Direct Sequence Spread Spectrum

Direct Sequence Spread Spectrum (DSSS) is the most widely used spread spectrum technique in modern wireless systems. It directly multiplies the data signal with a high-rate PN chip sequence before transmission, spreading the signal energy across a wide bandwidth. DSSS is the basis of CDMA cellular networks, IEEE 802.11b Wi-Fi, and GPS signal structure.

Core Concept Explanation

In DSSS, the binary data stream d(t) at rate Rb bits per second is multiplied (XOR-ed for binary signals) chip by chip with a PN code c(t) running at a much higher rate Rc chips per second. The product signal s(t) = d(t) times c(t) then modulates an RF carrier for transmission. Because c(t) has bandwidth proportional to Rc, the transmitted signal occupies bandwidth proportional to Rc rather than Rb. The ratio Rc/Rb is the **processing gain** and determines the degree of spreading.

At the receiver, the incoming signal is correlated with a locally generated synchronized copy of the same PN code. This despreading operation reverses the spreading: the data bandwidth collapses back to Rb, and any narrowband interference that was present in the wide band is itself spread by the despreading multiplication and then filtered out by the data-rate lowpass filter. This is the mechanism of interference rejection.

The **chip rate** Rc determines the null-to-null bandwidth of the spread signal as approximately 2Rc. Each chip duration Tc equals 1/Rc. If a user's data bit duration is Tb = 1/Rb, then each bit is divided into Rc/Rb chips. In CDMA, each user gets a unique PN code. Multiple users transmit simultaneously at the same carrier frequency, and the base station separates them by correlating with each user's code separately.

Mathematical Expression

The transmitted DSSS signal is written as s(t) = d(t) multiplied by c(t) multiplied by the carrier cos(2 pi fc t). The **chip energy to noise ratio** Ec/N0 relates to the bit energy to noise ratio Eb/N0 through the processing gain: Eb/N0 equals (Ec/N0) times (Rc/Rb). Because each bit consists of multiple chips, the bit energy is the sum of chip energies. The correlator integrates over one bit period, accumulating chip energies coherently for the desired user and incoherently (hence averaging down) for interferers.

In a CDMA system with K simultaneous users, the **signal-to-interference ratio (SIR)** at the correlator output is approximately PG divided by (K minus 1), assuming equal power users and ideal orthogonal codes. This expression shows directly that system capacity K is limited by the processing gain. Real systems use power control and forward error correction to approach this limit.

Given:
Data rate Rb = 9.6 kbps (IS-95 voice channel)
Chip rate Rc = 1.2288 Mcps (IS-95 standard)
Number of simultaneous users K = ?

Why this formula applies:
Capacity is tied to processing gain in CDMA DSSS.

Formula:
PG = Rc / Rb
Approximate capacity K ≈ PG + 1 (ideal orthogonal codes)

Substitution:
PG = 1.2288 × 10^6 / 9.6 × 10^3
PG = 128

Calculation:
PG = 128
K ≈ 128 users per sector (theoretical ideal)

Final Answer:
Processing gain = 128 (21.1 dB); theoretical CDMA capacity approximately 128 users per sector per carrier.

Practical Understanding

IEEE 802.11b (Wi-Fi) uses DSSS at 1 and 2 Mbps with an 11-chip Barker code. The Barker code has excellent autocorrelation sidelobes, providing multipath robustness in indoor environments. GPS C/A code uses a 1023-chip Gold code at 1.023 Mcps spread over 1 MHz bandwidth, enabling receivers to track multiple satellites simultaneously and measure precise ranging through code phase measurement.

DSSS is susceptible to the **near-far problem**: a strong nearby user can overwhelm a weak distant user at the base station even after despreading, because the PN code separation is not perfect. IS-95 CDMA solves this with tight power control — each mobile constantly adjusts its transmit power so all signals arrive at the base station at approximately equal strength.

Exam Tip: In GATE, DSSS numerical problems almost always require computing processing gain = Rc/Rb, then using PG to find jamming margin or CDMA capacity. Also remember: chip duration Tc = 1/Rc, and bandwidth of DSSS signal is approximately 2Rc for BPSK spreading.

Mechanism: Despreading and Interference Rejection

• Transmitter multiplies data d(t) with PN code c(t) chip by chip. Transmitted bandwidth equals approximately 2Rc.
• Receiver multiplies received signal with synchronized local PN replica. This despreads the desired data signal back to bandwidth 2Rb.
• A narrowband jammer occupying a small portion of the spread band is re-spread by the despreading multiplication, distributing its energy across the full spread bandwidth.
• The data-rate lowpass filter then removes the spread jammer energy, retaining only the collapsed data signal. Jammer rejection equals the processing gain in dB.
• Multiple CDMA users are separated at the base station by correlating with each user's unique code. Ideal orthogonal codes give zero cross-correlation and perfect separation.

Quick Revision

• DSSS: data XOR PN code then modulate. Bandwidth = 2Rc. Processing gain PG = Rc/Rb.
• Despreading at receiver restores data bandwidth; spreads interference over PG times original bandwidth.
• IS-95 CDMA: Rb = 9.6 kbps, Rc = 1.2288 Mcps, PG = 128 (21.1 dB).
• CDMA capacity K approximately equals PG under ideal conditions.
• Near-far problem is the main practical challenge in CDMA; solved by power control.
• IEEE 802.11b uses 11-chip Barker code DSSS; GPS uses 1023-chip Gold code DSSS.
• Trap: Chip duration Tc = 1/Rc, not 1/Rb. Confusing the two is a common exam error.