for massive MIMO. The MIMO book develops the complete theory:

Ch 8-10: Massive MIMO fundamentals — channel hardening, favorable propagation, pilot contamination
Ch 11: JSDM (Joint Spatial Division and Multiplexing) — a CommIT contribution by Adhikary/Nam/Ahn/Caire that enables FDD massive MIMO by exploiting spatial correlation structure
Ch 14-16: Cell-free massive MIMO — Ngo/Caire et al. on user-centric distributed MIMO with fronthaul constraints
Ch 17: Hybrid beamforming for mmWave massive MIMO

The JSDM framework is particularly relevant: it shows that FDD massive MIMO is feasible if users can be grouped by similar spatial signatures, reducing the feedback dimension from $M$ to the rank of each group's covariance matrix.

FDD

Frequency Division Duplex: a duplexing scheme in which uplink and downlink transmissions occur simultaneously on different frequency bands, separated by a guard band. Dominant in legacy cellular deployments (2G--4G).

Related: TDD, Channel Reciprocity

TDD

Time Division Duplex: a duplexing scheme in which uplink and downlink transmissions share the same frequency band but occur at different times within each frame. Enables channel reciprocity for massive MIMO CSI acquisition.

Related: FDD, Channel Reciprocity

Channel Reciprocity

The property that the uplink and downlink propagation channels are transpose-conjugates of each other when both use the same carrier frequency. Exploited in TDD systems to infer the downlink channel from uplink measurements, avoiding explicit feedback.

Related: TDD, FDD

Duplexing: FDD vs TDD