Ferkans — Interactive Telecom Tutor

From Military Secrecy to Commercial Cellular

Spread-spectrum communication was originally developed for military applications: by spreading a signal across a bandwidth far wider than necessary, the signal becomes difficult to detect and resistant to narrowband jamming. In the 1990s, Qualcomm's IS-95 standard brought Code Division Multiple Access (CDMA) to commercial cellular networks, demonstrating that spread spectrum could also serve as a powerful multiple access technique. Unlike FDMA and TDMA, CDMA allows all users to transmit simultaneously over the entire bandwidth, separating them by unique spreading codes. This approach trades hard resource partitioning for graceful degradation: adding a user increases interference for all, but the system does not hit a hard capacity wall. CDMA formed the basis of 3G (WCDMA, cdma2000) and its principles remain relevant in 5G positioning and IoT systems.

Definition:
Direct-Sequence Spread Spectrum (DS-SS)

In direct-sequence spread spectrum, user $k$ 's data symbol $b_k \in \{+1, -1\}$ is multiplied by a spreading code $\mathbf{c}_k = [c_{k,1}, c_{k,2}, \ldots, c_{k,N}]^T$ of length $N$ (the spreading factor or processing gain), where each chip $c_{k,n} \in \{+1/\sqrt{N}, -1/\sqrt{N}\}$ and $\|\mathbf{c}_k\|^2 = 1$ .

The transmitted chip-rate signal for user $k$ is:

$\mathbf{s}_k = \sqrt{P_k}\, b_k \,\mathbf{c}_k$

The received signal at the base station is:

$\mathbf{r} = \sum_{k=1}^{K} h_k \mathbf{s}_k + \mathbf{n} = \sum_{k=1}^{K} \sqrt{P_k}\, h_k\, b_k\, \mathbf{c}_k + \mathbf{n}$

where $h_k$ is user $k$ 's channel coefficient and $\mathbf{n} \sim \mathcal{CN}(\mathbf{0}, \sigma^2 \mathbf{I}_N)$ .

The despreading operation for user $k$ is a matched-filter (correlator) receiver:

$z_k = \mathbf{c}_k^H \mathbf{r} = \sqrt{P_k}\, h_k\, b_k + \sum_{j \neq k} \sqrt{P_j}\, h_j\, b_j\, \mathbf{c}_k^H \mathbf{c}_j + \mathbf{c}_k^H \mathbf{n}$

The processing gain $N$ is the ratio of the chip bandwidth to the data bandwidth: $N = W_{\text{chip}} / W_{\text{data}}$ .

After despreading, the noise power is unchanged ( $\sigma^2$ ) since the code is unit-norm, but the interference from user $j$ is scaled by the cross-correlation $\mathbf{c}_k^H \mathbf{c}_j$ . If codes are orthogonal, the interference vanishes exactly.

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Definition:
Walsh-Hadamard Codes and the Near-Far Problem

Walsh-Hadamard codes are a family of $N$ orthogonal binary sequences of length $N$ (where $N$ is a power of 2), constructed recursively via the Hadamard matrix:

$\mathbf{H}_1 = [1], \quad \mathbf{H}_{2N} = \begin{bmatrix} \mathbf{H}_N & \mathbf{H}_N \\ \mathbf{H}_N & -\mathbf{H}_N \end{bmatrix}$

Row $k$ of $\mathbf{H}_N / \sqrt{N}$ serves as the spreading code $\mathbf{c}_k$ . These codes satisfy $\mathbf{c}_i^H \mathbf{c}_j = 0$ for $i \neq j$ , eliminating multi-access interference in synchronous systems.

The near-far problem arises when users are at different distances from the base station. If user $j$ is much closer than user $k$ , then $P_j |h_j|^2 \gg P_k |h_k|^2$ , and the residual interference after despreading (due to imperfect code orthogonality in asynchronous or multipath channels) can overwhelm user $k$ 's signal:

$\text{SIR}_k = \frac{P_k |h_k|^2} {\sum_{j \neq k} P_j |h_j|^2 |\mathbf{c}_k^H \mathbf{c}_j|^2}$

Without power control, the near-far effect causes catastrophic performance degradation for distant users. Tight closed-loop power control (updating at $\sim$ 800 Hz in IS-95) is essential for CDMA systems.

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CDMA Spreading and Despreading

Visualise how spreading codes separate users in a CDMA system. The plot shows the BER performance as a function of the number of users and processing gain. Observe how increasing the processing gain $N$ allows the system to support more users at a given BER target, and how the SNR affects the MAI floor.

