CDMA Details

Code Division Multiple Access is the technology underlying 3G cellular systems and forms the basis for GPS signal reception and many military communication systems. Unlike FDMA and TDMA, CDMA does not partition the radio resource into orthogonal non-interfering pieces. Instead, every user shares the entire bandwidth simultaneously, and their signals are separated at the receiver using the mathematical properties of spreading codes. Understanding CDMA in depth requires grasping three core ideas: spreading and despreading, orthogonality of codes, and the near-far problem.

Core Concept Explanation

In CDMA, each user is assigned a unique PN spreading code of length N chips per data bit. At the transmitter, the data bit b(t) (valued +1 or -1) is multiplied chip-by-chip with the spreading code c(t), producing a wideband spread signal s(t) = b(t) * c(t). The bandwidth of s(t) is N times the original data bandwidth, which is why this ratio N is called the processing gain and is a key measure of CDMA performance.

At the receiver, the incoming signal is again multiplied by the same code c(t). Since c(t) * c(t) = 1 (each chip squared is always +1), the product r(t) * c(t) yields b(t) after integration over one bit period. For any other user with code c2(t) that is orthogonal to c(t), the product c(t) * c2(t) integrates to zero, so the other user's contribution is completely rejected. This is the mathematical basis for code-division separation.

Walsh codes are a class of strictly orthogonal codes used in IS-95 downlink (base to mobile). They are rows of a Hadamard matrix and satisfy the condition that cross-correlation is exactly zero for synchronized users. PN codes used in the uplink are not perfectly orthogonal but have very low cross-correlation values, providing practical separation.

Mathematical Expression

The processing gain G defines how much the signal is spread relative to the data rate:

G = W / R = chip rate / bit rate = N (chips per bit)

The signal-to-interference ratio at the despreader output for user 1 in a system with K simultaneous users, assuming equal power, is:

SINR = G / (K - 1)

The capacity of a CDMA cell (number of users K) given required Eb/N0:

K = 1 + G / (Eb/N0)

The near-far problem arises because the interference term (K-1) is weighted by the power of each user. If user 2 is much closer to the base station than user 1, user 2's signal arrives with much higher power, dramatically raising the interference floor for user 1. The received power from user 2 can be 20-30 dB higher than user 1, which can completely drown out user 1's signal despite orthogonal codes.

Practical Understanding

Power control is the solution to the near-far problem. In IS-95 and WCDMA, closed-loop power control adjusts each user's transmit power so that all signals arrive at the base station with approximately the same received power level. The power control loop operates at 800-1500 updates per second in 3G systems.

CDMA also benefits from the soft capacity property: adding more users gradually degrades quality rather than causing hard blocking. This is different from FDMA/TDMA where capacity is fixed by the number of channels or slots.

Given:
Chip rate W = 3.84 Mcps (WCDMA standard)
Data rate R = 12.2 kbps (speech)
Required Eb/N0 = 5 dB = 3.162 (linear)

Why this formula applies:
Processing gain determines how many users can be supported simultaneously.
Capacity formula assumes equal received power (power control applied).

Formula:
G = W / R
K = 1 + G / (Eb/N0)

Substitution:
G = 3,840,000 / 12,200 = 314.75 ≈ 315
K = 1 + 315 / 3.162

Calculation:
K = 1 + 99.6

Final Answer: K ≈ 100 simultaneous users per cell (theoretical, ideal power control)

Exam Tip: In GATE, near-far problem is solved by power control, NOT by changing codes. Also, Walsh codes have exactly zero cross-correlation (synchronized downlink only). PN codes used uplink have low but non-zero cross-correlation.

• Spreading: data bit multiplied by N-chip PN code, bandwidth expands by factor N (processing gain).
• Despreading: receiver multiplies received signal by same code; correlation = 1 for desired user, 0 for orthogonal codes.
• Walsh codes: strictly orthogonal, used in IS-95 downlink, cross-correlation exactly zero when chip-synchronized.
• Near-far problem: close user arrives with higher power, raises interference floor, can mask far user.
• Solution: closed-loop power control adjusts transmit power so all users arrive at equal power at base station.
• Capacity formula: K = 1 + G/(Eb/N0), degrades gracefully as K increases (soft capacity).

Quick Revision

• Processing gain G = W/R = chip rate / bit rate = chips per bit N.
• SINR after despreading = G/(K-1) for K equal-power users.
• Capacity: K = 1 + G/(Eb/N0) — higher G or lower required Eb/N0 means more users.
• Walsh codes: zero cross-correlation, orthogonal, used IS-95 forward link.
• Near-far problem: solved by fast closed-loop power control, not by code changes.
• GATE trap: CDMA has soft capacity (gradual degradation) unlike FDMA/TDMA (hard blocking).
• WCDMA chip rate = 3.84 Mcps; IS-95 chip rate = 1.2288 Mcps — common exam values.