SDMA

Space Division Multiple Access exploits the spatial dimension of radio propagation to allow multiple users to share the same frequency, time, and code resources by virtue of occupying different physical locations. SDMA relies on the use of directional antennas or antenna arrays at the base station that can steer narrow beams toward individual users. While FDMA, TDMA, and CDMA are well-established classical techniques, SDMA has become central to modern systems through massive MIMO in 4G and 5G networks.

Core Concept Explanation

SDMA is not a standalone access technique but a spatial layer added on top of FDMA, TDMA, or CDMA. The key enabling technology is the smart antenna or antenna array at the base station. By controlling the amplitude and phase of signals fed to each antenna element, the array creates a radiation pattern that concentrates energy in a specific direction (beamforming) while placing nulls in the directions of interfering users.

There are two main approaches to SDMA beamforming. Switched-beam systems use a predefined set of fixed beam patterns and select the one that best covers the user's direction. Adaptive beam systems, also called adaptive array systems, continuously adjust the beam based on received signal information and can steer nulls toward interferers in real time.

The spatial degree of freedom added by SDMA allows the same frequency and time resource to be reused for multiple users in different spatial directions. The number of simultaneous spatial streams is limited by the number of antenna elements M at the base station. In general, an M-element array can support up to M independent spatial streams, though practical systems support fewer due to channel correlation.

Mathematical Expression

For a uniform linear array (ULA) with M antenna elements separated by distance d, the array steering vector for a signal arriving from angle theta is:

a(theta) = [1, exp(j*2*pi*d*sin(theta)/lambda), exp(j*4*pi*d*sin(theta)/lambda), ..., exp(j*2*pi*(M-1)*d*sin(theta)/lambda)]^T

The beamformed output y for a received signal vector x is y = w^H * x, where w is the beamforming weight vector. For maximum ratio combining toward user 1 at angle theta1, the optimal weight vector is w = a(theta1) / ||a(theta1)||. The beam gain in direction theta is |w^H * a(theta)|^2, which achieves maximum M at theta = theta1 and creates nulls at other steered angles if designed with null-steering algorithms such as MVDR or LCMV.

The capacity gain of SDMA with K spatially separated users, each with SNR gamma, relative to a single user, is roughly K times the single-user capacity when beams are perfectly separated:

C_SDMA = K * log2(1 + gamma) bits/s/Hz (ideal spatial separation)

Practical Understanding

In 4G LTE, SDMA is implemented as Multi-User MIMO (MU-MIMO). The base station (eNodeB) uses multiple antennas to serve multiple users simultaneously on the same resource block. LTE supports up to 4 simultaneous spatial streams in downlink MU-MIMO. In 5G NR, massive MIMO arrays with 64, 128, or even 256 antenna elements are deployed, allowing dozens of simultaneous spatial streams.

The performance of SDMA depends critically on channel state information at the transmitter (CSIT). Each user must feed back its channel estimate so the base station can compute the appropriate beamforming vectors. In fast-fading mobile channels, this feedback may become outdated before it is used, limiting the effectiveness of spatial separation. This problem is especially severe at mmWave frequencies with high Doppler.

Given:
Number of antenna elements M = 64 (massive MIMO, 5G)
Number of simultaneous SDMA users K = 16
SNR per user gamma = 20 dB = 100 (linear)
Beams assumed perfectly orthogonal

Why this formula applies:
With ideal spatial separation, each user sees full SNR and capacity adds linearly.

Formula:
Single user capacity: C1 = log2(1 + gamma)
SDMA total capacity: C_SDMA = K * log2(1 + gamma)

Substitution:
C1 = log2(1 + 100) = log2(101)
C_SDMA = 16 * log2(101)

Calculation:
log2(101) = ln(101)/ln(2) = 4.615 / 0.693 = 6.66 bits/s/Hz
C_SDMA = 16 * 6.66 = 106.6 bits/s/Hz

Final Answer: C_SDMA ≈ 106.6 bits/s/Hz (ideal; practical limited by inter-beam interference)

Exam Tip: SDMA spatial capacity scales with the number of antenna elements M, not the number of users directly. M elements can null up to M-1 interferers. In GATE, MU-MIMO is the practical realization of SDMA. Always distinguish SDMA from spatial multiplexing (SU-MIMO) — SDMA serves multiple users; SU-MIMO sends multiple streams to one user.

• SDMA adds spatial dimension: same f/t resource reused for users in different spatial directions.
• Enabled by smart antennas: switched-beam (fixed patterns) or adaptive arrays (dynamic null steering).
• M-element array can support up to M simultaneous spatial streams; can null up to M-1 interferers.
• Steering vector for ULA: a(theta) = [1, e^(j*2*pi*d*sin(theta)/lambda), ..., e^(j*2*pi*(M-1)*d*sin(theta)/lambda)].
• Practical realization in LTE/5G: MU-MIMO; massive MIMO arrays have 64 to 256 elements in 5G NR.
• Requires CSIT (channel state information at transmitter); performance degrades in fast-fading channels.

Quick Revision

• SDMA: spatial reuse of f/t resource; enabled by directional antenna arrays.
• M antenna elements support up to M spatial streams; null up to M-1 interferers.
• ULA steering vector: a(theta) = [1, e^(j*2*pi*d*sin(theta)/lambda), ..., e^(j*2*pi*(M-1)*d*sin(theta)/lambda)].
• Capacity: C_SDMA = K * log2(1 + gamma) for K perfectly separated spatial users.
• MU-MIMO is the LTE/5G implementation; massive MIMO extends this to 64+ antennas.
• GATE trap: SDMA requires CSIT feedback; without it, beams cannot be steered correctly.
• Distinguish: SU-MIMO sends multiple streams to one user; MU-MIMO (SDMA) serves multiple users on same resource.