Parameters

N

(processing gain)16

K

(number of users)4

SNR per bit [dB]10

Near-Far Effect in CDMA

Explore how the near-far problem degrades CDMA performance. User distances from the base station determine received power through path loss. Adjust the near and far user distances, the number of users, and the path-loss exponent to see how the SIR of the far user collapses when near users transmit at the same power.

Parameters

d_{\mathrm{near}}

(near-user distance, normalised)0.1

d_{\mathrm{far}}

(far-user distance, normalised)1

K

(number of users)8

\alpha

(path-loss exponent)3.5

Rake Receiver for DS-CDMA

Complexity:

O(NL)

per symbol period:

L

despreading operations each of length

N

, plus

O(L)

for the MRC combining.

Input: Received signal

\mathbf{r}(t)

, spreading code

\mathbf{c}_k

,

channel estimates

\{\hat{h}_{k,\ell}, \hat{\tau}_\ell\}_{\ell=1}^{L}

for

L

multipath taps

Output: Decision statistic

z_k

for user

k

's symbol

1. for

\ell = 1, \ldots, L

do

2.

\quad

Delay-align:

\mathbf{r}_\ell \leftarrow \mathbf{r}(t - \hat{\tau}_\ell)

3.

\quad

Despread (finger

\ell

):

y_\ell \leftarrow \mathbf{c}_k^H \mathbf{r}_\ell

4. end for

5. Maximal-ratio combine across fingers:

6.

\quad z_k \leftarrow \sum_{\ell=1}^{L} \hat{h}_{k,\ell}^* \, y_\ell

7. Hard decision:

\hat{b}_k \leftarrow \text{sign}(\text{Re}(z_k))

8. return

\hat{b}_k

The Rake receiver exploits multipath diversity by treating each resolvable path as an independent copy of the signal. With $L$ resolvable paths and MRC combining, the effective diversity order is $L$ . The name "Rake" comes from the analogy of the receiver fingers collecting energy from scattered paths, like the tines of a garden rake. In WCDMA (3G), Rake receivers with 4--6 fingers were standard.

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Example: Processing Gain and CDMA Capacity

A DS-CDMA system operates with chip rate $W_c = 3.84$ Mcps (WCDMA standard) and data rate $R_b = 12.2$ kbps (voice). Assume equal received power for all users (perfect power control) and a required $E_b/N_0 = 7$ dB.

(a) Compute the processing gain $N$ . (b) Estimate the maximum number of users per cell. (c) What happens if the processing gain is halved (higher data rate)?

Solution

Processing gain

$N = \frac{W_c}{R_b} = \frac{3.84 \times 10^6}{12.2 \times 10^3} \approx 315$ $In dB:$ 10\log_{10}(315) = 25.0$ dB.

Maximum number of users

With a matched-filter receiver and perfect power control, the SIR for each user in a single cell is approximately:

$\text{SIR} \approx \frac{N}{K - 1}$

The required SIR equals $E_b/N_0 = 10^{0.7} = 5.01$ . Therefore:

$K - 1 \leq \frac{N}{E_b/N_0} = \frac{315}{5.01} = 62.9$

$K_{\max} \approx 63$ users.

Including a voice activity factor $\nu = 0.4$ (users speak only 40% of the time) and a frequency reuse factor $f = 0.65$ (inter-cell interference):

$K_{\max} \approx \frac{N}{\nu \cdot (E_b/N_0) \cdot (1 + f)} = \frac{315}{0.4 \times 5.01 \times 1.65} \approx 95$

Halving the processing gain

If the data rate doubles to $R_b = 24.4$ kbps, then $N = 157$ and $K_{\max}$ drops to roughly half. This illustrates the fundamental trade-off in CDMA: higher per-user data rates consume more spreading bandwidth and reduce the number of supportable users. $\blacksquare$

Quick Check

A CDMA system with processing gain $N = 64$ and $K = 16$ users (all with equal received power) uses a matched-filter receiver. What is the approximate SIR at the despreader output?

64 (18.1 dB)

4.27 (6.3 dB)

16 (12.0 dB)

1 (0 dB)

Correction:

4.27 (6.3 dB)

$\text{SIR} \approx N/(K-1) = 64/15 = 4.27$ (6.3 dB). Each additional user adds interference that the despreader cannot fully suppress.

Why This Matters: IS-95 and WCDMA (3G)

IS-95 (cdmaOne): The first commercial CDMA standard (1995), developed by Qualcomm. It used a chip rate of 1.2288 Mcps with 64-chip Walsh codes for the downlink and long PN sequences for the uplink. IS-95 demonstrated 6--10 $\times$ capacity improvement over analogue AMPS, primarily through voice activity detection, soft handoff, and aggressive power control (800 Hz update rate).

WCDMA (UMTS): The 3GPP standard for 3G (Release 99, 2001) used a chip rate of 3.84 Mcps with variable spreading factors (4--512) to support data rates from 12.2 kbps to 2 Mbps. Key features included Rake receivers, closed-loop power control, and soft/softer handoff. HSPA+ later added advanced receivers (interference cancellation, equalisation) to push peak rates beyond 40 Mbps.

The transition from 3G (CDMA-based) to 4G (OFDMA-based) was driven by the difficulty of supporting high data rates with CDMA: the near-far problem and MAI become severe when spreading factors are small. OFDMA's orthogonality eliminates these issues.

⚠️Engineering Note

Power Control Requirements in CDMA Systems

The near-far problem makes fast closed-loop power control the single most critical mechanism in CDMA systems. Without it, a user 10 dB closer to the base station creates 40 dB more interference (with path-loss exponent $\alpha = 4$ ), overwhelming distant users.

IS-95/cdmaOne requirements:

Closed-loop power control rate: 800 Hz (one update per 1.25 ms power control group)
Step size: $\pm 1$ dB per update
Target: equalise all users' received power at the BS to within $\pm 1$ dB

WCDMA (3G) requirements:

Inner loop: 1500 Hz update rate, $\pm 1$ dB steps
Outer loop: adjusts the SIR target based on measured BLER (typically targeting 1% BLER for voice)
Dynamic range: 80 dB (from -50 dBm to +30 dBm)

Why OFDM replaced CDMA (4G onwards): As data rates increased, the spreading factor $N$ decreased (e.g., $N = 4$ for HSDPA at 3.6 Mbps), reducing interference suppression. The near-far problem became intractable at low spreading factors, and OFDMA's inherent orthogonality eliminated the problem entirely.

Practical Constraints

•
IS-95: 800 Hz power control, ±1 dB steps
•
WCDMA: 1500 Hz, 80 dB dynamic range
•
Low spreading factor (N < 8): near-far problem becomes severe

📋 Ref: 3GPP TS 25.214 (WCDMA power control), TIA/EIA-95B (IS-95)

CDMA

Code Division Multiple Access: a multiple access technique in which all users transmit simultaneously over the same bandwidth, separated by unique spreading codes. Each user's signal is spread to a bandwidth $N$ times wider than necessary, where $N$ is the processing gain.

Related: DS-SS, Processing Gain

DS-SS

Direct-Sequence Spread Spectrum: a spread-spectrum technique in which the data signal is multiplied by a high-rate pseudorandom chip sequence, spreading the signal bandwidth by a factor of $N$ (the processing gain).

Related: CDMA, Processing Gain

Processing Gain

The ratio $N = W_{\text{chip}}/W_{\text{data}}$ of the spread bandwidth to the data bandwidth in a spread-spectrum system. It determines the interference suppression capability: each interfering user's power is reduced by approximately $1/N$ after despreading.

Related: CDMA, DS-SS

Near-Far Problem

The phenomenon in CDMA systems where a nearby high-power user overwhelms the desired signal from a distant low-power user, causing severe performance degradation. Mitigated by tight closed-loop power control or multi-user detection.

Related: CDMA

CDMA and Spread Spectrum

From Military Secrecy to Commercial Cellular

Definition: Direct-Sequence Spread Spectrum (DS-SS)

Definition: Walsh-Hadamard Codes and the Near-Far Problem

CDMA Spreading and Despreading

Parameters

Near-Far Effect in CDMA

Parameters

Rake Receiver for DS-CDMA

Example: Processing Gain and CDMA Capacity

Processing gain

Maximum number of users

Halving the processing gain

Quick Check

Why This Matters: IS-95 and WCDMA (3G)

Power Control Requirements in CDMA Systems

CDMA

DS-SS

Processing Gain

Near-Far Problem

Definition:
Direct-Sequence Spread Spectrum (DS-SS)

Definition:
Walsh-Hadamard Codes and the Near-Far Problem